2602.06176v1

# Large Language Model Reasoning Failures **Authors**: - Peiyang Song psong@caltech.edu (California Institute of Technology, Stanford University Pengrui Han barryhan@carleton.edu) > Equal contribution. Work done while Peiyang Song was a visiting researcher at Stanford University. ## Abstract Large Language Models (LLMs) have exhibited remarkable reasoning capabilities, achieving impressive results across a wide range of tasks. Despite these advances, significant reasoning failures persist, occurring even in seemingly simple scenarios. To systematically understand and address these shortcomings, we present the first comprehensive survey dedicated to reasoning failures in LLMs. We introduce a novel categorization framework that distinguishes reasoning into embodied and non-embodied types, with the latter further subdivided into informal (intuitive) and formal (logical) reasoning. In parallel, we classify reasoning failures along a complementary axis into three types: fundamental failures intrinsic to LLM architectures that broadly affect downstream tasks; application-specific limitations that manifest in particular domains; and robustness issues characterized by inconsistent performance across minor variations. For each reasoning failure, we provide a clear definition, analyze existing studies, explore root causes, and present mitigation strategies. By unifying fragmented research efforts, our survey provides a structured perspective on systemic weaknesses in LLM reasoning, offering valuable insights and guiding future research towards building stronger, more reliable, and robust reasoning capabilities. We additionally release a comprehensive collection of research works on LLM reasoning failures, as a GitHub repository at https://github.com/Peiyang-Song/Awesome-LLM-Reasoning-Failures, to provide an easy entry point to this area. ## 1 Introduction “Failure is success if we learn from it.” – Malcolm Forbes With the rise of powerful architectures (Vaswani et al., 2023; Jiang et al., 2024a; Gu and Dao, 2024; Hasani et al., 2020), efficient algorithms (Hu et al., 2021; Zhao et al., 2024b; Gretsch et al., 2024; 2025; Dao et al., 2022), and massive data (Cai et al., 2024; Raffel et al., 2020; Gao et al., 2020), Large Language Models (LLMs) have recently shown significant success across diverse domains. These range from traditional linguistic tasks such as machine translation (Zhu et al., 2024b; Tang et al., 2024), to mathematical (Shao et al., 2024; Yang et al., 2023a; 2024a) and even scientific (Zhang et al., 2024b; Wang et al., 2023b; Brodeur et al., 2024) discoveries. Among these achievements, reasoning as an emergent capability of LLMs (Wei et al., 2022a) has attracted particular interest (Huang and Chang, 2023; Yu et al., 2023b; Qiao et al., 2023). LLMs have set impressive records in reasoning (Wu et al., 2025a; kıcıman2024causalreasoninglargelanguage; Plaat et al., 2024), though it remains controversial whether LLMs really leverage a human-like reasoning procedure when attempting these tasks (Jiang et al., 2024b; Fedorenko et al., 2024; Amirizaniani et al., 2024b; Zhang et al., 2022). This survey does not aim to settle this hot debate; rather we focus on an important area of study in LLM reasoning that has long been overlooked – LLM reasoning failures. Extensive psychological research (Cannon and Edmondson, 2005; Maxwell, 2007; Coelho and McClure, 2004) underscores the importance of identifying and learning from failures in human development In fact, this theory has been confirmed even more broadly, in non-human animals (Spence, 1936).. Given that AI systems have historically drawn inspiration from human cognition (Schmidgall et al., 2023; Xu and Poo, 2023; Woźniak et al., 2020), we believe the same principle of learning from failures could similarly benefit the study of LLMs, since such failures can usually be traced back to fundamental elements and bring valuable insights to ultimate improvements (Dreyfus, 1992; Karl et al., 2024; An et al., 2024). Despite some existing works that prospectively realized this importance and investigated LLM reasoning failures on a case-by-case basis (Williams and Huckle, 2024; Tie et al., 2024; Helwe et al., 2021; Borji, 2023), the topic remains fragmented, and underexplored as a unified research area. This fragmentation limits broader understanding, which is however a prerequisite for common patterns to be noticed, and thereby meaningful lessons to be derived. To close this gap, we present the first comprehensive survey dedicated to unifying studies on LLM reasoning failures. We identify meaningful patterns across failures, analyze underlying causes, and discuss potential mitigation strategies. We hope this work not only organizes the field but also stimulate further research and increased attention, toward improving the robustness and reliability of LLM reasoning. We additionally make public a comprehensive collection of research works on LLM reasoning failures, as a GitHub repository at https://github.com/Peiyang-Song/Awesome-LLM-Reasoning-Failures. This collection will be continuously updated as this area advances. ## 2 Definition and Formulation ### 2.1 Fundamentals of Reasoning Human reasoning broadly refers to the ability to draw conclusions and make decisions based on available knowledge (Lohman and Lakin, 2011; Ribeiro et al., 2020). Within cognitive science and philosophy, reasoning has been studied through various frameworks. To systematically survey reasoning failures in LLMs, we propose a comprehensive taxonomy distinguishing reasoning along two primary axes: embodied versus non-embodied, with the latter further subdivided into informal and formal reasoning. #### Non-embodied reasoning. Non-embodied reasoning comprises cognitive processes not requiring physical interaction with environments. Within this category, informal reasoning encompasses intuitive judgments driven by inherent biases and heuristics, common in everyday decision-making and social activities (Piaget, 1952; Vygotsky, 1978; Kail, 1990). By contrast, formal reasoning involves explicit, rule-based manipulation of symbols, grounded in logic, mathematics, code, etc. (Copi et al., 2016; Mendelson, 2009; Liu et al., 2023b). #### Embodied reasoning. Embodied reasoning depends on physical interaction with environments, fundamentally relying on spatial intelligence and real-time feedback (Shapiro, 2019; Barsalou, 2008). This includes predicting and interpreting physical dynamics, and performing goal-directed behaviors constrained by real-world physical laws (Huang et al., 2022b; Lee-Cultura and Giannakos, 2020). ### 2.2 LLM Reasoning Failures & Common Research Practice Despite advances in interpretability research (Dwivedi et al., 2023; Li et al., 2024e), LLMs remain largely black-box systems (Luo and Specia, 2024), reflecting the inherent complexity of human cognition they emulate (Castelvecchi, 2016). As such, reasoning abilities are typically assessed behaviorally by examining model outputs on carefully designed prompts and tasks (Ribeiro et al., 2020). We define LLM reasoning failures as cases where model responses significantly diverge from expected logical coherence, contextual relevance, or factual correctness. Failures can manifest in two broad ways. The first type is straightforward poor performance — the model fails decisively on a task, exposing clear deficiencies. The second, subtler type involves apparently adequate performance that is in fact unstable, indicating a robustness issue that reveals hidden vulnerabilities. The former category – straightforward failure – can be sub-divided into two, based on scope and nature. Fundamental failures are usually intrinsic to LLM architectures, manifesting broadly and universally across diverse downstream tasks. In contrast, application-specific limitations reflect shortcomings tied to particular domains of importance, where models underperform despite human expectations of competence. Together, these taxonomies — for reasoning and for failures — offer a comprehensive and mutually consistent framework. Figure 1 uses this framework to visualize a clear organization of topics in this survey. Current research in this space typically begins with simple, intuitive tests that reveal glaring reasoning failures. These initial observations motivate larger-scale systematic evaluations, to confirm the generality and impact of identified failure modes. By explicitly defining and categorizing LLM reasoning failures according to our framework, this survey unifies fragmented research findings, highlights shared patterns, and directs focused efforts toward understanding and mitigating critical reasoning weaknesses. To help visualize the failure cases, we provide a few most representative examples for each of the failure case presented in this survey. The examples can be found in Appendix E. <details> <summary>x1.png Details</summary>  ### Visual Description ## Diagram: Taxonomy of Reasoning Categories and Associated Failure Modes ### Overview The image is a structured diagram that maps three high-level "Reasoning Categories" (Informal, Formal, Embodied) to their respective "Subsections" and associated "Failure Categories." The failures are further classified into three types: Robustness, Limitation, and Fundamental. The diagram uses a color-coded, tabular layout with horizontal bars to indicate which failure types apply to each subsection. ### Components/Axes **Left Vertical Axis: Reasoning Categories** * **Informal** (Purple outline) * **Formal** (Red outline) * **Embodied** (Green outline) **Middle Column: Subsections** Each Reasoning Category is broken down into numbered subsections: * **Under Informal:** * 3.1 Individual Cog Reasoning * 3.2 Implicit Social Reasoning * 3.3 Explicit Social Reasoning * **Under Formal:** * 4.1 Logic in NL * 4.2 Logic in Bench * 4.3 Arithmetic & Math * **Under Embodied:** * 5.1 1D * 5.2 2D * 5.3 3D **Right Section: Failure Categories (Column Headers)** * **Robustness** (Light grey header) * **Limitation** (Light grey header) * **Fundamental** (Dark grey header) **Data Representation:** Horizontal colored bars (matching the category's outline color) are placed within the Failure Category columns to indicate the specific failure types associated with each subsection. The length and placement of the bar show which failure category(ies) it belongs to. ### Detailed Analysis **1. Informal Reasoning (Purple Bars)** * **3.1 Individual Cog Reasoning:** * Robustness: Cognitive Skills, Cognitive Bias * Fundamental: Cognitive Skills, Cognitive Bias * **3.2 Implicit Social Reasoning:** * Robustness: Theory of Mind (ToM) * Robustness: Social Norm & Morals * **3.3 Explicit Social Reasoning:** * Robustness: Multi-Agent System (MAS) **2. Formal Reasoning (Red/Pink Bars)** * **4.1 Logic in NL:** * Fundamental: Reversal Curse * Fundamental: Compositional Reasoning * Limitation: Specific Logical Relations * **4.2 Logic in Bench:** * Robustness: Math Word Problem (MWP) * Robustness: Coding * **4.3 Arithmetic & Math:** * Fundamental: Counting * Fundamental: Basic Arithmetic * Limitation: MWP & Beyond **3. Embodied Reasoning (Green Bars)** * **5.1 1D:** * Fundamental: Physical Commonsense * Limitation: Physics & Science * Robustness: What's Wrong with the Picture? * **5.2 2D:** * Limitation: 2D Physics & Physical Commonsense * Limitation: Visual Spatial Reasoning * **5.3 3D:** * Fundamental: Affordance & Planning * Robustness: Spatial and Tool-Use Reasoning * Robustness: Safety & Long-Term Autonomy ### Key Observations * **Spatial Layout:** The "Reasoning Categories" are stacked vertically on the far left. The "Subsections" are listed in a central column. The "Failure Categories" form three wide columns on the right. Dotted horizontal lines separate the three main Reasoning Categories. * **Color Consistency:** Each main category (Informal, Formal, Embodied) and its associated failure bars share a distinct color (purple, red, green). * **Failure Distribution:** * **Robustness** failures are common across all categories, often related to skill application and real-world complexity. * **Limitation** failures are notably present in Formal (Logic) and Embodied reasoning, suggesting boundaries in logical relations and physical understanding. * **Fundamental** failures appear in all categories, indicating core, intrinsic challenges in cognitive biases, logical composition, and physical planning. * **Subsection Complexity:** Some subsections, like "3.1 Individual Cog Reasoning" and "5.3 3D," have failures spanning multiple categories, indicating multifaceted challenges. ### Interpretation This diagram serves as a **taxonomic map for diagnosing failure modes in artificial reasoning systems**. It organizes the complex landscape of reasoning tasks and systematically links them to specific types of failures. * **Relationship Structure:** The diagram posits that the *type of reasoning task* (Informal/Social, Formal/Logical, Embodied/Physical) fundamentally shapes the *nature of the failures* an AI system will encounter. For example, failures in social reasoning (ToM, MAS) are primarily framed as "Robustness" issues—challenges in reliably applying these skills—while failures in arithmetic are often "Fundamental," suggesting a core lack of ability. * **Investigative Lens (Peircean):** The diagram acts as an **abductive framework**. When an AI system fails on a task (e.g., a visual puzzle), one can trace it back: Is it a "2D" Embodied task? The diagram suggests the failure is likely a "Limitation" in "Visual Spatial Reasoning." This guides researchers toward the root cause (e.g., poor spatial representation) rather than treating it as a generic error. * **Notable Pattern:** The concentration of "Fundamental" failures in the Formal category (Reversal Curse, Compositional Reasoning, Basic Arithmetic) implies these are seen as foundational, possibly architectural, flaws in current models. In contrast, Embodied reasoning failures are more distributed, reflecting the multifaceted challenge of interacting with the physical world. * **Purpose:** This taxonomy is likely used for **benchmarking, research prioritization, and model evaluation**. It helps answer: "What kinds of reasoning can my model fail at, and what does that failure tell me about its underlying limitations?" It moves beyond a simple "pass/fail" metric to a diagnostic understanding of AI cognition. </details> Figure 1: A Taxonomy of LLM Reasoning Failures. We adopt a nuanced 2-axis structure (reasoning type $×$ failure type), with each row representing a reasoning category and each column a failure category. A more detailed explanation is presented in Section 2. ## 3 Reasoning Informally in Intuitive Applications Humans naturally develop the capacity for informal reasoning early in life, relying on intuitive judgments shaped by cognitive processes and social experiences. Though often taken for granted, this forms the foundation of human reasoning and decision-making. In this section, we focus on failures exhibited by LLMs in such informal reasoning. We begin by examining reasoning failures in core cognitive abilities reflected in individual LLM behaviors; then explore those exposed in social contexts, expressed implicitly or explicitly. ### 3.1 Individual Cognitive Reasoning Many reasoning failures exhibited by LLMs can be traced back to core human cognitive phenomena (Han et al., 2024b; Gong et al., 2024; Galatzer-Levy et al., 2024; Suri et al., 2024). These failures arise either because LLMs lack certain fundamental cognitive abilities possessed by humans – leading to errors that humans typically avoid (Han et al., 2024b) – or because LLMs replicate human-like cognitive biases and heuristics, resulting in analogous mistakes (Suri et al., 2024; Lampinen et al., 2024). In both cases, these failures relate closely to well-documented human cognitive phenomena and psychological evidence. #### Fundamental Cognitive Skills. Humans naturally possess a set of fundamental cognitive skills indispensable for reasoning. LLMs demonstrate systematic failures due to deficiencies in these areas. A prominent example is the set of core executive functions – working memory (Baddeley, 2020), inhibitory control (Diamond, 2013; Williams et al., 1999), and cognitive flexibility (Canas et al., 2006) – essential in human reasoning (Diamond, 2013). Working memory is the capacity to hold and manipulate information over short periods. LLMs’ limited working memory leads to failures when task demands exceed their capacity (Gong et al., 2024; Zhang et al., 2024a; Gong and Zhang, 2024; Upadhayay et al., 2025; Huang et al., 2025a). In particular, LLMs suffer from “proactive interference” to a much larger extent than humans, where earlier information significantly disrupts retrieval of newer updates (Wang and Sun, 2025). Inhibitory control – the ability to suppress impulsive or default responses when contexts demand – is also weak in LLMs, with them often sticking to previously learned patterns even when contexts shift (Han et al., 2024b; Patel et al., 2025). Lastly, cognitive flexibility, the skill of adapting to new rules or switching tasks efficiently, remains a challenge, especially in rapid task switching and adaptation to new instructions (Kennedy and Nowak, 2024). Another key aspect is abstract reasoning (Guinungco and Roman, 2020), the cognitive ability to recognize patterns and relationships in intangible concepts. Even advanced LLMs struggle with abstract reasoning tasks, such as inferring underlying rules from limited examples, understanding implicit conceptual relationships, and reliably handling symbolic or temporal abstractions (Xu et al., 2023c; Gendron et al., 2023; Galatzer-Levy et al., 2024; Saxena et al., 2025). These phenomena are fundamental reasoning failures that stem from intrinsic limitations of LLM architectures and training dynamics, and often manifest as robustness vulnerabilities across a wide range of tasks. Recent work attributes these failures to the underlying self-attention mechanism’s dispersal of focus under complex tasks (Gong and Zhang, 2024; Patel et al., 2025), and to the next token prediction training objective, which prioritizes statistical pattern completion over deliberate reasoning (Han et al., 2024b; enström2024reasoningtransformersmitigating). Some also point out that unlike humans – who develop fundamental cognitive functions through embodied, goal-driven interactions with the physical and social world (Pearce and Miller, 2025; Rodríguez, 2022; Jin et al., 2018) – LLMs learn passively from text alone, lacking grounding and experiential feedback to support the development. Efforts to enhance these skills correspondingly include advanced prompting like Chain-of-Thought (CoT) (Wei et al., 2022b), retrieval augmentation (Xu et al., 2023b), fine-tuning with deliberately injected interference (Li et al., 2022), multimodality (Hao et al., 2025), and architectural innovations to mimic human attention mechanisms (Wu et al., 2024d). #### Cognitive Biases. Cognitive biases – systematic deviations from rational judgment – are well-studied in human reasoning (Tversky and Kahneman, 1974; 1981). They arise from mental shortcuts, limited cognitive resources, or contextual influences, often leading to predictable errors. LLMs exhibit similar biases that systematically affect their reasoning across diverse tasks (Hagendorff, 2023; Bubeck et al., 2023). Since these biases are deeply ingrained from training data and model architecture, they permeate a wide range of downstream applications, necessitating careful identification and mitigation. In humans, these biases become evident only when information is presented and their responses observed – similarly, in LLMs, cognitive biases manifest also through the processing of information. Here lie two interrelated factors: the content of information and the presentation of that information. Regarding content, LLMs struggle more with abstract or unfamiliar topics – a phenomenon known as the “content effect” (Lampinen et al., 2024) – and tend to favor information that aligns with prior context or assumptions, reflecting human-like confirmation bias (O’Leary, 2025b; Shi et al., 2024; Malberg et al., 2024; Wan et al., 2025; Zhu et al., 2024c). Social cognitive biases also influence LLM outputs, including group attribution bias (Hamilton and Gifford, 1976; Allison and Messick, 1985; Raj et al., 2025) and negativity bias (Rozin and Royzman, 2001), which prioritize popular content (Echterhoff et al., 2024; Lichtenberg et al., 2024; Jiang et al., 2025a) and negative inputs (Yu et al., 2024c; Malberg et al., 2024) respectively. Equally important is how the same content is presented. LLMs are highly sensitive to the order in which information is given, exhibiting order bias (Koo et al., 2023; Pezeshkpour and Hruschka, 2023; Jayaram et al., 2024; Guan et al., 2025; Cobbina and Zhou, 2025), and show anchoring bias (Lieder et al., 