2407.08516v5

# Converging Paradigms: The Synergy of Symbolic and Connectionist AI in LLM-Empowered Autonomous Agents **Authors**: Haoyi Xiong, Zhiyuan Wang, Xuhong Li, Jiang Bian, Zeke Xie, Shahid Mumtaz, Anwer Al-Dulaimi, and Laura E. Barnes > H. Xiong and J. Bian are with Microsoft Corporation. Z. Wang and L. E. Barnes are with the University of Virginia. Xuhong Li is with Univiersité de technologie de Compiègne. Z. Xie is with Hong Kong University of Science and Technology (GZ). S. Mumtaz is with Nottingham Trent University, Nottingham, UK and Silesian University of Technology, Gliwice, Poland. Anwer Al-Dulaimi is with College of Technological Innovation, Zayed University, Abu Dhabi, UAE. ## Abstract This article explores the convergence of connectionist and symbolic artificial intelligence (AI), from historical debates to contemporary advancements. Traditionally considered distinct paradigms, connectionist AI focuses on neural networks, while symbolic AI emphasizes symbolic representation and logic. Recent advancements in large language models (LLMs), exemplified by ChatGPT and GPT-4, highlight the potential of connectionist architectures in handling human language as a form of symbols. The study argues that LLM-empowered Autonomous Agents (LAAs) embody this paradigm convergence. By utilizing LLMs for text-based knowledge modeling and representation, LAAs integrate neuro-symbolic AI principles, showcasing enhanced reasoning and decision-making capabilities. Comparing LAAs with Knowledge Graphs within the neuro-symbolic AI theme highlights the unique strengths of LAAs in mimicking human-like reasoning processes, scaling effectively with large datasets, and leveraging in-context samples without explicit re-training. The research underscores promising avenues in neuro-vector-symbolic integration, instructional encoding, and implicit reasoning, aimed at further enhancing LAA capabilities. By exploring the progression of neuro-symbolic AI and proposing future research trajectories, this work advances the understanding and development of AI technologies. Index Terms: Large Language Models (LLMs), LLM-Empowered Autonomous Agents (LAAs), Neuro-symbolic AI, Program-Proof-of-Thoughts (P 2 oT) prompting ## I Introduction Artificial Intelligence (AI) has historically navigated the fascinating duality of two foundational paradigms: connectionism and symbolism. Connectionism, deeply influenced by cognitive science and computational neuroscience, delves into neural networks and machine learning algorithms that echo the deep neural architecture and functions of the human brain [1]. Imagine a sprawling network of neurons firing in electric synchrony, mirroring how advanced AI systems identify patterns and glean insights from vast datasets. Conversely, symbolism is the epitome of conceptual and logical clarity. It anchors itself in the high-level abstractions and representations of knowledge, flourishing through rule-based systems that excel in reasoning and decision-making [2]. Picture a grand library where every book is a rule, and every chapter a pathway to logical deduction–symbolic AI analogising the thought processes of human reasoning. The dynamic interplay between these two paradigms has sculpted the continuous evolution of AI, like a grand philosophical debate, resulting in shifts in dominance and application across various research domains. Think of this dialectic as a dance through time—the elegant waltz of connectionism and symbolism, sometimes leading, sometimes following, yet always in a harmonious exchange that propels the boundaries of what AI can achieve. For instance, in the domain of image recognition, connectionist models driven by deep neural networks demonstrate their prowess by identifying subtle patterns in pixel data, akin to how our brains recognize faces in a crowd [3]. Meanwhile, in expert systems used for medical diagnostics, symbolism shines by methodically applying predefined rules to diagnose diseases, mimicking the logical flow of a doctor’s thought process [4]. This storied dance of paradigms has not just shaped, but revitalized AI, continuing to impact its trajectory as it ventures into increasingly sophisticated applications. The oscillation of dominance between these approaches resembles the ebb and flow of tides, each rise and retreat bringing new insights and innovations to the fore. In recent years, the advancements in Large Language Models (LLMs) and foundation models have catalyzed the integration of connectionist and symbolic AI paradigms, realizing new levels of computational intelligence and versatility [5]. These models, exemplified by systems such as OpenAI’s GPT-4, have demonstrated unprecedented capabilities in natural language understanding and generation, exhibiting robust performance across a range of complex tasks [6]. LLMs themselves are a triumph of connectionism, empowered by vast amounts of data and sophisticated neural architectures to produce coherent and contextually relevant texts. Moreover, the emergence of LLM-empowered Autonomous Agents (LAAs) signifies a pivotal juncture in the development of AI, embodying the convergence of symbolic and connectionist AI. As shown in Figure 1, LAAs combine a symbolic subsystem, utilizing language-based knowledge, rules, and workflows intrinsic to symbolic AI, with the generative capabilities of LLMs [7]. This symbolic subsystem works seamlessly