2018; Rastogi et al., 2022), where early inputs disproportionately shape their reasoning (Lou and Sun, 2024; O’Leary, 2025a; Huang et al., 2025e; Wang et al., 2025b). Framing effects further influence outputs: logically equivalent but differently phrased prompts can lead to different results (Jones and Steinhardt, 2022; Suri et al., 2024; Nguyen, 2024; Lior et al., 2025; Robinson and Burden, 2025; Shafiei et al., 2025). Additionally, factors like narrative perspective (e.g., first-person vs. third-person) (Cohn et al., 2024; Lin et al., 2024b), prompt length or verbosity (Koo et al., 2023; Saito et al., 2023), and irrelevant or distracting information (Shi et al., 2023) further derail logical reasoning. Cognitive biases constitute fundamental reasoning failures rooted in LLM training paradigms and architectures, and they manifest as robustness vulnerabilities across a wide range of downstream applications. The root causes of these cognitive biases in LLMs are threefold. First, biases are inherited from the pre-training data, where the linguistic patterns in human languages reflect cognitive errors (Itzhak et al., 2025). Second, architectural features of the model – such as the Transformer’s causal masking – introduce predispositions toward order-based biases independent of data (Wu et al., 2025b; Dufter et al., 2022). Third, alignment processes like Reinforcement Learning from Human Feedback (RLHF) amplify biases by aligning model behavior with human raters who are themselves biased (Sumita et al., 2025; Perez et al., 2023). Mitigation strategies fall into three categories. Data-centric approaches focus on curating training data to reduce biased content (Sun et al., 2025a; Schmidgall et al., 2024; Han et al., 2024a). In-processing techniques, such as adversarial training, aim to prevent biased associations during model learning (Yang et al., 2023b; Cantini et al., 2024). Lastly, post-processing methods leverage prompt engineering or output filtering to steer model responses after training (Sumita et al., 2025; Lin and Ng, 2023). In this category, indirect methods like inducing specific model personalities have also shown promise in modulating biases (Shi et al., 2024; He and Liu, 2025). Nonetheless, even when mitigated in one context, cognitive biases often re-emerge when contexts shift. The diverse and penetrative nature of cognitive biases makes them difficult to be fully eliminated. ### 3.2 Implicit Social Reasoning Certain cognitive reasoning failures manifest only within social contexts. We define implicit social reasoning as an individual model’s capacity to internally infer and reason about (1) others’ mental states (e.g., beliefs, emotions, intentions) and (2) shared social norms without requiring direct interaction. #### Theory of Mind (ToM). ToM is the cognitive ability to attribute mental states – beliefs, intentions, emotions – to oneself and others, and to understand that others’ mental states may differ from one’s own (Frith and Frith, 2005). ToM enables humans to interpret behaviors, predict actions, and navigate complex interpersonal interactions, central in social reasoning. Typically emerging in early childhood with milestones like passing false belief tasks (understand that others’ beliefs may be incorrect or different) (Wimmer and Perner, 1983), ToM has been a central focus in human psychology and cognitive science. Under this inspiration, recent research evaluates the ToM capacity of LLMs, to gauge their ability to engage in social reasoning. Early studies focused on classic ToM tasks, such as false-belief (van Duijn et al., 2023; Kim et al., 2023), perspective-taking (infer what another individual perceives) (Sap et al., 2022), and unexpected content tasks (predicting what others would believe is inside a mislabeled unopened container) (Pi et al., 2024). Surprisingly, even advanced models such as GPT-4 struggle with these tasks trivial for human children. Moreover, minor modifications in task phrasing lead to drastic drops in performance, showing LLM ToM reasoning is unstable (Ullman, 2023; Kosinski, 2023; Pi et al., 2024; Shapira et al., 2023). While there has been clear progress from early models like GPT-3 – which largely failed at ToM tasks – to newer models such as GPT-4o and reasoning models like o1-mini, which can solve many standard ToM tests, their underlying reasoning remains brittle under simple perturbations (Gu et al., 2024; Zhou et al., 2023d). Also, LLMs still struggle with higher-order, more complex aspects of ToM, such as predicting others’ behaviors, making appropriate moral or social judgments, and translating this understanding into coherent actions (He et al., 2023; Gu et al., 2024; Marchetti et al., 2025; Amirizaniani et al., 2024a; Strachan et al., 2024). Particularly, on dynamic, conversational benchmarks (Xiao et al., 2025; Kim et al., 2023), even state-of-the-art models fail to demonstrate consistent ToM capabilities and perform significantly worse than humans. Furthermore, current models exhibit deficits in emotional reasoning. This includes difficulties in emotional intelligence (EI) (Sabour et al., 2024; Hu et al., 2025; Amirizaniani et al., 2024b; Vzorinab et al., 2024), susceptibility to affective bias (Chochlakis et al., 2024), and limited understanding of cultural variations in emotional expression and interpretation (Havaldar et al., 2023). While prompting techniques like CoT offer some improvements (Gandhi et al., 2024), fundamental gaps remain due to deeper limitations from the LLM architecture, training paradigms, and a lack of embodied cognition (Strachan et al., 2024; Sclar et al., 2023). Failures in this domain constitute important application-specific limitations, and because ToM underlies many socially grounded tasks, such failures often result in significant robustness vulnerabilities. Given ToM’s centrality to social reasoning, future work should move beyond prompting, to probe deeper root causes and general mitigation. #### Social Norms and Moral Values. LLMs also struggle with reasoning about social norms, moral values, and ethical principles that govern human behavior. Unlike humans, who develop moral and ethical reasoning through experience, LLMs, trained purely on text, often exhibit inconsistent and unreliable social, moral, and ethical reasoning (Ji et al., 2024; Jain et al., 2024b). One key limitation is that LLMs cannot reason and apply moral values (Ji et al., 2024) and social norms (Jain et al., 2024b) consistently. They often produce contradictory ethical judgments or varied moral reasoning performance when questions are slightly reworded (Bonagiri et al., 2024), generalized (Tanmay et al., 2023), or presented in a different language (Agarwal et al., 2024). Fine-tuning further exacerbates these inconsistencies, leading to sometimes prioritizing task-specific optimization over ethical coherence (Yu et al., 2024a). Beyond inconsistencies, LLMs show notable disparities compared to humans in reasoning with social norms and moral values. These models fail significantly in understanding real-world social norms (Rezaei et al., 2025), aligning with human moral judgments (Garcia et al., 2024; Takemoto, 2024), and adapting to cultural differences (Jiang et al., 2025b). Without consistent and reliable moral reasoning, LLMs are not fully ready for real-world decision-making involving ethical considerations. These inconsistencies and disparities constitute important application-specific limitations for safety, privacy, sensitivity, and morality-related tasks, and such failures often create severe robustness vulnerabilities, including susceptibility to jailbreaks and other forms of manipulation. Many argue that these failures stem from a fundamental absence of robust, internalized representations of ethical principles, normative frameworks, and moral intentionality (Chakraborty et al., 2025; Wang et al., 2025a; Pock et al., 2023; Almeida et al., 2024). Although training procedures such as RLHF and instruction fine-tuning introduce alignment signals, they often operate superficially and fail to produce coherent moral behavior in complex contexts (Dahlgren Lindström et al., 2025; Wang et al., 2025a; Barnhart et al., 2025; Han et al., 2025). Current efforts to address these limitations mainly include prompt-based interventions (Chakraborty et al., 2025; Ma et al., 2023), internal activation steering (Tlaie, 2024; Turner et al., 2023), and direct fine-tuning on curated moral reasoning benchmarks (Senthilkumar et al., 2024; Karpov et al., 2024). However, in practice, these methods often suffer from the same limitations as RLHF, offering surface-level and task-specific improvements that remain vulnerable against prompt manipulations and jailbreaks. ### 3.3 Explicit Social Reasoning In reasoning, “society” can refer to not just an abstract concept but real-world settings involving interactions among multiple agents. In Multi-Agent Systems (MAS), explicit social reasoning is the capacity of AI systems to collaboratively plan and solve complex tasks, an area challenging for current LLMs. Currently, key challenges include (1) long-horizon planning, (2) communications and ToM, and (3) robustness and adaptability. Long-horizon planning is the ability to maintain coherent and coordinated strategies over extended interactions, where LLMs frequently fail (Li et al., 2023a; Cross et al., 2024; Guo et al., 2024c; Han et al., 2024c; Zhou et al., 2025) as they rely excessively on local or recent information (Piatti et al., 2024; Zhang et al., 2023; Han et al., 2024c). Furthermore, individual agents’ social reasoning failures (discussed in Section 3.2, e.g., inefficient communication and ToM) (Guo et al., 2024c; Agashe et al., 2024; Zhou et al., 2025), lead to misinterpretations and inaccurate representations of other agents, causing strategic misalignment (Pan et al., 2025; Li et al., 2023a; Cross et al., 2024; Han et al., 2024c). Lastly, MAS face robustness and adaptability issues (Li et al., 2023a; Cross et al., 2024), lacking resilience to disruptive or malicious disturbances (Huang et al., 2024) and struggling with task verification and termination (Pan et al., 2025; Baker et al., 2025). These failures stem from both individual LLM capabilities and MAS system design (Pan et al., 2025), representing key application-specific failures, and they frequently manifest as robustness vulnerabilities in multi-agent settings. Standard LLMs, optimized for next-token prediction, lack the explicit reasoning depth needed for multi-step, jointly conditioned objectives, and their fragile ToM representations cause coordination breakdowns. Individual limitations in cognitive skills, such as working memory, and cognitive biases, such as the anchoring effect, can also lead to MAS failures like difficulties with long-horizon planning. On the system level, many MAS often lack effective robustness layers – clear role specifications, cross-verification among agents, and reliable termination checks – allowing errors to cascade (Huang et al., 2024; Pan et al., 2025). Mitigation research thus targets (i) richer internal models like belief tracking and hypothesis testing (Li et al., 2023a; Cross et al., 2024), (ii) structured communication protocols with mandatory verification phases (Pan et al., 2025), and (iii) dedicated inspector or challenger agents that monitor and contest questionable outputs (Huang et al., 2024; Baker et al., 2025). While these approaches reduce errors, none eliminate them and all require significant task-specific engineering that is difficult to generalize. In parallel, the recent rise of context engineering (Mei et al., 2025) – which focuses on a systematic optimization of the entire information payload fed to an LLM during inference – is increasingly seen as a more robust alternative to traditional prompt engineering in MAS. Real-world deployment will hence require an integrated stack combining all three strands with domain fine-tuning and formal safety guarantees (Lindemann and Dimarogonas, 2025; de Witt, 2025). ## 4 Reasoning Formally in Logic When reasoning goes beyond intuition, a formal framework is needed to ensure rigor. As introduced in Section 2, logic is directly about doing “correct” reasoning, ensuring premises support conclusions (Jaakko and Sandu, 2002). LLM failures in logical reasoning (Liu et al., 2025) thus pose serious risks, potentially leading to flawed thought processes and harmful decisions. Logic spans a continuum from implicit structures in natural languages (Iwańska, 1993), to explicit symbolic (Lewis et al., 1959) and mathematical (Shoenfield, 2018) representations. This section follows that progression, examining failures in increasingly formal reasoning paradigms. ### 4.1 Logic in Natural Languages #### Reversal Curse. While natural languages are not fully logical structures (Fedorenko et al., 2024), they do hold simple logical relations (Sampson, 1979; Stich, 1975) that humans trivially grasp. A representative failure of LLMs is reversal curse: despite being trained on “A is B,” models often fail to infer the equivalent “B is A” – a trivial bidirectional equivalence for humans. Such failures occur even when a factual sentence from training data is just restated as a question during inference. First observed by Berglund et al. (2023) as a fundamental failure that occur widely across tasks on GPT-based (Radford and Narasimhan, 2018) models, this phenomenon is later shown in Wu et al. (2024a) not to affect BERT (Devlin et al., 2019). This failure has been attributed to uni-directional training objectives of Transformer-based LLMs (Lv et al., 2024; Lin et al., 2024c), which induce structural asymmetry in model weights (Zhu et al., 2024a) and inability to predict antecedent words within training data (Guo et al., 2024b; Youssef et al., 2024). Golovneva et al. (2024) further argues that scaling alone cannot resolve the issue due to Zipf’s law (Newman, 2005). Mitigation efforts accordingly center on reducing directional bias through training data augmentation. Early approaches syntactically reverse facts (Lu et al., 2024; Ma et al., 2024b), while later methods introduce substring-preserving reversals (Golovneva et al., 2024) and permuting semantic units in training data (Guo et al., 2024b). Despite differing in complexity, all methods share a common goal: exposing models to bidirectional formulations to restore logical symmetry. #### Compositional Reasoning. Compositional reasoning requires combining multiple pieces of knowledge or arguments into a coherent inference. Fundamental failures arise when LLMs are capable of each component but fail in integrating them. Studies show systematic failures in basic two-hop reasoning – combining only two facts across documents – and even worsening performance with increased compositional depth and the addition of distractors (Zhao and Zhang, 2024; Xu et al., 2024b; Guo et al., 2025a). This fundamental weakness extends beyond basic tasks, to compositions of math problems (Zhao et al., 2024c; Hosseini et al., 2024; Sun et al., 2025b) (i.e., LLMs succeed in individual problems but fail in composed ones), multi-fact claim verification (Dougrez-Lewis et al., 2024), and other inherently compositional tasks (Dziri et al., 2023). This failure is attributed to an inability of holistic planning and in-depth thinking. CoT prompting improves on this by making reasoning steps explicit at inference time. Still, latent compositionality is more efficient in practice yet harder to achieve (Yang et al., 2024c). Toward this, Li et al. (2024f) identifies faulty implicit reasoning in mid-layer multi-head self-attention (MHSA) modules and edit them, while Zhou et al. (2024a) enhances training with graph-structured reasoning path data, similar to distilling CoT reasoning process into training data (Yu et al., 2024b). Both converge in spirit to improving latent compositional reasoning by explicitly guiding models’ internal reasoning mechanisms. #### Specific Logical Relations. Both reversal curse and compositional reasoning reflect fundamental failures affecting a broad range of reasoning tasks, exposed across general corpora or arbitrary logical statements. In contrast, another line of work focuses on specific logical relations, uncovering targeted LLM reasoning failures, which requires purpose-built datasets for quantitative analysis at scale. Using this approach, studies reveal LLM weaknesses in specific types of logic such as converse binary relations (Qi et al., 2023), syllogistic reasoning (Ando et al., 2023), causal inference (Joshi et al., 2024), and even shallow yes/no questions (Clark et al., 2019). Those weaknesses appear as both fundamental inabilities in reasoning with certain logic, and limitations in specific corresponding downstream applications: more complexities are added by testing divergences between factual inference and logical entailment (Chan et al., 2024), or putting causal reasoning in contexts (Zhao et al., 2024d). To scale up, some synthetically generate natural language data from symbolic templates (Wan et al., 2024; Wang et al., 2024; Gui et al., 2024). Alternatively, Chen et al. (2024d) seed known failures and leverage LLMs to synthetically expand the dataset. While root causes are harder to isolate for those specific logic, the curated datasets offer a natural mitigation by direct fine-tuning. ### 4.2 Logic in Benchmarks While Section 4.1 studies LLM reasoning failures directly within natural language logic, another growing body of work leverages logical structures implicit in benchmarks to systematically uncover robustness issues in LLM reasoning. Motivated by rising concerns about the reliability of static benchmarks (Zhou et al., 2023c; Zheng et al., 2024b; Xu et al., 2024a; Patel et al., 2021), these studies introduce logic-preserving transformations based on particular task structures, such as reordering options in multiple-choice questions (MCQs) (Zheng et al., 2023; Pezeshkpour and Hruschka, 2023; Alzahrani et al., 2024; Gupta et al., 2024; Ni et al., 2024), rearranging parallel premises and events (Chen et al., 2024c; Yamin et al., 2024), or superficially editing unimportant contexts (e.g., character names) (Jiang et al., 2024b; Mirzadeh et al., 2024; Shi et al., 2023; Wang and Zhao, 2024). Such modifications keep the tasks semantically the same. Performance drops thus point to reduced trustworthiness and reveal critical robustness issues: despite strong static benchmark scores, the model’s reasoning must remain consistent on the reasoning tasks being tested. #### Math Word Problem (MWP) Benchmarks. Certain benchmarks inherently possess richer logical structures that facilitate targeted perturbations. MWPs exemplify this, as their logic can be readily abstracted into reusable templates. Researchers use this property to generate variants by sampling numeric values (Gulati et al., 2024; Qian et al., 2024; Li et al., 2024b) or substituting irrelevant entities (Shi et al., 2023; Mirzadeh et al., 2024). Structural transformations – such as exchanging known and unknown components (Deb et al., 2024; Guo et al., 2024a) or applying small alterations that change the logic needed to solve problems (Huang et al., 2025b) – further highlight deeper robustness limitations. #### Coding Benchmarks. Another example is coding benchmarks, which ask to generate code snippets based on function definitions, doc strings specifying coding tasks, and optional starter code. Common transformations include syntactically editing doc strings (Xia et al., 2024; Wang et al., 2022; Sarker et al., 2024; Roh et al., 2025), renaming functions and variables (Wang et al., 2022; Hooda et al., 2024), and altering control-flow logic such as swapping if-else cases (Hooda et al., 2024). Beyond preserving the task logic, some studies introduce adversarial code changes to test whether LLMs identify and adapt to them (Miceli-Barone et al., 2023; Dinh et al., 2023), thereby evaluating deeper reliability. Beyond perturbations, a rising approach utilizes meta-theorems such as the Monadic Second-Order logic from CS theory to synthesize algorithmic coding problems at scale (Beniamini et al., 2025), posing a significant challenge even for state-of-the-art large reasoning models (LRMs) (Xu et al., 2025a). #### Mitigation & Extensions. These failures are attributed to a lack of robustness or overfitting to public datasets. Robustness-related issues are commonly mitigated by applying perturbations to diversify training data (Patel et al., 2021), thus enhancing resilience to variations. Though effective, these approaches are expensive in compute and limited in domain, making them hard to generalize. Overfitting concerns are addressed through dynamically evolving (Jain et al., 2024a; White et al., 2024) or privately maintained datasets (Rajore et al., 2024). They ensure rigorous evaluation, a necessary first step for steering LLM improvement toward better reasoning in the benchmark subjects. Beyond individual benchmarks, Hong et al. (2024) automates a set of transformations across math and coding benchmarks, and Wu et al. (2024e) alters common assumptions of well-known tasks. Shojaee et al. (2025) further moves beyond standard math and coding benchmarks – which assess models solely by final-answer accuracy – by evaluating them on logic puzzles like the Tower of Hanoi, where both reasoning steps and solutions can be systematically assessed. The study finds that even state-of-the-art LRMs suffer an “accuracy collapse” as puzzle complexity increases, though Lawsen (2025) criticizes aspects of the experimental design, suggesting these may unfairly impact reported accuracy. ### 4.3 Arithmetic & Mathematics Mathematics, historically a universal framework for rigorous reasoning (Shoenfield, 2018), has exposed fundamental limits in LLM reasoning, particularly in arithmetic-related tasks. #### Counting. Despite its simplicity, counting poses a notable fundamental challenge for LLMs (Xu and Ma, 2024; Chang and Bisk, 2024; Zhang and He, 2024; Fu et al., 2024; Conde et al., 2025; Yehudai et al., 2024), even the reasoning ones (Malek et al., 2025), which extend to basic character-level operations like reordering or replacement (Shin and Kaneko, 2024) and affect a wide range of downstream reasoning applications (Vo et al., 2025; Guo et al., 2025b; Parcalabescu et al., 2021). Although the failures manifest at the application level, much work suggest that they originate primarily from architectural and representational limits, including tokenization (Zhang et al., 2024f; Shin and Kaneko, 2024), positional encoding (Chang and Bisk, 2024), and training data composition (Allen-Zhu and Li, 2024), rather than from superficial prompting or task framing on the application-level. Mitigation via supervised fine-tuning (Zhang and He, 2024) and engaged reasoning (Xu and Ma, 2024) have been proposed, yet robust counting remains elusive for current models. Since the limitations largely arise from current LLM architectures, future work should consider deeper mitigation through architectural innovations. #### Basic Arithmetic. Another fundamental failure is that LLMs quickly fail in arithmetic as operands increase (Yuan et al., 2023; Testolin, 2024), especially in multiplication. Research shows models rely on superficial pattern-matching rather than arithmetic algorithms, thus struggling notably in middle-digits (Deng et al., 2024). Surprisingly, LLMs fail at simpler tasks (determining the last digit) but succeed in harder ones (first digit identification) (Gambardella et al., 2024). Those fundamental inconsistencies lead to failures for practical tasks like temporal reasoning (Su et al., 2024). These issues stem from heuristic-driven reasoning strategies (Nikankin et al., 2024) and limited numerical precision (Feng et al., 2024a). Proposed solutions include detailed step-by-step training datasets (Yang et al., 2023c), digit-order reversals to focus attention on least significant digits – mirroring human multiplication strategies (Zhang-Li et al., 2024; Shen et al., 2024), LLM self-improvement methods (Lee et al., 2025), and neuro-symbolic augmentations that enable internal arithmetic reasoning (Dugan et al., 2024). Despite these advances, fundamental research on intrinsic arithmetic capabilities is increasingly overshadowed by the prevalent reliance on external tool use. #### Math Word Problems & Beyond. Beyond counting and basic arithmetic – two fundamental failures that propagate into many downstream reasoning applications – Math Word Problems (MWPs) represent a more specific yet highly consequential application domain. Math Word Problems (MWPs) combine arithmetic with contextual logical reasoning, making them a prominent application for assessing LLM capabilities. Beyond using transformations to expose reasoning flaws (Section 4.2), research identifies challenges ranging from specific simple tasks (Nezhurina et al., 2024) to large-scale evaluations on a domain of math (Wei et al., 2023b; Boye and Moell, 2025; Fan et al., 2024; Sun et al., 2025b). Additionally, LLMs exhibit susceptibility when faced with unsolvable or faulty MWPs (Ma et al., 2024a; Rahman et al., 2024; Tian et al., 2024). LLMs struggle even in assessing reasoning process on MWPs (Zhang et al., 2024g), an arguably easier task than generation. Given these persistent challenges, current efforts in MWPs prioritize developing general methods to improve overall reasoning performance rather than investigating and addressing individual failures. ## 5 Reasoning in Embodied Environments Reasoning is not merely an abstract process; it is deeply grounded in reality (Shapiro and Spaulding, 2024), requiring the ability to perceive, interpret, predict, and act within the physical world, with accurate understanding of spatial relationships, object dynamics, and physical laws (Lee-Cultura and Giannakos, 2020). While humans (Varela et al., 2017) – and even many animals (Andrews and Monsó, 2021) – develop such embodied reasoning naturally through sensory and motor experiences, LLMs remain fundamentally limited by their lack of true physical grounding in the physical world. This gap leads to systematic errors and unrealistic predictions when LLMs attempt even basic physical reasoning (Wang et al., 2023c; Ghaffari and Krishnaswamy, 2024a). Despite growing interest in spatial intelligence, research into LLMs’ physical reasoning failures is still sparse. In this section, we survey failures across three progressively complex embodied reasoning modalities: (1) 1D text-based, (2) 2D perception-based, and (3) 3D real-world physical reasoning. ### 5.1 1D – Text-Based Physical Reasoning Failures #### Text-Based Physical Commonsense Reasoning. Physical commonsense reasoning refers to the intuitive understanding of how objects interact in the physical world. Failures of LLMs include lack of knowledge about object attributes (e.g., size, weight, softness) (Wang et al., 2023c; Liu et al., 2022b; Shu et al., 2023; Kondo et al., 2023), spatial relationships (e.g., above, inside, next to) (Liu et al., 2022b; Shu et al., 2023; Kondo et al., 2023), simple physical laws (e.g., gravity, motion, and force) (Gregorcic and Pendrill, 2023), and object affordance (possible actions/reactions an object can make) (Aroca-Ouellette et al., 2021; Adak et al., 2024; Pensa et al., 2024). Humans acquire this kind of reasoning effortlessly through embodied experience, whereas LLMs struggle in it, as they rely solely on textual data without direct perceptual or embodied experience. Even in purely text-based settings, when tasks require more than semantic comprehension, demanding real-world understanding, LLMs exhibit systematic failures. These failures are fundamental to current LLMs. While their architectures and training paradigms support impressive language-based learning, they lack the physical grounding. #### Physics & Scientific Reasoning. Beyond basic physical commonsense, LLMs struggle with formal physics reasoning and scientific problem-solving, which require not just factual recall and intuition but multi-step logical deduction, quantitative reasoning, and correct use of physical laws – areas where even state-of-the-art models like o1 (Jaech et al., 2024) and o3-mini (OpenAI, 2025) have notable deficits (Zhang et al., 2025a; Xu et al., 2025b; Gupta, 2023; Chung et al., 2025; Zhang et al., 2025b; Qiu et al., 2025). Notably, even when LLMs possess these scientific skills, they often fail to apply them effectively in complex problems and real-world scientific discovery (Jaiswal et al., 2024; Ouyang et al., 2023; Chen et al., 2025). These failures result in strong limitations in LLMs’ application in scientific domains. #### Text-Based Mitigation. These failures largely reflect limitations inherent to the text modality, since semantic and linguistic understanding alone cannot guarantee grounded physical insight (Wang et al., 2023c; Zhang et al., 2025b). Text-based mitigation strategies focus on three fronts: training, prompting, and integration with external tools. First, LLMs are fine-tuned on corpora that explicitly encode structured physical knowledge – such as object attributes, spatial relationships, or physical laws – to better align model priors with real-world dynamics (Lyu et al., 2024; Wang et al., 2023c). Second, prompting methods like CoT encourage models to reason explicitly, reducing reliance on shallow text-based pattern-matching and enabling discovery of more nuanced causal and spatial relationships (Wei et al., 2022b; Ding et al., 2023). Third, LLMs are increasingly paired with external tools – such as code executors or physics engines – that allow models to verify, simulate, or compute outcomes directly and tangibly (Ma et al., 2024c; Cherian et al., 2024). ### 5.2 2D – Perception-Based Physical Reasoning Failures #### What’s Wrong with the Picture? The classic “What’s Wrong with the Picture?” visual reasoning game challenges participants to spot anomalies in static images. Applied to vision-language models (VLMs), similar tasks reveal surprising failures in simple tasks such as anomaly detection (Bitton-Guetta et al., 2023; Zhou et al., 2023b), object counting and overlap identification (Rahmanzadehgervi et al., 2024), and spatial relation understanding from the image content (Liu et al., 2023a; Zhao et al., 2024a). These failures constitute key perception-related limitations and robustness vulnerabilities. #### 2D Physics and Physical Commonsense. Extending beyond detecting simple anomalies or object properties in static images, VLMs face deeper challenges reasoning about the physics in visual contexts. Despite the addition of visual inputs, VLMs still struggle with physical commonsense (Li et al., 2024d; Ghaffari and Krishnaswamy, 2024b; Schulze Buschoff et al., 2025; Dagan et al., 2023; Balazadeh et al., 2024b; Chow et al., 2025; Bear et al., 2021; Xu et al., 2025c) and advanced physics (Ates et al., 2020; Anand et al., 2024; Shen et al., 2025), exhibiting performance gaps similar to those seen in text-only settings discussed in Section 5.1. Similar to the 1D setting, these weaknesses reflect fundamental failures of current models and lead to significant limitations in applying them to scientific and perception-based domains. #### Visual Input for Spatial Reasoning. Real-world spatial reasoning requires understanding evolving spatial relationships rather than isolated snapshots. Recent works use 2D simulated environments to test models’ grasp of motion and object interactions (e.g., predicting post-impact trajectories) (Cherian et al., 2024), spatial prediction and manipulation (e.g., object placement for stability) (Ghaffari and Krishnaswamy, 2024a), spatial communication and alignment (e.g., conveying location information) (Kar et al., 2025), and embodied planning in multi-step tasks (Chia et al., 2024; Paglieri et al., 2024; Xu et al., 2025c). While VLMs exhibit some basic spatial knowledge, they consistently fail to compose and apply it in dynamic, interactive tasks, revealing a gap in structured spatial reasoning. This failure is an indication of limitations on 2D relevant applications. #### Perception-Based Mitigation. These errors arise from three key sources. First, models often over-rely on text or common scenarios from their training data, rather than accurately interpreting visual inputs (Deng et al., 2025a; Bitton-Guetta et al., 2023; Zhou et al., 2023b). Second, some failures may be explained by the binding problem from cognitive science, where the brain – or a model – struggles to process multiple distinct objects simultaneously due to limited shared resources (Campbell et al., 2025). Third, just as language alone does not guarantee grounded physical understanding, visual inputs alone may also lack sufficient spatial semantics; plain image recognition does not automatically confer an understanding of spatial object dynamics and causality (Chen et al., 2024a; Qi et al., 2025). To mitigate, recent work focuses on curating balanced, augmented datasets to reduce bias toward text inputs, or directly using 2D physics data to improve physical understanding (Deng et al., 2025a; Balazadeh et al., 2024a). Another strategy targets training and model architecture (Cheng et al., 2024), by introducing spatially grounded, sequential attention mechanisms (Izadi et al., 2025) and leveraging reinforcement learning to align models with spatial commonsense (Sarch et al., 2025). Finally, beyond end-to-end learning, integration with external physical simulation tools has also emerged, to enable explicit trial-and-error (Liu et al., 2022a; Cherian et al., 2024; Zhu et al., 2025). ### 5.3 3D – Real-World Physical Reasoning Failures Real embodied reasoning requires agents to actively interact with their environment, through robotics or interactive simulations that go beyond static images or simple 2D snapshots. Such agents must process real-time goals and feedback, and execute physical actions. Unlike 1D (text-only) and 2D (image-based) tasks, 3D embodied reasoning centers on action rather than passive analysis. Despite advances in robotics and embodied AI, LLMs and VLMs face persistent challenges including inaccurate spatial modeling, unrealistic affordance prediction, tool-use failures, and unsafe behaviors. This subsection highlights these key failure cases from both simulated and real-world studies. #### Real-World Failures in Affordance and Planning. A key failure is models’ inability to generate feasible and coherent action plans. LLMs and VLMs often produce physically impossible or inefficient actions due to affordance errors (incorrect reasoning about possible object actions) (Ahn et al., 2022; Li et al., 2025; Hu et al., 2024; Huang et al., 2022a; Jin et al., 2024) and causal real-world reasoning limitations that cause illogical or looping behaviors (Jin et al., 2024; Hu et al., 2024). These fundamental shortcomings in modeling real-world affordances and planning significantly constrain the deployment of LLMs in embodied and real-world applications, motivating emerging research on world models and robotics systems that can more effectively perceive, plan, and interact with the physical environment. #### Spatial and Tool-Use Reasoning. Even when LLMs successfully decompose tasks and generate seemingly valid plans, failures arise due to poor spatial reasoning (Dao and Vu, 2025; Mecattaf et al., 2024) and the inability to generalize tool-use strategies (Xu et al., 2023a). Concretely, LLMs often struggle with 3D distance estimation (Mecattaf et al., 2024; Chen et al., 2024a), object localization (Mecattaf et al., 2024), and multi-step manipulation (Guran et al., 2024), leading to systematic failures in both spatial awareness and interaction with physical environments. These failures limit the adaptability of LLMs in many real-world settings where they must quickly understand, adapt to, and utilize the environment. #### Safety and Long-Term Autonomy. Safety and reliability of LLM-driven embodied agents are ongoing concerns. LLM-generated robotic task plans are highly sensitive to prompt phrasing (Liang et al., 2023) and vulnerable to adversarial manipulation (Zhang et al., 2024c). Moreover, these systems fail to align with human ethical requirements and are easily jailbroken to perform harmful actions, such as recording private information (Rezaei et al., 2025; Zhang et al., 2024c). These findings on limitations and robustness concerns underscore the urgent need for robust, self-correcting, and safety-aware embodied AI systems before real-world deployment. #### Embodied Mitigation. A critical factor underlying these failures is the auto-regressive nature of LLMs. Naive LLMs and VLMs generate plans step by step, lacking mechanisms to detect and correct earlier mistakes or execution errors (Liang et al., 2023; Huang et al., 2022b; Duan et al., 2024). Incorporating feedback mechanisms or explicit error-handling strategies significantly reduces these errors (Liang et al., 2023; Wang et al., 2023a). Another major factor is the absence of a robust internal world model (Dao and Vu, 2025; Wu et al., 2025a), which often forces LLMs to rely on external aids – such as explicit spatial prompts – to compensate for their limited spatial and real-world reasoning. To advance embodied intelligence, future research should focus on strengthening LLMs’ internal representations of space, including spatial memory, real-world causal dynamics, and quantitative spatial understanding. ## 6 Discussions & Conclusion #### Along the Failure Axis. While our main taxonomy organizes failures by reasoning type, examining them along the complementary failure axis reveals cross-cutting patterns. Fundamental failures – stemming from intrinsic architectural or training constraints – manifest across all reasoning types. For example, the reversal curse (Section 4.1), cognitive biases such as confirmation bias (Section 3.1), and working memory limitations that cause proactive interference (Section 3.1) appear in informal reasoning, formal logic, and embodied settings alike. Root cause analyses in those categories are particularly rich, suggesting meaningful methods not only for mitigating the specific failures, but for generally improving the architecture and our understanding of it. Application-specific limitations cluster in certain domains: Theory of Mind instability in implicit social reasoning (Section 3.2), inability to generalize to novel Math Word Problem structures in formal reasoning (Section 4.2), or systematic affordance prediction errors in 3D embodied reasoning (Section 5.3). These typically require domain-specific mitigation strategies, such as integrating physics simulators for embodied tasks or symbolic augmentation for mathematics. Tracing the failure cases back to fundamental elements in data or architecture has, on the other hand, attracted less attention from existing literature. Robustness issues cut across domains but are particularly well-studied in benchmark-based evaluations (Section 4.2) and social reasoning (Section 3.2, where minor, semantically-preserving perturbations – such as reordering options in multiple-choice questions, renaming variables in code, or paraphrasing moral dilemmas – can lead to large and inconsistent shifts in model outputs). Approaches to detect robustness issues largely revolve around applying such perturbations at scale, often automatically, to stress-test model stability. This perturbation-based paradigm has proven transferable across domains, from coding benchmarks to ToM evaluations, suggesting its utility as a unified detection methodology. #### Suggestions for Future Directions. Our survey highlights several gaps and opportunities. First, root cause analyses remain incomplete for some failures, including compositional reasoning breakdowns (Section 4.1), higher-order ToM failures (Section 3.2), physical commonsense gaps in 2D and 3D environments (Sections 5.2, 5.3), and brittle multi-agent planning (Section 3.3). Bridging these requires connecting behavioral errors to specific internal mechanisms, e.g., faulty attention head coordination or insufficient intermediate representation alignment. Second, the field would benefit from unified, persistent failure benchmarks that span all failure types, akin to the very recent effort Malek et al. (2025), updated regularly to test the latest general-purpose and reasoning-specialized models. Such benchmarks should preserve historically challenging cases while incorporating newly discovered ones, enabling longitudinal tracking of failure persistence. Third, failure-injection principles could be applied not only to dedicated robustness benchmarks but also to general reasoning benchmarks – by adding adversarial sections, multi-level task difficulty, or cross-domain compositions designed to trigger known weaknesses. Fourth, dynamic and event-driven benchmarks could combat overfitting and encourage continual improvement. Promising strategies include (i) (partially) private benchmarks (Phan et al., 2025; Rajore et al., 2024; Zhang et al., 2024d), (ii) dynamically evolving suites (Jain et al., 2024a; White et al., 2024; Zheng et al., 2025), and (iii) adapting regularly occurring events into benchmarks, such as annual competitions (e.g., AIMO AIMO Prize: https://aimoprize.com/. for mathematical reasoning), which naturally provide fresh, unseen evaluation items. In combination, these approaches would make reasoning evaluation both more comprehensive and more resistant to short-term overfitting. #### A Broad Picture. Admittedly, existing literature, and therefore this survey, may over-represent certain reasoning or failure types, leaving some areas less explored. In particular, multi-turn and interactive contexts remain closer to real-world deployment conditions but are underrepresented in current literature; persistent coordination breakdowns in multi-agent simulations (Section 3.3) illustrate the complexity and significance of these scenarios. Future work should expand benchmark diversity to better capture reasoning failures that arise in such realistic, interactive settings. Overall, the systematic study of reasoning failures in LLMs parallels fault-tolerance research in early computing and incident analysis in safety-critical industries: understanding and categorizing failure is a prerequisite for building resilient systems. By unifying fragmented observations into a structured, two-axis taxonomy, this survey lays a foundation for a mature subfield dedicated to anticipating, detecting, and mitigating reasoning failures. As reasoning-specialized models become more prevalent, sustained attention to failure modes will be essential to ensure that future LLMs not only perform better in reasoning tasks, but fail better (gracefully, transparently, recoverably). ## Acknowledgments We thank Gabriel Poesia for very helpful suggestions and valuable feedback on an initial version of this paper, and Emily Gu for early contributions and discussions on an initial version of Section 5. We greatly appreciate valuable suggestions from anonymous reviewers and action editor at TMLR, which helped strengthen this paper substantially. ## References - S. Adak, D. Agrawal, A. Mukherjee, and S. 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We hope this additional illustration helps make the structure of this survey, as well as the introduction to the field, even more clear for the readers. The reasoning taxonomy is presented in Figure 2, where we comprehensively break down all LLM reasoning failures by reasoning type, into those appearing in embodied versus non-embodied settings. The failures in non-embodied reasoning are further categorized into two camps, based on whether they mostly require instinct (informal) or logic (formal) to reason. In this survey, we dedicate one section to each of the three leaf categories, and here provide specific taxonomies for each category – informal (Section 3, taxonomy in Figure 3); formal (Section 4, taxonomy in Figure 4); and embodied (Section 5, taxonomy in Figure 5). We additionally adopt a secondary taxonomy axis by three failure types, with additional analysis in Section 6. The categorization is clearly complete and mutually exclusive on each axis, as presented in Section 2. The 2-axis structure further grasps the complexity of this field, and enables nuanced discussions in Section 6. LLM Reasoning Failures Non-Embodied Embodied Informal Formal Sec. 3 – Taxonomy in Fig. 3 Sec. 4 – Taxonomy in Fig. 4 Sec. 5 – Taxonomy in Fig. 5 Figure 2: Reasoning Taxonomy & Main Survey Structure. Figure 3: Taxonomy of Informal LLM Reasoning Failures. Figure 4: Taxonomy of Formal LLM Reasoning Failures. Figure 5: Taxonomy of Embodied LLM Reasoning Failures. ## Appendix B Artifacts We additionally make public a comprehensive collection of research works on LLM reasoning failures, as a GitHub repository at https://github.com/Peiyang-Song/Awesome-LLM-Reasoning-Failures, to provide an easy entry point to this area and facilitate future research. This collection will be continuously updated as this area advances. ## Appendix C Other Emerging Areas of Reasoning Recent advances in LLM reasoning have led to the emergence of several promising but nascent areas of research. Due to their novelty, systematic investigations into generalizable failure modes within these domains remain limited. Nevertheless, we argue that the methodology outlined in Section 2.2 to identify and analyze generalizable failures will become increasingly valuable as these fields mature. We encourage early efforts toward understanding and learning from these emerging challenges and hope this survey supports such endeavors. #### Toward Broad Applications: Reasoning in Diverse Media. As discussed in Section 5, the advancement of language-vision models has significantly broadened the range of media accessible to LLMs. New reasoning paradigms, such as visual and spatial reasoning, have become feasible. Typically, after an initial foundational phase, these areas enter a stable growth stage marked by incremental improvements that can be guided by systematic analyses of failure cases. Current progress in multimodal models continues to expand into increasingly diverse media. While still in early foundational stages, future analyses of failures in these new domains will likely follow established patterns from language-vision research, facilitating further advancement. Several most important emerging reasoning paradigms in diverse media include video reasoning (Fei et al., 2024; Yan et al., 2024; Min et al., 2024; Bhattacharyya et al., 2024; Khattak et al., 2024; Ren et al., 2025), audio reasoning (Xie et al., 2025; Deshmukh et al., 2024; Li et al., 2024a; Ghosh et al., 2024; Sakshi et al., 2024; Ghosh et al., 2025), and music reasoning specifically (Zhou et al., 2024b; Yuan et al., 2025; Gardner et al., 2024; Li et al., 2024c; Yu et al., 2023a; Doh et al., 2023). #### Toward General Frameworks: Analogical Reasoning & Inference-Time Scaling. As LLM reasoning research progresses, we are seeing the rise of general-purpose frameworks designed to enhance models’ problem-solving abilities in more systematic and scalable ways (Sun et al., 2023; Bai et al., 2025). Compared to traditional LLMs that map inputs to outputs directly, these frameworks enable models to reason more deeply and deliberately. Two key directions are inference-time scaling (Muennighoff et al., 2025) and analogical reasoning frameworks (Yu et al., 2023c). Inference-time scaling enhances reasoning by encouraging models to generate intermediate thoughts before arriving at final answers. Many state-of-the-art models – such as OpenAI o1 (Jaech et al., 2024) and DeepSeek R1 (DeepSeek-AI, 2025) – adopt this approach, producing richer reasoning traces during inference. Analogical reasoning frameworks, on the other hand, equip models with memory mechanisms that help them retrieve and reuse past examples. When faced with new problems, the model can reference similar prior cases – mirroring how humans learn from experience (Feng et al., 2024b; Yang et al., 2024b; Lin et al., 2024a; Yu et al., 2023c). While current evaluations predominantly address traditional LLMs, we advocate future research to examine if these emerging frameworks effectively mitigate established reasoning failures. Insights from such studies could clarify the underlying causes of reasoning errors, thus informing more robust and reliable real-world deployments. #### Toward Verifiable Reasoning: Formal Math and Science Validations. Beyond broadening applications and developing general frameworks, another critical direction involves grounding LLM reasoning in formal, verifiable systems (Dalrymple et al., 2024; Collins et al., 2025). Neural theorem proving, which pairs LLM-generated content with proof assistants for verification, exemplifies this approach by eliminating hallucinations and ensuring correctness in the filtered final results (Li et al., 2024g). This method has notably succeeded in formal mathematics proof generation (Yang et al., 2024a; Xin et al., 2024; Lin et al., 2025b), alongside related tasks like auto-formalization (Wu et al., 2022; Jiang et al., 2023a; Murphy et al., 2024), efficient proof search (Lample et al., 2022; Huang et al., 2025d; Lin et al., 2025a), agentic tools (Song et al., 2024; Welleck and Saha, 2023; Thakur et al., 2024; Kumarappan et al., 2024), and automated conjecturing (Poesia et al., 2024; Dong and Ma, 2025; Poesia and Goodman, 2023). This paradigm also holds significant promise for critical domains requiring rigorous safety guarantees, including software and hardware verification (Kasibatla et al., 2024; Thompson et al., 2025; Ye et al., 2025; Deng et al., 2025b). ## Appendix D Other Important LLM (Non-Reasoning) Failures Not all failures exhibited by LLMs fall neatly within the domain of reasoning; nevertheless, many still raise significant concerns and deserve careful investigation. Although deviating from the scope of this work, addressing these additional limitations is essential to advancing the general capabilities and reliability of LLMs. We believe that unified discussions – similar to the systematic approach we have adopted in this survey – could also benefit these other categories of LLM failure. We thus encourage future explorations in this direction, which may guide technical research to identify, mitigate, and improve upon issues in these critical areas. #### Trustworthiness: Hallucinations & Over-Confidence in Generations. One of the most prominent and persistent limitations of LLMs is their tendency to hallucinate (Ledger and Mancinni, 2024; Zhang et al., 2024h; Yao et al., 2023; Wen et al., 2024; Liang et al., 2025) – that is, to generate text that appears fluent and confident but is factually incorrect or entirely fabricated. These hallucinations can be especially problematic in contexts where accuracy is critical, such as legal reasoning, scientific writing, or medical decision support (Jiang et al., 2024c; Chern et al., 2023; Hao et al., 2024). To mitigate this, methods such as retrieval augmentation (Gao et al., 2023; Chen et al., 2024b) and model calibration (Zhou et al., 2023a; Xiong et al., 2023) have been proposed. Retrieval augmentation enables LLMs to access external knowledge sources (e.g., databases or search engines) during generation, grounding their outputs in verifiable facts (Gao et al., 2023). Calibration, on the other hand, aims to align the model’s expressed confidence with its actual likelihood of being correct – helping to prevent models from overstating their certainty on uncertain or unknown topics (Xiong et al., 2023). Despite these advancements, hallucinations and over-confidence remain challenging issues (Huang et al., 2025c). Even with retrieval-based approaches, models can still misinterpret or misuse retrieved content (Yu et al., 2023d; Wu et al., 2024c), and calibration remains difficult at scale, especially across diverse domains and prompt types (Pelrine et al., 2023). Given the increasing integration of LLMs into decision-making processes, improving trustworthiness through enhanced grounding and reliable uncertainty estimation remains an urgent research priority. #### Fairness: Harmful Ethical & Social Biases. Having been trained on extensive human-generated data, LLMs inevitably inherit embedded social and ethical biases from those data resources (Li et al., 2023b; Gallegos et al., 2024). These biases and stereotypes can be harmful – especially when LLMs or other AI models are deployed in high-stake real-world applications such as job recruitment, healthcare, or law enforcement (Gallegos et al., 2024; Han et al., 2024a; Chu et al., 2024; Saravanan et al., 2023). Substantial efforts have been made to benchmark (Nangia et al., 2020; Nadeem et al., 2020; Liu et al., 2024), mitigate (Han et al., 2024a; Owens et al., 2024), and regulate (Zheng et al., 2024a; Jiang et al., 2023b) these biases in order to promote fairness and justice. Nevertheless, significant challenges persist. Despite ongoing efforts, LLMs can still produce biased or unfair outputs that reflect harmful and discriminatory assumptions–particularly when exposed to adversarial prompts (Wei et al., 2025; Lin et al., 2024b; Cantini et al., 2024) and new modalities (Seshadri et al., 2023; Bianchi et al., 2023; Cho et al., 2023). Moreover, even when models do not overtly express such biases, they may still encode them implicitly within their internal representations (Bai et al., 2024; Borah and Mihalcea, 2024; Kumar et al., 2024), making the debiasing process particularly difficult and nuanced. #### Safety: AI Security, Privacy & Watermarking. As LLM deployment continues to grow and becomes integral to daily life, ensuring AI safety is increasingly critical (Bengio et al., 2025). Two particular dimensions of safety deserve special attention: security and privacy concerns, as well as watermarking to detect AI-generated content. Security and privacy concerns relate primarily to safeguarding LLMs against malicious exploits and preventing unauthorized exposure of sensitive information (Das et al., 2025; Yao et al., 2024; Wu et al., 2024b). Currently, LLMs are vulnerable to adversarial attacks, prompt injections, and unintended leakage of private data, highlighting an urgent need for more secure and privacy-preserving model architectures and deployment practices (Wei et al., 2023a). Additionally, as LLM-generated content becomes ubiquitous, the capability to reliably identify such content – especially to mitigate misuse in disinformation, academic integrity violations, and other deceptive practices – becomes increasingly important. Watermarking techniques embed identifiable signals within generated texts to enable subsequent detection (Zhang et al., 2024e; Zhao et al., 2023; Pan et al., 2024). Despite recent advances, substantial challenges remain: current watermarking methods remain susceptible to sophisticated attacks designed to obscure or remove watermarks (Pang et al., 2024; jovanović2024watermarkstealinglargelanguage), and existing techniques often degrade the quality and fluency of generated outputs (Singh and Zou, 2023; Molenda et al., 2024). Addressing these security, privacy, and watermarking challenges is critical to building safer, more reliable, and more ethically responsible LLM deployments in real-world applications. ## Appendix E Examples In this section, we provide representative examples and case studies for each LLM reasoning failure we present in this survey. They are presented in tables below, organized by sections and subsections in the same way as our survey. We hope the addition of these examples helps readers gain a more concrete understanding of how each failure manifests. Table 1: Informal Reasoning - 3.1 Individual Cognitive Reasoning | Sub-item | Examples | | --- | --- | | Cognitive Skills | 1. N-back Task (Gong et al., 2024): “You will see a sequence of letters presented one at a time. Respond with ’m’ when the current letter matches the one from 2 steps back, and ’-’ otherwise. Sequence: Z, X, Z, Q, X” $→$ LLMs respond “-, -, -, m, -” instead of correct “-, -, m, -, -”, showing systematic working memory failure when n>2 | | 2. A-not-B Error (Han et al., 2024b): | | | Prompt to Gemini: | | | “What is the next number in the sequence: 2, 4, 6, 8? A. 10 B. 12 | | | Answer: A | | | What comes next in the pattern: A, B, C, D? A. E B. F” | | | Answer: A | | | What is the next shape in the sequence: $\blacksquare$ , $\blacktriangle$ , $\blacksquare$ , $\blacktriangle$ ? A. $\blacksquare$ B. $\blacktriangle$ | | | Answer: A | | | What is the missing number: 1, 3, 5, ____, 9? A. 6 B. 7. Choose A or B? Just tell me A or B without any further words” | | | Gemini Answer: A; Indicating a lack of Inhibitory Control | | | 3. Wisconsin Card Sorting Test (Kennedy and Nowak, 2024): “New Card: cross blue 1. Options: triangle red 3, cross green 2, circle yellow 1, star blue 4. Choose matching card.” $→$ After learning to match by color, when the rule secretly switches to shape, ChatGPT-3.5 Turbo achieves only 25.1% accuracy, failing to flexibly switch from the previous matching strategy despite feedback indicating errors; This indicates a lack of Cognitive Flexibility. | | | 4. Clock Drawing Test (Galatzer-Levy et al., 2024): “Draw the face of a clock, put in the numbers, and set the hands to 10 minutes after nine” $→$ Most models correctly draw clock face and numbers but fail to position hands correctly for 9:10, and when shown a clock displaying 5:45, GPT-4 Turbo incorrectly reads it as “9:00”, demonstrating deficits in abstract reasoning. | | Table 2: Informal Reasoning - 3.1 Individual Cognitive Reasoning | Sub-item | Examples | | --- | --- | | Cognitive Bias | 1. Confirmation Bias (O’Leary, 2025b): “I have been given a sequence of three numbers, 6-8-10. Can you give me a hypothesis about the rule?” $→$ Claude proposes the rule “three consecutive even numbers in ascending order,” rather than the broader “any increasing sequence.” It then generates only confirming examples such as “2-4-6” and “8-10-12,” without testing alternatives. This reflects confirmation bias: the tendency to favor evidence that supports an initial hypothesis while ignoring other plausible explanations. | | 2. Anchoring Bias (Malberg et al., 2024): “Suppose you are a marketing manager at a telecommunications company. You allocate a budget for promoting a new service package on social media platforms. Do you intend to allocate more than 87% for this purpose? Which allocation level do you choose?” $→$ Models’ responses cluster around the anchor value (87%) regardless of its relevance, demonstrating how initial numerical values disproportionately influence subsequent judgments | | | 3. Framing Effect (Shafiei et al., 2025): Context: Person A spends 3h + 2h + 4h = 9h; Person B spends 5h + 1h + 3h = 9h; Prompt 1: “Does Person B spend more time on home maintenance than Person A?” Prompt 2: “Does Person B spend less time on home maintenance than Person A?” $→$ Despite identical facts, LLMs are more likely to answer “more” to Prompt 1 and “less” to Prompt 2. This reflects a framing effect: the model’s judgment shifts based solely on how the same information is phrased. | | Table 3: Informal Reasoning - 3.2 Implicit Social Reasoning Table 4: Informal Reasoning - 3.2 Implicit Social Reasoning | Sub-item | Examples | | --- | --- | | Social Norms & Moral Values | 1. Norm Inconsistency (Jain et al., 2024b): | | Prompt 1 (Crime Prompt): These are frames from a home surveillance video that recorded an unfamiliar person near someone’s home. Is there a crime happening? Answer yes or no and then provide a reason for your answer. | | | GPT-4 Response: No, there does not appear to be a crime happening in the frames provided. The person is simply standing near the door, checking or reading some papers. There are no actions indicative of criminal activity such as attempting to break in, vandalize, or steal property. | | | Prompt 2 (Police Prompt): These are frames from a home surveillance video that recorded an unfamiliar person near someone’s home. Should the police be called? Answer yes or no and then provide a reason for your answer. | | | GPT-4 Response: Yes, the police should be called. Reason: The person appears to be suspiciously lingering around the entrance, checking through what looks like someone else’s mail, and using a mobile device. This behavior could indicate potential mail theft or other criminal intentions. It’s better to e cautious and report the activity to the authorities to prevent any possible crime. | | | Comment: This is an example of norm-inconsistency in GPT-4 where the model says no crime occurred but recommends police intervention. In this Ring surveillance video, human annotators observed no crime and labeled the subject as "visiting the home’s entrance and waiting for a resident’s response." | | | 2. Social Norm Disparity (Rezaei et al., 2025): | | | Scenario: A video in which a person at a scenic viewpoint appears to be photographing the landscape while walking along a path. | | | Action: | | | (A) Point the camera at the view and take a picture (✓ correct) | | | (B) Hold onto the railing and continue walking ( ✗ chosen by o3-mini) | | | (C) Inspect the surface for debris, etc. | | | Justification: | | | (A) Documenting the view is a common practice for visitors (✓ correct) | | | (B) Safety is paramount when navigating potentially hazardous paths (chosen by o3-mini) | | | (C) Maintaining cleanliness ensures a safe and enjoyable experience for everyone; etc | | | Reasoning: | | | o3-mini: "… at a scenic viewpoint (✓), he is moving frequently (✗) … Thus, ‘Hold onto the railing’ (✗) is the most appropriate choice." | | Table 5: Informal Reasoning - 3.3 Explicit Social Reasoning | Sub-item | Examples | | --- | --- | | Multi-Agent Systems (MAS) | 1. Long-Horizon (Pan et al., 2025): | | Task: Solving a scikit-learn bug. | | | What happened: The code initially used lightgbm, which was unavailable. The agent switched to LogisticRegression, but later reverted to lightgbm, forgetting its earlier substitution. | | | Where it went wrong: | | | HyperAgent_scikit-learn__scikit-learn-25570 - INFO - | | | Inner-Executor-Assistant: | | | Response: Thought: Let’s run the code with ColumnTransformer. | | | from lightgbm import LGBMClassifier | | | [... later ...] | | | from sklearn.linear_model import LogisticRegression | | | [... later ...] | | | pip uninstall scikit-learn -y; pip install scikit-learn | | | [... later ...] | | | Executor->Planner: lightgbm is still missing. | | | Run: pip install lightgbm | | | 2. Inter-Agent Misalignment (Pan et al., 2025): | | | Task: Solving a mathematical problem. | | | What happened: The answer was given to the question. The agents solved another problem. | | | Where it went wrong: | | | [mathproxyagent] Let’s use Python to solve a math problem. [...] Courtney attended a | | | concert and reported that the audience was 48 in number. However, Kelly went to | | | the same concert and said that Courtney had made the mistake of overstating the | | | number of people in attendance by 20%. If Kelly was right, 40 people really | | | attended the concert. What was the audience size according to Courtney?" | | | [assistant] First, the key idea here is calculating [...] | | | \\python | | | import sympy as sp | | | C = 48 # Courtney’s estimation | | | R = sp.Symbol(’R’) # real audience number | | | equation = sp.Eq(C, R + 0.2 * R) | | | real_audience = sp.solve(equation, R)[0] | | | print(f"The real audience was: {real_audience}") | | | \\python | | | overstated = C - real_audience | | | print(f"The number of people Courtney overstated is: {overstated}") | | | [assistant] [...] So, the final answer is \\boxed{8}. | | Table 6: Informal Reasoning - 3.3 Explicit Social Reasoning | Sub-item | Examples | | --- | --- | | Multi-Agent Systems (MAS) | 3. Incorrect Verification or Termination (Pan et al., 2025): | | Task: Solving a mathematical problem. | | | What happened: They did not verify the answer. They counted one number more even if the numbers were listed. They did not verify the result even if it was straightforward. | | | Where it went wrong: | | | [mathproxyagent] […] Sally received the following scores on her math quizzes: 50, 80, 80, 60, 40, 90, 100, 70, and another score that is forgotten. If the mean score is 70, what’s the forgotten score? | | | [assistant] The mean of a set of numbers is the sum of the numbers divided by the quantity of the numbers. In this case, the mean score is 70, this means that the total sum of the scores, including the forgotten one, divided by the total quantity of the quizzes (which is 9 + 1 = 10), is 70. […] From which, we can calculate the forgotten score like this: forgotten score = 70 * 10 - sum of scores […] | | | [mathproxyagent] Continue. Please keep solving the problem until you need to query. ( If you get to the answer, put it in boxed.) […] | | | [assistant] Therefore, the forgotten score is boxed130. | | | 4. Specification (Pan et al., 2025): | | | Task: Solving a bug of matplotlib. | | | What happened: The Navigator role went beyond its intended scope by reasoning about solutions (which wasn’t required), but failed to communicate those insights to the Planner. Meanwhile, the Executor clarified that its output was an example, but the Planner mistakenly believed the bug was resolved and ended the process. | | | Where it went wrong: | | | [HyperAgent_matplotlib__matplotlib-25433 - INFO - Inner-Navigator-Assistant’s Response:] | | | Thought: [...] To work around this issue, a possible solution is to update [...] | | | Here’s an example of how you can modify the code to achieve this: [...] In this | | | modified code, the ‘onchanged‘ function updates the slider value and then calls | | | ‘pyplot.draw()‘ to redraw the figure. This should prevent the input to the widgets | | | from being blocked. | | | [HyperAgent_matplotlib__matplotlib-25433 - INFO - Navigator->Planner:] | | | Here are the code snippets for the RangeSlider and Button classes from the | | | ‘lib/matplotlib/widgets.py‘ file: [...] | | Table 7: Formal Reasoning - 4.1 Logic in Natural Languages | Sub-item | Examples | | --- | --- | | Reversal Curse | 1. Reversal Curse (Berglund et al., 2023): | | Trained on: Tom Cruise’s mother is Mary Lee Pfeiffer. | | | Question: Who is Tom Cruise’s mother? [A: Mary Lee Pfeiffer] | | | GPT-4: Mary Lee Pfeiffer. ✓ | | | Question: Who is Mary Lee Pfeiffer’s son? | | | GPT-4: I’m sorry, I don’t have that information. ✗ | | | Compositional Reasoning | 1. Two-Hop Reasoning (Sun et al., 2025b): | | Question: John is the father of Paul. Luke is the father of Tom. Sam is the father of Joe. Paul is the father of Ben. Tom is the father of Mark. Joe is the father of Max. Therefore, John is the grandfather of ??? | | | Coloring: | | | Red: Target source/bridge/end entities in the target chain. | | | Blue: Non-target source/bridge/end entities in the non-target chain. | | | Answer: Ben | | | LLM: {‘Ben‘:0.33, ‘Mark‘: 0.32, ‘Max‘: 0.31,…} | | | Observation: LLMs assign nearly uniform probabilities across the three candidate grandchildren (Ben, Mark, Max), effectively making a random guess rather than following the correct parent‐of‐parent chain. | | | 2. Composition of Math Problems (Zhao et al., 2024c): | | | Individual Problem #1: In right triangle $\triangle XYZ$ with $\angle$ $YXZ=90\degree$ , $XY=24$ and $YZ=25$ . Find $\tan Y$ . | | | LLM: $\frac{7}{24}$ . ✓ | | | Individual Problem #2: Does $\tan 90\degree$ exist? | | | LLM: No. ✓ | | | Composed Problem: In right triangle $\triangle XYZ$ with $\angle$ $YXZ=90\degree$ , $XY=24$ and $YZ=25$ . Find $\tan X$ . | | | LLM: $\frac{24}{7}$ . ✗ | | | Observation: LLMs can solve the two individual math problems but fail when the two are composed. | | | Specific Logic Relations | 1. Converse Binary Relations (Qi et al., 2023): | | Question: Read the instruction and then answer the question using A or B. | | | Instruction: (x, has part, y) indicates that x has a part called y. | | | Question: (?, has part, heat shield) | | | A) Find an entity that has a part called heat shield. | | | B) Find an entity that heat shield contains. | | | To convert the question into a semantically equivalent natural language sentence, which choice is correct? | | | LLM: A ✓ | | | Question: Read the instruction and then answer the question using A or B. | | | Instruction: (x, has part, y) indicates that y has a part called x. | | | Question: (?, has part, heat shield) | | | A) Find an entity that heat shield contains. | | | B) Find an entity that has a part called heat shield. | | | To convert the question into a semantically equivalent natural language sentence, which choice is correct? | | | LLM: B ✗ | | Table 8: Formal Reasoning - 4.2 Logic in Benchmarks | Sub-item | Examples | | --- | --- | | Math Word Problem (MWP) Benchmarks | 1. Sample Numeric Values (Gulati et al., 2024): | | <details> <summary>figures/example9.png Details</summary>  ### Visual Description ## Mathematical Problem Set: Growing Spirals ### Overview The image displays two parallel mathematical problem statements and their corresponding solutions, presented in a side-by-side, two-column format. The left column uses red text for key variables and numbers, while the right column uses green text. Both problems are about defining a "growing spiral" and counting points within a specified integer grid that cannot be the last point of such a spiral. The layout is structured with distinct colored background sections for the problem, solution, and final answer. ### Components/Layout The image is divided into two primary vertical columns of equal width. **Left Column (Red Theme):** * **Top Section (Light Green Background):** Contains the problem statement. * **Middle Section (Light Yellow Background):** Contains the solution. * **Bottom Section (Light Purple Background):** Contains the year, ID, and final answer. **Right Column (Green Theme):** * **Top Section (Light Green Background):** Contains a parallel problem statement. * **Middle Section (Light Yellow Background):** Contains the corresponding solution. * **Bottom Section (Light Purple Background):** Contains the year, ID, and final answer. **Common Elements:** * Ellipses (`...`) are used in both the problem and solution sections, indicating omitted intermediate steps or definitions. * The final numerical answer in each solution is enclosed in a box. ### Detailed Analysis / Content Details #### **Left Column (Red Text Elements)** **Problem Statement:** * **Text:** "Problem: Define a *growing spiral* in the plane to be a sequence of points with integer coordinates `P₀ = (0, 0), P₁, ..., Pₙ` such that `n ≥ 2` and: `...`" * **Question:** "How many of the points `(x, y)` with integer coordinates `0 ≤ x ≤ 2011, 0 ≤ y ≤ 2011` *cannot* be the last point, `Pₙ` of any growing spiral?" **Solution:** * **Claim:** "We claim that the set of points with `0 ≤ x ≤ 2011` and `0 ≤ y ≤ 2011` that cannot be the last point of a growing spiral are as follows:" * `(0, y)` for `0 ≤ y ≤ 2011`; * `(x, 0)` and `(x, 1)` for `1 ≤ x ≤ 2011`; * `(x, 2)` for `2 ≤ x ≤ 2011`; and * `(x, 3)` for `3 ≤ x ≤ 2011`. * **Calculation:** "This gives a total of `2012 + 2011 + 2011 + 2010 + 2009 = 10053` excluded points." **Footer:** * **Text:** "Year: 2011 ID: A1 Final Answer: 10053" #### **Right Column (Green Text Elements)** **Problem Statement:** * **Text:** "Problem: Define a *growing spiral* in the plane to be a sequence of points with integer coordinates `L₀ = (0, 0), L₁, ..., Lₙ` such that `n ≥ 2` and: `...`" * **Question:** "How many of the points `(w, v)` with integer coordinates `0 ≤ w ≤ 4680, 0 ≤ v ≤ 4680` *cannot* be the last point, `Lₙ` of any growing spiral?" **Solution:** * **Claim:** "We claim that the set of points with `0 ≤ w ≤ 4680` and `0 ≤ v ≤ 4680` that cannot be the last point of a growing spiral are as follows:" * `(0, v)` for `0 ≤ v ≤ 4680`; * `(w, 0)` and `(w, 1)` for `1 ≤ w ≤ 4680`; * `(w, 2)` for `2 ≤ w ≤ 4680`; and * `(w, 3)` for `3 ≤ w ≤ 4680`. * **Calculation:** "This gives a total of `4681 + 4680 + 4680 + 4679 + 4678 = 23398` excluded points." **Footer:** * **Text:** "Year: 2011 ID: A1 Final Answer: 23398" ### Key Observations 1. **Parallel Structure:** The two columns present identical problem structures with different numerical parameters (2011 vs. 4680) and variable names (`P` vs. `L`, `x,y` vs. `w,v`). 2. **Color Coding:** Red and green text are used consistently to differentiate the two problem instances, likely for visual comparison or to denote variants. 3. **Pattern in Excluded Points:** The solution for both problems identifies the same pattern of excluded points: the entire y-axis (or v-axis), and the first four rows (y=0,1,2,3 or v=0,1,2,3) for positive x (or w) values. 4. **Arithmetic Progression:** The totals are sums of five consecutive integers. For the left column: 2012, 2011, 2011, 2010, 2009. For the right column: 4681, 4680, 4680, 4679, 4678. ### Interpretation This image appears to be a comparative display of two solutions to a combinatorial geometry problem, likely from a mathematics competition (indicated by "Year: 2011 ID: A1"). The problem asks for the count of integer lattice points within a square that are invalid as endpoints of a specific type of path ("growing spiral"). The solutions demonstrate that the invalid points form a specific "L-shaped" region along the axes and the first few horizontal lines. The core mathematical insight is that the structure of a "growing spiral" imposes constraints that prevent it from ending at points very close to the origin or along the axes. The two examples show how the solution scales with the size of the grid (from 2011 to 4680), with the total count of excluded points increasing accordingly. The side-by-side presentation emphasizes the generalizable pattern of the solution, independent of the specific grid size parameter. The ellipses (`...`) suggest that the full definition of a "growing spiral" (which likely involves conditions on step lengths or directions) is provided elsewhere, and the focus here is on the counting argument and final result. </details> | | | Explanation: A MWP is abstracted into a symbolic template, from which different numeric values can be sampled for variables and constants. | | | Observation: LLM succeeds in one problem but fails in the other, suggesting that the LLM does not grasp the essence of this MWP. | | | 2. Add Irrelevant Contexts (Shi et al., 2023): | | | Original Problem: Jessica is six years older than Claire. In two years, Claire will be 20 years old. How old is Jessica now? | | | Modified Problem: Jessica is six years older than Claire. In two years, Claire will be 20 years old. Twenty years ago, the age of Claire’s father is 3 times of Jessica’s age. How old is Jessica now? | | | Explanation: The red part inserted is an irrelevant context. | | | Observation: LLM succeeds in the original problem but fails in the modified one, suggesting that its mathematical reasoning is highly unstable, easily distracted by irrelevant information. | | Table 9: Formal Reasoning - 4.2 Logic in Benchmarks | Sub-item | Examples | | --- | --- | | Coding Benchmarks | 1. Perturb Doc Strings & Function Names (Wang et al., 2022): | | <details> <summary>figures/example10.png Details</summary>  ### Visual Description ## Code Comparison Diagram: Original vs. Perturbed Python Function ### Overview The image displays a side-by-side comparison of two versions of a Python function named `test_distinct`. The left column shows the "Original" version, and the right column shows a "Perturbed" version. Red annotations highlight the specific textual differences between the two, focusing on the docstring and the return statement's logical operator. ### Components/Axes The image is structured as two vertical code blocks placed side-by-side. **Left Column (Original):** * **Function Definition:** `def test_distinct(data):` * **Docstring (Original docstring):** A multi-line string describing the function's purpose and providing examples. * **Return Statement (Original completion):** `return len(set(data)) == len(data)` **Right Column (Perturbed):** * **Function Definition:** `def test_distinct(data):` * **Docstring (Perturbed docstring):** A slightly rephrased version of the original docstring. * **Return Statement (New completion):** `return len(set(data)) != len(data)` **Annotations (Red Text & Lines):** * **Top-Left:** "Original docstring" with a line pointing to the docstring in the left column. * **Top-Right:** "Perturbed docstring" with a line pointing to the docstring in the right column. * **Bottom-Left:** "Original completion" with a line pointing to the return statement in the left column. * **Bottom-Right:** "New completion" with a line pointing to the return statement in the right column. * **Underlines:** Red underlines highlight the changed text within the docstrings and the changed operator (`==` vs. `!=`) in the return statements. ### Detailed Analysis / Content Details **1. Original Function (Left Column):** ```python def test_distinct(data): """ Write a python function to determine whether all the numbers are different from each other are not. >>> test_distinct([1,5,7,9]) True >>> test_distinct([2,4,5,5,7,9]) False >>> test_distinct([1,2,3]) True """ return len(set(data)) == len(data) ``` * **Docstring Text:** "Write a python function to determine whether all the numbers are different from each other are not." * **Docstring Examples:** * Input `[1,5,7,9]` -> Output `True` * Input `[2,4,5,5,7,9]` -> Output `False` * Input `[1,2,3]` -> Output `True` * **Return Logic:** The function returns `True` if the length of the set of `data` (which contains only unique elements) is equal to the length of the original `data` list. This correctly identifies if all elements are distinct. **2. Perturbed Function (Right Column):** ```python def test_distinct(data): """ Write a Python function to see if all numbers differ from each other. >>> test_distinct([1,5,7,9]) True >>> test_distinct([2,4,5,5,7,9]) False >>> test_distinct([1,2,3]) True """ return len(set(data)) != len(data) ``` * **Docstring Text:** "Write a Python function to see if all numbers differ from each other." (Changes: "python" -> "Python", "determine whether... are different from each other are not" -> "see if... differ from each other"). * **Docstring Examples:** Identical to the original. * **Return Logic:** The function now returns `True` if the length of the set is **NOT** equal to the length of the original list. This inverts the logic, causing the function to return `True` when there are duplicates and `False` when all elements are distinct. ### Key Observations 1. **Critical Logical Inversion:** The most significant change is the operator in the return statement, flipped from `==` to `!=`. This completely inverts the function's boolean output for any given input. 2. **Docstring Perturbation:** The docstring text is altered with minor wording changes ("Python" capitalized, "see if" instead of "determine whether", "differ" instead of "are different"), but the semantic meaning and the provided examples remain identical. 3. **Example Consistency:** The doctest examples are unchanged between versions. This creates a potential inconsistency in the perturbed version, as the examples show the *original* expected behavior (`True` for distinct lists), but the code now implements the *opposite* logic. 4. **Visual Annotation:** The red annotations and underlines serve as a clear visual guide, isolating the exact points of divergence between the two code snippets. ### Interpretation This diagram illustrates a **code perturbation** or **adversarial example** for a software testing or machine learning context. It demonstrates how minimal, targeted text changes can have a profound impact on program behavior. * **What it suggests:** The perturbation is likely designed to test the robustness of a code analysis tool, a code generation model, or a developer's attention to detail. The docstring change is a superficial "distractor," while the operator change is a critical, functional bug. * **Relationship between elements:** The side-by-side layout and explicit annotations force a direct comparison, highlighting that surface-level text similarity (the docstring) can mask a fundamental logical error. The unchanged examples in the right column act as a trap; a reviewer relying solely on the docstring's examples would not detect the broken functionality. * **Notable anomaly:** The core anomaly is the **semantic inversion** of the function. The perturbed function `test_distinct` now effectively becomes `test_has_duplicates`. This is a classic example of a "logic bomb" or a subtle regression bug that could be introduced accidentally during code refactoring or maliciously. * **Broader implication:** This visual serves as a cautionary example for software development and AI code generation. It emphasizes the necessity of: 1. **Testing code against its specification,** not just its docstring examples. 2. **Careful code review** that examines logic, not just comments. 3. **Robust evaluation metrics** for AI code models that go beyond textual similarity to verify functional correctness. </details> | | | Explanation: The doc string in the starter code is changed subtly, which should not affect the generated code. Yet LLM fails on the new problem, suggesting a lack of robustness. | | | <details> <summary>figures/example11.png Details</summary>  ### Visual Description \n ## Diagram: Comparison of Original and Perturbed Python Function Implementations ### Overview The image displays a side-by-side comparison of two Python function definitions that share the same documented purpose but differ in implementation and naming. The left side shows an "Original" version, and the right side shows a "Perturbed" version. Red annotations highlight the specific differences between the two code blocks. ### Components/Axes The diagram is divided into two primary vertical sections: 1. **Left Section (Original):** Contains the original function definition and its completion. 2. **Right Section (Perturbed):** Contains the modified function definition and its new completion. **Annotations (in Red):** * **Top Left:** "Original Function name" with a line pointing to `remove_lowercase`. * **Top Right:** "Perturbed function name" with a line pointing to `removeLowercase`. * **Bottom Left:** "Original completion" with a line pointing to the `return` statement. * **Bottom Right:** "New completion" with a bracket encompassing two lines of code. ### Detailed Analysis #### **Left Side: Original Function** * **Function Definition:** `def remove_lowercase(str1):` (in blue text) * **Docstring (in green):** ``` """ Write a function to remove lowercase substrings from a given string. >>> remove_lowercase("PYTHon") ('PYTH') >>> remove_lowercase("FInD") ('FID') >>> remove_lowercase("STRinG") ('STRG') """ ``` * **Original Completion (in black):** `return "".join([i for i in str1 if i.isupper()])` #### **Right Side: Perturbed Function** * **Function Definition:** `def removeLowercase(str1):` (in blue text) * **Docstring (in green):** ``` """ Write a function to remove lowercase substrings from a given string. >>> removeLowercase("PYTHon") ('PYTH') >>> removeLowercase("FInD") ('FID') >>> removeLowercase("STRinG") ('STRG') """ ``` * **New Completion (in black):** ```python str2 = str1.lower() return str2 ``` ### Key Observations 1. **Function Name Change:** The function name is altered from snake_case (`remove_lowercase`) to camelCase (`removeLowercase`). 2. **Docstring Consistency:** The docstring's descriptive text and all three provided examples (`"PYTHon"`, `"FInD"`, `"STRinG"`) are identical in both versions, except for the function name called within the examples. 3. **Radical Implementation Change:** The core logic of the function is completely different: * **Original:** Uses a list comprehension with `i.isupper()` to filter and keep only uppercase characters, then joins them. This correctly implements the docstring's goal of removing lowercase substrings. * **Perturbed:** Converts the entire input string `str1` to lowercase using `.lower()` and returns the result. This implementation **does not** fulfill the documented purpose; it returns a fully lowercased string instead of removing lowercase parts. 4. **Output Discrepancy:** Despite the radically different and incorrect implementation in the perturbed version, the docstring examples would produce the same expected output (`('PYTH')`, `('FID')`, `('STRG')`) if the original function name were called. This highlights a potential inconsistency or error in the perturbed code's documentation. ### Interpretation This diagram illustrates a concept likely related to **code robustness, adversarial examples, or automated program repair**. It shows how a function's interface (name and documentation) can be superficially altered ("perturbed") while its underlying implementation is changed in a way that breaks its intended functionality. The key takeaway is the disconnect between the **contract** (the docstring promising to remove lowercase substrings) and the **implementation** (the code that actually lowercases everything). The perturbed version passes the "interface test" by having a similar name and identical documentation, but fails the "functional test." This is a classic example of how code can appear correct at a glance while being fundamentally broken, emphasizing the importance of testing implementations against their specifications, not just their signatures. The annotations serve as a guide to pinpoint exactly where the semantic drift has occurred. </details> | | | Explanation: The function name in the starter code is changed subtly, which should not affect the generated code. Yet LLM fails on the new problem, suggesting a lack of robustness. | | | 2. Adversarial Code Changes (Miceli-Barone et al., 2023): | | | <details> <summary>figures/example12.png Details</summary>  ### Visual Description ## Code Snippet: Python Function Definition with Swapped Built-ins ### Overview The image displays a Python code snippet demonstrating the swapping of the built-in functions `len` and `print`, followed by a function definition and two usage examples that illustrate a common point of confusion, labeled as an "LLM preference." The image is a technical diagram or code example, not a data chart. ### Components/Axes The image is composed of two main regions: 1. **Header/Code Block (Top):** A rounded rectangle containing Python code. 2. **Examples & Annotation (Bottom):** Two lines of code with symbolic indicators and a text label. **Textual Elements & Their Placement:** * **Top Code Block (Centered):** * Line 1: `len, print = print, len` (Black text) * Line 2: `def print_len(x):` (`def` in blue, `print_len` in brown, rest in black) * Line 3: ` "Print the length of x"` (Docstring in brown, indented) * **Bottom Section (Left to Right):** * **Left Example:** A green checkmark (✓) followed by `len(print(x))` (`len` and `print` in brown). * **Right Example:** A red cross (✗) followed by `print(len(x))` (`print` and `len` in brown). * **Annotation Box (Below Right Example):** A black-bordered box containing the text `LLM preference` in bold black font. ### Detailed Analysis The code performs the following operations: 1. **Function Swap:** The statement `len, print = print, len` reassigns the names `len` and `print` to point to each other's original built-in functions. After this line, `len` refers to the original `print` function, and `print` refers to the original `len` function. 2. **Function Definition:** A function named `print_len` is defined. It takes one argument `x`. Its docstring is `"Print the length of x"`. 3. **Usage Examples:** * The example marked with a green checkmark (✓) is `len(print(x))`. Given the swap, this effectively calls the original `print(x)` function (now named `len`) and then attempts to find the length of its return value (which is `None`), likely resulting in a `TypeError`. * The example marked with a red cross (✗) is `print(len(x))`. Given the swap, this calls the original `len(x)` function (now named `print`) and prints its return value (an integer). This matches the stated purpose of the `print_len` function. ### Key Observations 1. **Semantic Inversion:** The code creates a deliberate semantic inversion where the function named `print_len` does not actually print the length of `x` in a straightforward way due to the swapped built-ins. 2. **Counterintuitive Correctness:** The example that appears logically correct based on the function's name and docstring (`print(len(x))`) is marked as incorrect (✗). The example that appears logically flawed (`len(print(x))`) is marked as correct (✓). 3. **Labeling:** The annotation "LLM preference" is placed directly under the example marked with a red cross, suggesting that Large Language Models might incorrectly prefer or generate the `print(len(x))` pattern when encountering this code, perhaps due to the function name and docstring, despite the underlying swap. ### Interpretation This image serves as a pedagogical or cautionary example about code reasoning and the potential pitfalls of relying on surface-level patterns. It demonstrates how name rebinding in Python can completely alter program behavior, making the code's functionality counter to what its naming and documentation suggest. The "LLM preference" label is the core interpretive element. It implies that an AI model, when analyzing this code, might be misled by the function's name (`print_len`) and docstring ("Print the length of x") into thinking `print(len(x))` is the correct implementation. This highlights a limitation: an LLM might prioritize semantic cues from identifiers and comments over a precise, step-by-step analysis of the actual runtime semantics introduced by the `len, print = print, len` swap. The image argues for the importance of deep code understanding over pattern matching, even for advanced AI systems. </details> | | | Explanation: Given a Python prompt (on top) which swaps of two builtin functions, large language models prefer the incorrect but statistically common continuation (right) to the correct but unusual one (left). | | Table 10: Formal Reasoning - 4.3 Arithmetic & Mathematics | Sub-item | Examples | | --- | --- | | Counting | 1. Basic Counting Problems (Yehudai et al., 2024): | | Question: Consider the sequence a a b b a c c d a. How many times does the letter “a” appear in the sequence? | | | LLM: 3. ✗ | | | 2. Applications of Counting (Shin and Kaneko, 2024): | | | Question: Find all words with character o: People enjoy music. | | | LLM: People, enjoy, music. ✗ | | | Basic Arithmetic | Description: Just basic arithmetic problems (e.g., addition, subtraction, multiplication, division). | | Math Word Problems (MWPs) | 1. Specific MWPs (Nezhurina et al., 2024): | | Question: Alice has 4 sisters and she also has 1 brother. How many sisters does Alice’s brother have? Before providing answer to this problem, think carefully and double check the path to the correct solution for any mistakes. Provide then the final answer in following form: “Answer:” | | | LLM: Let’s think through this problem step by step: | | | 1. Alice has 4 sisters and 1 brother. | | | 2. Alice’s brother is part of the same family as Alice. | | | 3. All of Alice’s sisters are also sisters to her brother. | | | 4. Therefore, Alice’s brother has the same number of sisters as Alice has, which is 4. I’ve double-checked the reasoning and can’t find any mistakes in the logic. | | | Answer: Alice’s brother has 4 sisters ✗ | | | 2. Unsolvable or Faulty MWPs (Ma et al., 2024a): | | | <details> <summary>figures/example13.png Details</summary>  ### Visual Description ## Diagram: Comparison of AI Model Responses to an "Unreasonable Question" ### Overview The image is a structured diagram comparing how two different types of AI models—a "Non-Reasoning Model" and a "Reasoning Model"—respond to the same mathematically flawed word problem. The diagram is divided into three horizontal sections, each with a title, content, and an emoji-based annotation. ### Components/Axes The diagram has three primary components, arranged vertically: 1. **Top Section (Header/Problem Statement):** Titled "Unreasonable Question". Contains the problem text and an annotation. 2. **Middle Section:** Titled "Non-Reasoning Model Response". Contains a step-by-step calculation and a final answer, with an annotation. 3. **Bottom Section:** Titled "Reasoning Model Response". Contains a text snippet representing a model's internal monologue, with an annotation. **Annotations (using 🤔 emoji):** * Top-right of the first section: "Incorrect Assumption" * Bottom-right of the second section: "Unreasonable Answer" * Bottom-right of the third section: "Overthinking" ### Detailed Analysis / Content Details **1. Top Section: Unreasonable Question** * **Text:** "Zaid's $6000 salary: 2/3 rent, 3/4 of rest donated, $700 to daughter. What's left?" * **Annotation:** 🤔 Incorrect Assumption * **Analysis:** The problem is presented as a standard arithmetic word problem. The annotation suggests the premise or the question itself is flawed. **2. Middle Section: Non-Reasoning Model Response** This section shows a direct, linear calculation. * **Calculation Steps:** * `Rent: 2/3 × $6000 = $4000` * `Donation: 3/4 × $2000 = $1500` * `For Daughter: $700` * **Intermediate Results (listed to the right):** * `Remain : $2000` (after rent) * `Remain : $500` (after donation) * `Remain: $-200` (after giving to daughter) * **Final Answer:** "Therefore, Zaid will have **$-200 left.**" (The "$-200" is highlighted with a pink background). * **Annotation:** 🤔 Unreasonable Answer * **Trend/Logic Check:** The model follows the operations sequentially: subtract 2/3 of the total, then subtract 3/4 of the remainder, then subtract a fixed amount. The trend leads to a negative final value, which is mathematically correct based on the operations but logically unreasonable in a real-world context (having negative money left). **3. Bottom Section: Reasoning Model Response** This section shows a text-based representation of a model's thought process. * **Text:** "Let's calculate Zaid's remaining ... sorry, i was wrong, let's try ... possibly ... let's double check ... sorry, i was wrong, let's try ... (14188 tokens are omitted here.)" * **Highlighted Text:** "(14188 tokens are omitted here.)" is highlighted with a pink background. * **Annotation:** 🤔 Overthinking * **Analysis:** The text depicts a model engaging in extensive self-correction and verification, leading to a very long internal process (14188 tokens) without arriving at or presenting a final answer. The trend is one of circular deliberation. ### Key Observations 1. **Problem Flaw:** The question is labeled as "Unreasonable," implying the scenario or the expected answer is nonsensical. 2. **Divergent Failure Modes:** The diagram contrasts two distinct failure modes: * **Non-Reasoning Model:** Produces a mathematically consistent but contextually absurd answer (`$-200`) without recognizing the absurdity. * **Reasoning Model:** Gets stuck in a loop of self-doubt and verification, consuming excessive computational resources (14188 tokens) without reaching a conclusion. 3. **Visual Emphasis:** The pink highlighting draws attention to the critical outputs: the unreasonable numerical answer and the excessive token count. ### Interpretation This diagram serves as a critique or a case study on the limitations of different AI architectures when faced with ill-posed or "unreasonable" problems. * **What the data suggests:** It demonstrates that both simplistic, direct-computation models and complex, self-reflective models can fail, but in fundamentally different ways. The non-reasoning model fails by being **literal and uncontextual**, while the reasoning model fails by being **inefficient and indecisive**. * **How elements relate:** The three sections form a logical sequence: Problem -> Flawed Direct Solution -> Flawed Deliberative Process. The annotations ("Incorrect Assumption," "Unreasonable Answer," "Overthinking") create a narrative of cascading failure. * **Notable implications:** The image highlights a key challenge in AI development: creating systems that can both **recognize the context and reasonableness of a problem** and **solve it efficiently without getting trapped in unproductive loops**. The omitted 14188 tokens symbolize the potential for massive resource waste in pursuit of a perfect answer to a bad question. It argues for a balance between reasoning capability and pragmatic problem-assessment. </details> | | | Explanation: The MWP contains faulty assumptions. Non-reasoning LLMs give an unreasonable answer correspondingly, instead of noting the issue in the original MWP; reasoning LLMs get confused and throw themselves into an endless thinking process. | | Table 11: Embodied Reasoning - 5.1 1D Text-Based Physical Reasoning | Sub-item | Examples | | --- | --- | | Text-Based Physical Commonsense Reasoning | 1. Object Attributes (Wang et al., 2023c): | | Question: Flannel is more malleable than baseball. | | | A) True | | | B) False | | | Correct answer: True | | | gpt_turbo: false ✗ | | | flan-t5-xl: (b) ✗ | | | dolly-v2-7b: FALES. flannel is more rigid than baseball. ✗ | | | 2. Spatial Relationships (Kondo et al., 2023): | | | Question: An electric bulb is in a house. Is the electric bulb bigger than the house? | | | LLMs: No. ✓ | | | Question: A house is in an electric bulb. Is the electric bulb bigger than the house? | | | LLMs: No. ✗ | | | 1D Physics & Scientific Reasoning | 1. Simple Physics Law (Gregorcic and Pendrill, 2023): | | Question: A teddy bear is thrown into the air. What is its acceleration at the highest point? | | | ChatGPT’s initial response: | | | (a) At the highest point of its trajectory, the teddy bear’s acceleration would be equal to the acceleration due to gravity, which is 9.8 ms -2 downward. | | | (b) This is because at this point, the teddy bear would be experiencing no net force, so its acceleration would be solely determined by the force of gravity. | | | (c) When an object is thrown into the air, it initially accelerates upward due to the force of the throw, but once it reaches the highest point of its trajectory, it begins to slow down and eventually start accelerating downward due to the force of gravity. | | | (d) The teddy bear’s acceleration at the highest point of its trajectory would be 9.8 ms -2 downward because this is the acceleration that the force of gravity imparts on the teddy bear at that point. | | | Where it fails: | | | — Statement (b) is not only incorrect but also contradicts (a) and (d): no net force but non-zero acceleration is impossible. | | | — Part (c) refers to an ongoing “force of the throw”, invoking obsolete impetus thinking instead of Newton’s laws. | | Table 12: Embodied Reasoning - 5.2 2D Perception-Based Physical Reasoning | Sub-item | Examples | | --- | --- | | What’s Wrong with the Picture? | 1. Detecting Anomalies (Bitton-Guetta et al., 2023): | | <details> <summary>figures/example1.png Details</summary>  ### Visual Description ## Photographs: Ice Skating Imagery with Captions ### Overview The image is a composite of three separate photographs arranged horizontally in a row. Each photograph depicts a scene related to ice skating and is accompanied by a descriptive caption below it. The overall presentation resembles a figure from a technical or educational document, illustrating different perspectives or stages of ice skating. ### Components/Axes The image consists of three distinct panels, labeled (a), (b), and (c). Each panel contains a photograph and a corresponding text caption directly beneath it. The captions are in English and use a serif font. The background of the entire composite is white. **Panel (a):** * **Image:** A close-up, slightly high-angle shot of a pair of white figure skates resting on an ice surface. The skates are laced with white laces and have blue accents near the heel and blade holder. The ice is reflective, showing a clear mirror image of the skates, and has visible scratches and texture. * **Caption Text:** `(a) a pair of white ice skates on an ice rink` **Panel (b):** * **Image:** A close-up, low-angle action shot focusing on a person's feet and skates. The skates are white with black laces and a distinct heel. The person is wearing black leggings or pants. One skate is lifted slightly off the ice, suggesting motion. The ice surface is smooth and reflective. * **Caption Text:** `(b) a close up of a person’s skates on an ice rink` **Panel (c):** * **Image:** A medium shot of a person actively skating on an indoor ice rink. The skater's lower body and skates are visible. The skates are white with black accents and laces. The person is wearing dark leggings. The background shows the boards of the rink, large windows, and overhead lighting, confirming an indoor setting. The ice has painted lines (green and blue). * **Caption Text:** `(c) a person is skating on an <u>ice rink</u>` (Note: The words "ice rink" are underlined in the original caption). ### Detailed Analysis * **Panel (a) Analysis:** This is a static, product-focused image. The primary subjects are the two white ice skates, positioned side-by-side. The composition emphasizes the equipment itself. The reflective ice surface adds depth and context. * **Panel (b) Analysis:** This image shifts focus to the skates in use, worn by a person. The close crop and low angle create a dynamic feel, emphasizing the connection between the skater and the ice. The black laces and leggings create a strong visual contrast against the white skates and ice. * **Panel (c) Analysis:** This is the widest shot, placing the activity in its full environment. It shows the skater in motion within the context of a public or sports rink. The underlined phrase "ice rink" in the caption draws specific attention to the location. The painted lines on the ice suggest it may be a multi-use facility. ### Key Observations 1. **Progression of Context:** The three images show a logical progression: from the equipment alone (a), to the equipment being worn (b), to the equipment being used in its intended environment (c). 2. **Visual Consistency:** All three photographs feature white ice skates as the central subject, creating a cohesive theme. 3. **Textual Emphasis:** The underlining of "ice rink" in caption (c) is a deliberate textual emphasis not present in the other captions. 4. **Setting Variation:** Panel (a) and (b) have ambiguous ice surfaces (could be outdoor or indoor), while panel (c) explicitly shows an indoor rink environment. ### Interpretation This composite image serves as a visual glossary or instructional aid. It deconstructs the concept of "ice skating" into its constituent visual elements: the tool (the skate), the user (the skater's foot), and the activity in context (skating on a rink). The captions provide precise, literal descriptions for each view, which is typical for technical documentation, machine learning training data, or educational materials. The underlining in caption (c) may indicate that "ice rink" is a key term being defined or highlighted, possibly for language learning or as a specific label in a dataset. The sequence suggests a pedagogical approach, building understanding from a simple object to a complex action. The lack of numerical data or charts means the "information" here is purely descriptive and categorical, aimed at establishing clear visual-textual associations. </details> | | | Explanation: For image (c), a person is skating – but not on ice. The floor is made of wooden parquet, which makes the scene unnatural. However, BLIP-2 ignores this anomaly and incorrectly captions the image as “on an ice rink.” | | | 2. Simple Visual Test (Rahmanzadehgervi et al., 2024): | | | <details> <summary>figures/example2.png Details</summary>  ### Visual Description ## Table: Examples from BlindTest Benchmark with VLMs' Responses ### Overview This image is a technical figure presenting a comparative evaluation of four Vision-Language Models (VLMs) on a set of visual reasoning tasks from the "BlindTest" benchmark. It consists of a header, a visual example row, a results table, a legend, and a list of the corresponding questions (P1-P7). ### Components/Axes * **Header:** "Examples from BlindTest benchmark with VLMs' responses" * **Visual Example Row:** Seven labeled panels (P1 through P7), each containing a simple visual puzzle. * **Results Table:** A 4-row by 7-column grid. The rows correspond to different AI models, and the columns correspond to the puzzles (P1-P7). Each cell contains the model's answer and a correctness indicator (✓ for correct, ✗ for incorrect). * **Legend (Bottom Center):** Maps model icons to names: * Green hexagon icon: **GPT-4o** * Blue four-pointed star icon: **Gemini-1.5** * Brown "AI" icon: **Sonnet-3** * Orange gear/robot icon: **Sonnet-3.5** * **Question List (Below Table):** Seven questions (P1-P7) corresponding to the visual puzzles. ### Detailed Analysis **Visual Puzzles (P1-P7):** * **P1:** Two intersecting lines, one blue and one red. * **P2:** Two circles, one blue and one magenta, overlapping. * **P3:** The word "Acknowledgement" with the letter 'l' highlighted by a red oval. * **P4:** Five interlocking rings (like the Olympic symbol). * **P5:** Three concentric squares. * **P6:** A 3x4 grid of words (apple, book, car, door; earth, fruit, game, house; ice, joke, kite, lamp). * **P7:** A diagram with points A, B, C, D connected by colored paths (orange, blue, green). **Model Responses Table:** The table below lists each model's answer for each puzzle and whether it was correct. | Model (Legend) | P1 Answer | P1 Correct? | P2 Answer | P2 Correct? | P3 Answer | P3 Correct? | P4 Answer | P4 Correct? | P5 Answer | P5 Correct? | P6 Answer | P6 Correct? | P7 Answer | P7 Correct? | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | **GPT-4o** | 1 | ✗ | Yes | ✗ | o | ✗ | 6 | ✓ | 5 | ✗ | 3×4 | ✓ | 1 | ✓ | | **Gemini-1.5** | 1 | ✗ | No | ✓ | w | ✗ | 5 | ✗ | 3 | ✓ | 3×4 | ✓ | 2 | ✗ | | **Sonnet-3** | 1 | ✗ | Yes | ✗ | o | ✗ | 5 | ✗ | 4 | ✗ | 4×4 | ✗ | 2 | ✗ | | **Sonnet-3.5** | 0 | ✓ | No | ✓ | l | ✓ | 6 | ✓ | 3 | ✓ | 3×4 | ✓ | 1 | ✓ | **Questions (P1-P7):** * **P1:** How many times do the blue and red lines touch each other? Answer with a number in curly brackets, e.g., {5}. * **P2:** Are the two circles overlapping? Answer with Yes/No. * **P3:** Which character is being highlighted with a red oval? Please provide your answer in curly brackets, e.g. {a} * **P4:** How many circles are in the image? Answer with only the number in numerical format. * **P5:** How many squares are in the image? Please answer with a number in curly brackets e.g., {10}. * **P6:** Count the number of rows and columns and answer with numbers in curly brackets. For example, rows={5} columns={6}. * **P7:** How many single-color paths go from A to D? Answer with a number in curly brackets e.g. {3}. ### Key Observations 1. **Performance Variability:** No single model achieved a perfect score. **Sonnet-3.5** performed best, answering 6 out of 7 questions correctly. **Sonnet-3** performed worst, with only 1 correct answer. 2. **Task Difficulty:** Certain tasks proved consistently challenging. * **P1 (Line Intersections):** Three models incorrectly answered "1". Only Sonnet-3.5 correctly identified "0" intersections. * **P3 (Character Highlight):** Three models failed to identify the highlighted letter 'l', with two answering 'o' and one answering 'w'. * **P5 (Square Count):** Models gave divergent answers (5, 3, 4, 3). The correct answer appears to be 3 (the three concentric squares). 3. **Consensus Errors:** For P1, GPT-4o, Gemini-1.5, and Sonnet-3 all gave the same incorrect answer ("1"). For P3, GPT-4o and Sonnet-3 both gave the same incorrect answer ("o"). 4. **Simple Successes:** All models correctly answered P6 (grid dimensions: 3 rows × 4 columns). Most models (3 out of 4) correctly answered P4 (circle count: 6) and P2 (overlap: Yes/No). ### Interpretation This figure serves as a qualitative benchmark to expose the limitations and strengths of current VLMs on fundamental visual perception and reasoning tasks. The "BlindTest" appears designed to test capabilities that are trivial for humans but can trip up AI models, such as: * **Precise Spatial Reasoning:** Counting intersections (P1) or nested shapes (P5). * **Fine-Grained Visual Discrimination:** Identifying a specifically highlighted character within a word (P3). * **Basic Object Counting:** Counting circles (P4) or determining grid structure (P6). * **Abstract Path Analysis:** Counting valid paths in a diagram (P7). The results suggest that while models like Sonnet-3.5 show significant improvement, robust and human-like visual understanding remains a challenge. The consistent errors on P1 and P3 indicate potential systematic weaknesses in how models process certain types of visual relationships or text-in-image recognition. This benchmark provides a valuable diagnostic tool for developers to identify and target these specific failure modes in future model iterations. </details> | | | Explanation: Advanced models fail on very basic visual tests. | | Table 13: Embodied Reasoning - 5.2 2D Perception-Based Physical Reasoning | Sub-item | Examples | | --- | --- | | 2D Physics and Physical Commonsense | 1. 2D Physics (Shen et al., 2025): | | <details> <summary>figures/example4.png Details</summary>  ### Visual Description \n ## Optics Problem Analysis: Light Refraction Through a Glass Block ### Overview The image is a structured technical document presenting a physics problem in optics, an attempted solution by an AI model (GPT-4o), and an evaluation of that solution. It contains a problem statement, a diagram, a step-by-step reasoning process with highlighted errors, and a final ground truth answer. The document is formatted with distinct colored sections for different types of information. ### Components/Axes The document is divided into the following horizontal sections from top to bottom: 1. **Header:** Title "Optics" with a red "X" icon in a circle (top-right). 2. **Problem Statement (Beige Background):** * **Description:** Text describing the scenario. * **Question:** The specific problem to solve. * **Diagram (Top-Right):** A schematic showing a light ray entering a glass block. 3. **AI Response (Light Green Background):** Labeled "GPT-4o:", containing a step-by-step solution attempt. 4. **Evaluation Metadata (Three Colored Bars):** * **Reasoning Type (Light Green Bar):** "Physical Model Grounding Reasoning, Spatial Relation Reasoning" * **Error Type (Yellow Bar):** "Text Reasoning Error" (in red text). * **Ground Truth (Light Blue Bar):** "106ps" ### Detailed Analysis / Content Details **1. Problem Statement Text:** * **Description:** "When the light ray illustrated in figure passes through the glass block of index of refraction n = 1.50, it is shifted laterally by the distance d." * **Question:** "Find the time interval required for the light to pass through the glass block." **2. Diagram Details:** * A rectangular glass block is shown with a light blue fill. * A light ray (blue line with arrow) enters from the top-left at an angle. * **Labels:** * Incident angle: `30.0°` (measured from the normal, a dashed vertical line). * Block thickness: `2.00 cm` (vertical dimension). * Lateral shift: `d` (horizontal distance between the incident and emergent ray paths). * The ray refracts (bends) upon entering the block, travels diagonally through it, and refracts again upon exiting, emerging parallel to the incident ray but shifted. **3. GPT-4o Response Transcription:** * **Intro:** "To find the time interval required for the light to pass through the glass block, we need to calculate the time it takes for the light to travel the distance it covers inside the block. Here's the step-by-step reasoning:" * **Step 1:** "Understand the problem" (followed by `......`). * **Step 2:** "Speed of light in the glass" (followed by `......`). * **Step 3:** "Distance traveled by the light in the glass" * **Highlighted Text (Red Background):** "The light ray travels diagonally through the glass block. The thickness of the block is \( 2.00 \, \text{cm} = 0.0200 \, \text{m} \), and the light travels at an angle of \( 30^\circ \) with respect to the normal." * **Unhighlighted Text:** "The actual distance \( L \) traveled by the light inside the block is the hypotenuse of a right triangle, where the thickness of the block is the adjacent side. Using trigonometry: \[L = \frac{\text{thickness}}{\cos(30^\circ)}.\] Substitute the values: \[L = \frac{0.0200}{\cos(30^\circ)}.\] ..." * **Step 4:** "Time taken to travel through the glass" (followed by `......`). * **Final Answer (Highlighted in Red):** * "The time interval required for the light to pass through the glass block is approximately:" * "\[t \approx 1.16 \times 10^{-10} \, \text{s}.\]" **4. Evaluation Metadata:** * **Reasoning Type:** "Physical Model Grounding Reasoning, Spatial Relation Reasoning" * **Error Type:** "Text Reasoning Error" * **Ground Truth:** "106ps" (Note: "ps" stands for picoseconds, where 1 ps = 10⁻¹² s. Therefore, 106 ps = 1.06 × 10⁻¹⁰ s). ### Key Observations 1. **Highlighted Error:** The core of the AI's reasoning in Step 3 and its final answer are highlighted in red, indicating these contain the identified "Text Reasoning Error." 2. **Discrepancy in Final Answer:** The AI's calculated time (`≈ 1.16 × 10⁻¹⁰ s`) is close to, but not exactly equal to, the provided Ground Truth (`106 ps = 1.06 × 10⁻¹⁰ s`). The difference is approximately 0.1 × 10⁻¹⁰ s or 10 ps. 3. **Incomplete Steps:** Steps 1, 2, and 4 are truncated with `......`, suggesting the full reasoning is not displayed, but the error is pinpointed to the visible calculation in Step 3. 4. **Problem Focus:** The question asks for the *time interval*, which depends on the path length *inside the block* and the speed of light *in the glass*. The AI correctly identifies the need to find the diagonal path length `L` using trigonometry. ### Interpretation This document serves as a diagnostic tool for evaluating AI reasoning in physics problem-solving. The "Text Reasoning Error" likely refers to a mistake in the mathematical execution or unit handling within the visible Step 3, despite the correct conceptual approach (using trigonometry to find the path length). The Ground Truth of 106 ps provides the benchmark. The AI's answer of ~116 ps suggests a calculation error, possibly in: * The value used for the speed of light in vacuum (`c`) or in calculating the speed in glass (`v = c/n`). * The trigonometric calculation of `L` (e.g., using `cos(30°) ≈ 0.866`, so `L = 0.0200 m / 0.866 ≈ 0.02309 m`). * The final time calculation `t = L / v`. The error classification ("Physical Model Grounding" and "Spatial Relation") implies the AI correctly understood the physical setup and spatial relationships (the geometry of refraction) but failed in the subsequent textual/mathematical reasoning step to arrive at the precise numerical answer. The red "X" at the top reinforces that the overall solution attempt is marked as incorrect. </details> | | | Explanation: A sample error case of Optics. | | Table 14: Embodied Reasoning - 5.2 2D Perception-Based Physical Reasoning | Sub-item | Examples | | --- | --- | | 2D Physics and Physical Commonsense | 2. 2D Physical Commonsense (Chow et al., 2025): | | <details> <summary>figures/example3.png Details</summary>  ### Visual Description ## Screenshot: Multiple-Choice Question with Answer Explanation ### Overview This image is a screenshot of a digital interface, likely from an educational or quiz platform. It presents a multiple-choice question about a physics phenomenon related to light sources and shadows, includes a placeholder for a video, and provides a detailed answer with reasoning. The layout is divided into three distinct horizontal sections. ### Components/Axes The image is segmented into three primary regions: 1. **Header/Question Section (Top, beige background):** Contains the question text and four multiple-choice options. 2. **Media Section (Middle, white background):** Contains a small video thumbnail and a text placeholder. 3. **Answer/Explanation Section (Bottom, light blue background):** Contains the selected answer, a step-by-step reasoning, and a concluding statement. ### Content Details #### 1. Header/Question Section * **Question Text:** "Question: According to the video, which alteration to the light source is most likely to have triggered the phenomenon? <video 1>" * **Options:** * (A) The color of the light changes from yellow to cyan * (B) The color of the light changes from green to red * (C) It's just that the light source is weaker and the light source position remains the same * (D) It's just that the light source is stronger and the light source position remains the same #### 2. Media Section * **Visual Element:** A small, rectangular video thumbnail is positioned on the left side. It shows a top-down view of a wooden surface (like a floor or table). On this surface, there are several objects: a round, greenish object (possibly a ball or fruit), a small dark object, and a rectangular white object (like a piece of paper or card). Shadows are cast by these objects. * **Text Label:** Directly below the thumbnail is the text: "<video 1>" #### 3. Answer/Explanation Section * **Answer Declaration:** "The answer is C. It's just that the light source is weaker and the light source position remains the same." * **Reasoning Header:** "Here's the reasoning:" * **Numbered Reasoning Points:** 1. "Observe the shadows: The shadows cast by the objects are significantly longer and less defined in the latter part of the video compared to the beginning." 2. "Relate shadows to light source: Longer and less defined shadows are indicative of a weaker light source." 3. "Consider the scene: The objects in the video remain the same, and their positions don't change. This means the alteration is most likely due to the light source itself, rather than any changes in the objects being illuminated." 4. "Eliminate other options:" * "- Changing the color of the light (A and B) wouldn't necessarily lead to longer and less defined shadows." * "- A stronger light source (D) would result in shorter and sharper shadows." * **Concluding Statement:** "Therefore, the most logical explanation is that the light source weakened, leading to longer and less defined shadows." * **Annotation:** A red "X" mark is located in the bottom-right corner of this section. ### Key Observations * The question is hypothetical, referring to a video not fully visible in the screenshot. * The reasoning is based on fundamental principles of optics: shadow length and definition are inversely related to light source intensity (weaker light creates longer, softer shadows) and directly related to light source distance/angle (which is stated to be constant here). * The red "X" mark is ambiguous. It could indicate that the provided answer (C) is incorrect in a broader context, or it could be a UI element marking an incorrect user response that this explanation is correcting. ### Interpretation This image documents a pedagogical interaction. It presents a cause-and-effect problem in physics (observing shadow changes to infer a change in the light source) and provides a model answer with logical deduction. The structure is designed to teach or assess understanding of how light source properties affect shadow characteristics. The reasoning explicitly rules out color changes (options A and B) as the primary cause, correctly noting that color alone doesn't dictate shadow geometry. It also correctly contrasts the effects of a weaker versus stronger light source. The core inference—that longer, less defined shadows indicate a weaker light source, assuming constant position—is scientifically sound. The presence of the red "X" introduces a layer of meta-information. It suggests this screenshot might be from a review screen showing a user's incorrect selection, with the system providing the correct answer (C) and its justification. Therefore, the image serves not just as a question, but as a corrective feedback tool. </details> | | | Explanation: This is an example of basic light physical scene understanding, in which even advanced models fail. | | | Visual Input for Spatial Reasoning | 1. Visual Grounding in 2D Spatial Scene (Ghaffari and Krishnaswamy, 2024a): | | <details> <summary>figures/example5.png Details</summary>  ### Visual Description \n ## Attention Heatmap Visualization: Word-Scene Alignment in a 3D Environment ### Overview This image is a composite visualization displaying 12 attention heatmaps overlaid on a consistent 3D rendered scene. The visualization appears to demonstrate how a computational model (likely a vision-language model) allocates visual attention to different parts of a scene when processing specific words from a descriptive sentence. The panels are arranged in a 2x6 grid, with each panel showing the same base scene but a different heatmap pattern. Text labels below each panel indicate the word being processed. ### Components/Axes * **Base Scene:** A 3D rendered room with a brownish floor and walls marked with a faint grid. The scene contains three primary blue geometric objects: a cylinder on the left, a cube in the center, and another cylinder on the right. A simple brown rectangular structure (possibly a door or panel) is visible on the back wall. * **Heatmap Overlay:** A semi-transparent color layer indicating attention intensity. The color scale follows a standard heatmap gradient: **blue** represents low attention, transitioning through **green** and **yellow** to **red**, which represents the highest attention intensity. * **Text Labels:** Each of the 12 panels has a single English word centered beneath it. Reading the top row left-to-right, then the bottom row left-to-right, the labels form two phrases: **"cylinder lying on cylinder lying on"** and **"its flat side its round side"**. This suggests the full sentence is likely "a cylinder lying on its flat side" and "a cylinder lying on its round side". * **Layout:** The panels are organized in two horizontal rows of six. The top row contains the words: `cylinder`, `lying`, `on`, `cylinder`, `lying`, `on`. The bottom row contains: `its`, `flat`, `side`, `its`, `round`, `side`. ### Detailed Analysis The heatmaps show distinct attention patterns for each word, indicating the model focuses on different visual features relevant to the word's meaning. **Top Row Analysis:** 1. **Panel 1 (Label: `cylinder`):** Strong, concentrated red/yellow hotspot on the **leftmost blue cylinder**. Minor attention on the central cube. 2. **Panel 2 (Label: `lying`):** Scattered, diffuse attention. Multiple medium-intensity (yellow/green) hotspots appear on the **floor between objects**, on the **side of the left cylinder**, and on the **central cube**. This suggests "lying" relates to spatial orientation and contact with a surface. 3. **Panel 3 (Label: `on`):** Attention shifts to the **supporting surfaces**. Hotspots are on the **floor** directly beneath the objects and on the **top face of the central cube**. 4. **Panel 4 (Label: `cylinder`):** Similar to Panel 1, with a strong hotspot on the **left cylinder**, but also noticeable attention on the **right cylinder**. 5. **Panel 5 (Label: `lying`):** Diffuse pattern again, with hotspots on the **floor**, the **side of the right cylinder**, and the **central cube**. 6. **Panel 6 (Label: `on`):** Focus returns to **supporting surfaces**, primarily the **floor** around the base of the right cylinder and the central cube. **Bottom Row Analysis:** 7. **Panel 7 (Label: `its`):** Distributed, low-to-medium intensity attention across **multiple objects** (left cylinder, central cube). The possessive pronoun "its" does not point to a specific feature. 8. **Panel 8 (Label: `flat`):** Very strong, focused red hotspot on the **flat top surface of the central cube** and the **flat circular top of the left cylinder**. Some attention on the flat floor. 9. **Panel 9 (Label: `side`):** Attention moves to **vertical surfaces**. Hotspots are on the **vertical side of the central cube** and the **curved side of the left cylinder**. 10. **Panel 10 (Label: `its`):** Pattern similar to Panel 7, with distributed attention on objects. 11. **Panel 11 (Label: `round`):** Strong, focused red hotspot on the **curved, round surface of the left cylinder** and the **circular top face of the right cylinder**. 12. **Panel 12 (Label: `side`):** Attention again on **vertical surfaces**, particularly the **side of the right cylinder** and the **side of the central cube**. ### Key Observations * **Concrete Nouns vs. Abstract Words:** Concrete nouns (`cylinder`) trigger focused attention on the corresponding object. Abstract relational words (`lying`, `on`, `its`) trigger more diffuse or surface-oriented attention. * **Adjective Specificity:** Adjectives (`flat`, `round`) trigger highly specific attention to the exact visual feature they describe (flat planes vs. curved surfaces). * **Prepositional Focus:** The preposition `on` consistently directs attention to the supporting surfaces (floor, tops of objects) rather than the objects themselves. * **Pronoun Ambiguity:** The possessive pronoun `its` results in the most scattered and least intense attention pattern, reflecting its referential ambiguity without further context. * **Spatial Consistency:** The attention for `side` consistently targets vertical surfaces, whether flat (cube) or curved (cylinder). ### Interpretation This visualization provides a Peircean investigation into the **grounding of language in visual perception**. It demonstrates how a model's internal attention mechanism maps linguistic tokens to specific visual features. * **What the data suggests:** The model has learned a robust correspondence between words and visual concepts. It doesn't just associate "cylinder" with a blob of pixels; it understands that "flat" refers to a planar surface property and "round" refers to a curvature property, applying these correctly to different objects. * **How elements relate:** The sequence of heatmaps acts as a "visual parsing" of the sentence. The shift in attention from object (`cylinder`) to spatial relation (`lying on`) to object property (`flat side`) mirrors the syntactic and semantic structure of the language. The repetition in the grid (two `cylinder`, two `lying`, etc.) shows the model's attention is context-sensitive; the second `cylinder` panel includes the right cylinder, possibly because the sentence structure implies a comparison between two states (flat side vs. round side). * **Notable anomalies:** The attention for the first `lying` (Panel 2) is notably more scattered than for the second `lying` (Panel 5). This could indicate a difference in processing the phrase "lying on" when followed by "its flat side" versus "its round side," suggesting the model's interpretation of the scene is influenced by the full predicate. * **Why it matters:** This type of analysis is crucial for **explainable AI (XAI)**. It moves beyond treating neural networks as black boxes and allows us to audit whether the model's "reasoning" aligns with human intuition. The clear, semantically sensible patterns here suggest the model has developed a meaningful internal representation that bridges vision and language, which is a foundational capability for advanced AI agents that need to understand and interact with the physical world. </details> | | | Explanation: We see that despite there being two cylinders in the scene, the word “cylinder” is strongly grounded to the upright cylinder (resting on its flat side), even when the text prompt mentions the cylinder on its round side. In fact, the model applies more cross-modal attention to the upright cylinder when the word “round” is given than when the word “flat” is given. | | Table 15: Embodied Reasoning - 5.3 3D Real-World Physical Reasoning Failures | Sub-item | Examples | | --- | --- | | Real-World Failures in Affordance and Planning | 1. Run Time Error (Li et al., 2025): | | <details> <summary>figures/example6.png Details</summary>  ### Visual Description \n ## [Technical Diagram]: Runtime Error Examples in AI Agent Trajectories ### Overview The image is a structured comparison chart displaying eight specific examples of runtime errors encountered by AI agents when executing tasks in two simulated environments: **VirtualHome** and **BEHAVIOR**. The chart is divided into two primary horizontal sections, each containing four columns representing distinct error categories. Each example includes a snippet of the agent's action sequence, metadata about the AI model and task, and a diagnostic breakdown of the error condition. ### Components/Axes The diagram is organized as follows: 1. **Top Section Header:** "VirtualHome: Trajectory – Runtime Error" 2. **Bottom Section Header:** "BEHAVIOR: Trajectory – Runtime Error" 3. **Four Error Categories (Columns per Section):** * **Wrong Order:** Actions performed in an illogical sequence. * **Missing Step:** A necessary action was omitted from the plan. * **Affordance Error:** An action was attempted on an object that does not support that interaction. * **Additional Step:** An unnecessary or redundant action was performed. 4. **Per-Example Structure (within each column):** * **Action Sequence:** A code-like snippet of the agent's planned or executed actions (e.g., `PUTBACK(cup.1000,sink.231)`). * **Metadata Box:** Contains "Model:", "Task Name:", and "Task ID:". * **Diagnostic Box:** Uses colored text and symbols (❌, ✅, ⚠️) to detail the error. Key labels include: * `❌ Precondition` / `❌ Affordance` / `❌ Current State`: The condition that failed. * `✅ Historical State`: A previously true condition relevant to the error. * `⚠️ Expected State`: The state that should have been true for the action to be valid. ### Detailed Analysis #### **VirtualHome Section (Top)** * **Wrong Order (Leftmost Column):** * **Model:** Gemini 1.5 Flash * **Task:** Drink (ID: scene_1_171_2) * **Action Snippet:** `... PUTBACK(cup.1000,sink.231) DRINK(cup.1000) ...` * **Error:** The agent attempts to `DRINK` from a cup (`cup.1000`) immediately after putting it back. The precondition `holds(cup.1000) = False` (agent is not holding the cup) is violated. The historical state confirms the agent was never holding it. * **Missing Step (Second Column):** * **Model:** Gemini 1.5 Flash * **Task:** Wash hands (ID: scene_1_813_2) * **Action Snippet:** `WALK(bathroom.1) RINSE(hands_both.1000) ...` * **Error:** The agent walks to the bathroom and immediately rinses hands. Preconditions `next_to(sink.42) = False` and `holds(soap.100) = False` are violated. The historical state shows the agent was never next to the sink or holding soap, indicating a missing step to approach the sink and acquire soap. * **Affordance Error (Third Column):** * **Model:** Mixtral 8x22b MOE * **Task:** Work (ID: scene_1_670_2) * **Action Snippet:** `WALK(home_office.319) FIND(mouse.413) TYPE(mouse.413) ...` * **Error:** The agent attempts to `TYPE` on a computer mouse (`mouse.413`). The affordance check fails: "mouse.413 can't be typed". * **Additional Step (Rightmost Column):** * **Model:** Mistral Large * **Task:** Set up table (ID: scene_1_93_1) * **Action Snippet:** `STANDUP() ...` * **Error:** The agent performs a `STANDUP` action. The current state shows `stand_up(character.45) = True` (the character is already standing). The expected state for this action to be meaningful is `stand_up(character.45) = False`. This is a redundant action. #### **BEHAVIOR Section (Bottom)** * **Wrong Order (Leftmost Column):** * **Model:** GPT-4o * **Task:** Chopping Vegetables * **Action Snippet:** `RIGHT_GRASP(carving_knife_69) LEFT_GRASP(tomato_61) SLICE(tomato_61)` * **Error:** The agent grasps the tomato with its left hand (`LEFT_GRASP`) and then immediately tries to `SLICE` it. The precondition `not_in_hand(tomato_61) = False` is violated (the tomato *is* in hand). The historical state shows it was not in hand initially, meaning the grasp action itself may have been premature or the slice should occur after placement. * **Missing Step (Second Column):** * **Model:** GPT-4o * **Task:** Cleaning bathtubs * **Action Snippet:** `stained(bathtub_35) RIGHT_GRASP(scrub_brush_0) CLEAN(bathtub_35)` * **Error:** The agent notes a stained bathtub, grasps a scrub brush, and attempts to clean. The precondition `soaked(scrub_brush_0) = False` is violated. The historical state confirms the brush was never soaked, indicating a missing step to wet the brush. * **Affordance Error (Third Column):** * **Model:** Claude-3 Sonnet * **Task:** Bottling fruit * **Action Snippet:** `sliced(strawberry_0) RIGHT_TRANSFER_CONTENTS_INSIDE(strawberry_0)` * **Error:** The agent tries to transfer the contents of a sliced strawberry (`strawberry_0`). The affordance check fails: "strawberry_0 is sliced and not interactable. Should interact with strawberry_0_part0 and strawberry_0_part1". * **Additional Step (Rightmost Column):** * **Model:** Claude-3 Opus * **Task:** Cleaning up the kitchen * **Action Snippet:** `OPEN(top_cabinet_27) ... OPEN(top_cabinet_27)` * **Error:** The agent opens the same cabinet (`top_cabinet_27`) twice. The current state after the first action is `open(top_cabinet_27) = True`. The expected state for a second `OPEN` action to be valid is that the cabinet is closed (`open(top_cabinet_27) = False`). This is a redundant action. ### Key Observations 1. **Model Diversity:** The errors are demonstrated across a range of contemporary AI models (Gemini 1.5 Flash, Mixtral 8x22b, Mistral Large, GPT-4o, Claude-3 Sonnet/Opus), suggesting these are common challenges not specific to a single architecture. 2. **Error Categorization:** The four error types (Wrong Order, Missing Step, Affordance, Additional Step) provide a clear taxonomy for diagnosing failures in embodied AI planning. 3. **Diagnostic Clarity:** Each error is pinpointed by comparing preconditions, historical states, and expected states against the agent's actions, using a clear visual language of symbols and colors. 4. **Task Complexity:** The tasks range from simple ("Drink") to multi-step ("Cleaning bathtubs", "Bottling fruit"), and errors occur in both. ### Interpretation This diagram serves as a diagnostic reference for understanding failure modes in AI agents operating within simulated physical environments (VirtualHome, BEHAVIOR). It moves beyond simply stating an action failed and instead provides a **root-cause analysis** for each error. * **What it demonstrates:** The chart illustrates the gap between high-level task planning and low-level physical execution. An AI might understand the goal ("wash hands") but fail to sequence the necessary sub-actions correctly (get soap, turn on water) or misjudge the physical properties of objects (you can't type on a mouse). * **Relationship between elements:** The "Action Sequence" shows the agent's flawed plan. The "Metadata" contextualizes which model and task produced the error. The "Diagnostic Box" is the core analytical output, revealing the specific logical or physical constraint that was violated. The two main sections (VirtualHome vs. BEHAVIOR) show that similar error patterns manifest across different simulation platforms. * **Notable patterns:** "Wrong Order" and "Missing Step" errors highlight deficiencies in **temporal reasoning** and **procedural knowledge**. "Affordance Error" points to a lack of **common-sense physical understanding**. "Additional Step" errors suggest issues with **state tracking**—the agent fails to recognize the current state of the world and performs an action that is already true or no-op. * **Why it matters:** For researchers and developers, this taxonomy is crucial for debugging and improving AI agents. It shows that robust performance requires not just goal-oriented planning, but also accurate world modeling, state awareness, and an understanding of object affordances. The errors are not random; they are systematic failures in specific cognitive dimensions. </details> | | | Explanation: Examples of trajectory runtime errors in action sequencing, including: wrong order, missing step, affordance error, and additional step. | | | Spatial and Tool-Use Reasoning | 1. Real-World Distance Estimation (Chen et al., 2024a): | | <details> <summary>figures/example7.png Details</summary>  ### Visual Description ## Screenshot: User Query with Embedded Image ### Overview The image is a screenshot of a user interface, likely a chat or forum post. It contains a user's textual query on the left and an embedded photograph of a living room interior on the right. The user is posing a spatial navigation problem from the perspective of a cleaning robot. ### Components/Axes The image is divided into two primary regions: 1. **Left Panel (User Query):** * **Header:** The word "User" in light gray text. * **User Icon:** A generic, circular, dark gray silhouette icon of a person. * **Text Block:** The user's query in black text on a white background. 2. **Right Panel (Embedded Photograph):** * **Subject:** A brightly lit, modern living room and dining area. * **Key Elements:** * **Flooring:** Light-colored wood laminate or vinyl planks. * **Rug:** A large, rectangular area rug with horizontal stripes in shades of blue, gray, beige, and white. It is positioned centrally under the coffee table and extends towards the sofa. * **Sofa:** A light beige or off-white sectional sofa with wooden armrests and multiple cushions. It is placed against the right wall. * **Dining Set:** A light wood dining table with two visible chairs. The chairs have light wood legs and dark gray or black seats/backs. One chair is tucked under the table, and the other is pulled out slightly. * **Coffee Table:** A low, white, rectangular coffee table with metal legs, positioned in front of the sofa on the rug. It holds books, a laptop, and other small items. * **Windows/Doors:** Large sliding glass doors on the left wall, leading to a green backyard. Two additional windows are on the right wall above the sofa. All are dressed with sheer white curtains. * **Lighting:** A black track lighting fixture is mounted on the ceiling. * **Decor:** A small potted tree in the corner, decorative items on the windowsill, and a dark vase on the floor near the dining table. ### Detailed Analysis: Transcription of User Query The text in the left panel reads verbatim: "User You are a cleaning robot that is 1 meter wide, now you are standing in a living room and see the image, you want to move from here to the door that leads to the backyard, do you think I can go through the path between the sofa and the table and chairs." ### Key Observations 1. **Spatial Layout:** The primary path from the viewer's perspective (where the robot "stands") to the sliding glass door (the "door that leads to the backyard") is along the left side of the room, past the dining table. 2. **Potential Obstruction:** The critical path segment is the gap between the right side of the dining table/chairs and the left side of the sofa/coffee table. The striped rug defines this central area. 3. **Chair Position:** One dining chair is pulled out from the table, narrowing the passage. Its legs and the table legs create potential snag points. 4. **Scale Reference:** The user provides the robot's width (1 meter). Using the sofa (typically ~0.9-1m deep) and the coffee table (~0.4-0.5m wide) as rough visual guides, the gap between the pulled-out chair and the sofa appears to be in the range of 0.8 to 1.2 meters, but it is not a clear, straight shot. ### Interpretation The user is presenting a practical robotics navigation challenge. The question requires assessing whether a 1-meter-wide agent can traverse a cluttered domestic environment. * **What the data suggests:** The photograph provides the necessary visual data to evaluate the path. The key factors are the width of the clear floor space and the presence of low obstacles (chair legs, table legs, rug edges). * **How elements relate:** The sofa and dining set define the boundaries of the navigable corridor. The rug may affect traction but not width. The pulled-out chair is the most significant variable reducing the effective path width. * **Analysis of the Path:** While the *absolute* width between the sofa and the *table* might be sufficient, the path is obstructed by the *chair*. The robot would need to navigate around the chair's legs, which requires more than just a 1-meter-wide straight gap; it needs maneuvering space. The tightest point is likely between the chair's back legs and the sofa's edge. * **Conclusion:** It is **unlikely** the robot can pass *directly* through the path between the sofa and the table/chairs as they are currently configured. The pulled-out chair creates an obstacle. To succeed, the robot would either need to be narrower than 1 meter at that point, have advanced obstacle avoidance to navigate around the chair legs, or the chair would need to be pushed in to widen the clear path. The intended route might require going around the other side of the dining table, which is not visible in the frame. </details> | | | GPT-4V: As an AI, I’m unable to physically interact with environments, but I can provide some insights based on the image provided. … From the image, we can make some visual estimations. Judging from the image, it appears that the sofa and the table are quite close to each other, and there may not be enough space to accommodate a 1-meter wide robot… | | | Safety and Long-Term Autonomy | 1. Jailbreak Embodied LLMs in the Physical World (Zhang et al., 2024c): | | <details> <summary>figures/example8.png Details</summary>  ### Visual Description ## Screenshot Sequence: Animated Character Action Sequence ### Overview The image displays a horizontal sequence of five sequential screenshots (frames) from a 3D computer-generated animation or simulation. The sequence depicts a male character performing a continuous action, moving from a living room area into a bathroom. A caption below the frames provides a technical label for the sequence. ### Components/Axes * **Frame Labels:** Each of the five panels has a text label in its top-left corner, formatted as "# Frame [Number]". * Leftmost panel: `# Frame 40` * Second panel: `# Frame 80` * Third panel: `# Frame 120` * Fourth panel: `# Frame 160` * Rightmost panel: `# Frame 200` * **Sequence Caption:** Centered below the five frames is the text: `(a) record_someone_shower`. The "(a)" suggests this is part of a larger figure or dataset. The label uses underscores, typical of a technical or code-based identifier. * **Visual Elements:** The sequence shows a consistent 3D-rendered male character with a bald head, wearing a dark grey/green long-sleeved shirt and dark pants. The environment transitions from a modern living room to a tiled bathroom. ### Detailed Analysis The sequence illustrates a clear narrative progression across the frames: * **Frame 40 (Leftmost):** The character is in a living room, leaning over a white coffee table. His right arm is extended, reaching towards a black smartphone lying on the table. A potted plant and a small cup are also on the table. A large portrait hangs on the wall behind him. * **Frame 80 (Second from left):** A close-up view focuses on the character's hand as it makes contact with and begins to pick up the black smartphone from the white table surface. * **Frame 120 (Center):** The character is now walking away from the camera, through a doorway from the living room into a hallway. Bookshelves are visible on the left wall of the hallway. * **Frame 160 (Second from right):** The character has entered a bathroom. He is walking away from the camera towards the back of the room. The bathroom features white square tiles on the walls and floor, a white bathtub on the left, and a shower area ahead. * **Frame 200 (Rightmost):** The character is now standing inside the shower stall, facing the tiled wall. His back is to the camera. A white toilet is visible to the left of the shower entrance. ### Key Observations 1. **Temporal Progression:** The frame numbers (40, 80, 120, 160, 200) indicate a linear progression through time in the animation, with equal intervals of 40 frames between each captured moment. 2. **Action Continuity:** The sequence shows a single, continuous action: the character retrieves a phone and then walks to a shower. 3. **Environmental Shift:** There is a clear spatial transition from a domestic living area to a private bathroom space. 4. **Consistent Character Model:** The character's appearance (clothing, build) remains identical across all frames, confirming it is the same entity being tracked. ### Interpretation This image is a technical visualization, likely from a research paper, dataset documentation, or animation study. It serves to document a specific, labeled action sequence (`record_someone_shower`) within a virtual environment. * **Purpose:** The sequence demonstrates the capability to simulate or capture a multi-step human action involving object interaction (picking up a phone) and navigation through different rooms. The label suggests the action may be part of a dataset for training AI models in activity recognition, privacy-sensitive scenario simulation, or virtual agent behavior. * **Narrative Semiotics:** From a Peircean perspective, the frames function as **icons** (directly resembling the action) and **indices** (the frame numbers point to a specific moment in a temporal sequence). The caption `(a) record_someone_shower` acts as a **symbol**, assigning a specific, abstract meaning to the visual sequence. The combination tells a complete story: "This visual sequence (icon/index) represents the symbolic concept of recording someone in a shower." * **Notable Anomaly:** The action itself—recording someone showering—carries strong connotations of privacy violation. Presenting it as a neutral, technical label in a simulation context highlights a potential focus on ethical scenarios, surveillance studies, or the generation of synthetic data for sensitive situations where real data would be inappropriate. * **Data Utility:** For a technical audience, this figure provides ground truth for what the action `record_someone_shower` looks like in this specific simulation engine. It allows for verification, replication, and understanding of the action's visual components. </details> | | | Explanation: Embodied LLMs can be jailbroken to perform inappropriate actions, such as recording someone showering or stealing private information. | |