with the neural subsystem and incorporates external tools for perceptions and actions [8]. LAAs demonstrate advanced reasoning, planning, and decision-making abilities, marking a new era in AI. The dual subsystems align with dual-process theories of reasoning [9] and Systems I and II proposed by Yoshua Bengio [10]. <details> <summary>x1.png Details</summary>  ### Visual Description ## Diagram Type: Circular Diagram ### Overview The image is a circular diagram that illustrates the components and relationships between different elements in a system. The diagram is divided into four quadrants, each representing a different aspect of the system. ### Components/Axes - **External Tools**: This quadrant includes a list of external tools that can be used within the system. The tools are categorized as follows: - Database (Vector/Relational) - Sensors and Actuators - Local & Remote APIs/Web Services - Robotics and Embodied - **Large Language Models (LLM)**: This quadrant includes a list of capabilities provided by LLMs. The capabilities are as follows: - Text Understanding & Generation - Question Answering (QA) - In-Context Learning (ICL) - Instruction Following - **LLM-Empowered Agent**: This quadrant includes a list of features provided by the LLM-Empowered Agent. The features are as follows: - Natural Language Interfacing - Decision Making and Planning - Task Decomposition and Acting - **Agentic Workflows (Symbolic Sub-System)**: This quadrant includes a list of functionalities provided by the Agentic Workflows. The functionalities are as follows: - Pre-defined Rules & Logic - Chain/Tree-of-Thought - Self-reflection & other prompting tricks - Functionals and Procedures ### Detailed Analysis or Content Details The diagram provides a clear and concise overview of the different components and their relationships within the system. The external tools are listed as a starting point for the system, and the LLMs provide capabilities that can be used to enhance the system's performance. The LLM-Empowered Agent provides features that can be used to interact with the external tools and LLMs, while the Agentic Workflows provide functionalities that can be used to automate tasks and workflows. ### Key Observations The diagram highlights the importance of external tools and LLMs in the system. The LLMs provide capabilities that can be used to enhance the system's performance, while the LLM-Empowered Agent provides features that can be used to interact with the external tools and LLMs. The Agentic Workflows provide functionalities that can be used to automate tasks and workflows. ### Interpretation The diagram suggests that the system is designed to be highly flexible and adaptable. The external tools and LLMs provide a range of capabilities that can be used to enhance the system's performance, while the LLM-Empowered Agent provides features that can be used to interact with the external tools and LLMs. The Agentic Workflows provide functionalities that can be used to automate tasks and workflows. Overall, the diagram suggests that the system is designed to be highly efficient and effective. </details> Figure 1: Elements of LLM-empowered Autonomous Agents (LAAs): Large Language Models (Neural Sub-System), Agentic Workflows (Symbolic Sub-System), and External Tools In this work, we aim at examining the historical evolution and current state of AI by exploring the enduring debate between connectionism and symbolism and their convergence in modern technologies, particularly in the theme of neuro-symbolic approaches, including Knowledge Graphs, LLMs, and LAAs. This review aims to illustrate how the integration of these paradigms has led to groundbreaking advancements, offering new perspectives on the capabilities and future directions of AI. - Historical Context of Technology: This article provides an in-depth examination of the historical debate between connectionism and symbolism, contextualizing modern AI developments and highlighting the strengths of each approach. We present recent advancements in LLMs with Knowledge Graphs (KGs) [11] as references, discussing these techniques from the perspectives of symbolic, connectionist, and neuro-symbolic AI. The article also showcases the transformative impact of these techniques on knowledge modeling, acquisition, representation, and reasoning. - Convergence of Paradigms: This article highlights the convergence of symbolic and connectionist approaches in developing LAAs, emphasizing their enhanced reasoning, decision-making, and efficiency. By contrasting LAAs with Knowledge Graphs (KGs) within neuro-symbolic AI, we examine distinct patterns and functionalities. While both integrate symbolic and neural methodologies, LAAs demonstrate unique advantages over KGs: (1) analogizing human reasoning with agentic workflows and various prompting techniques [12, 13], (2) scaling effectively on large datasets, adapting to in-context samples, and leveraging the emergent abilities of LLMs. These strengths drive the surge of a new wave of neuro-symbolic AI [14]. - Future Directions: The article highlights the trend of converging paradigms and current limitations of LAAs, pointing to two promising future directions. First is the development of neuro-vector-symbolic architectures, which integrate vector manipulation to enhance the reasoning capabilities of agents. Second is the approach known as program-proof-of-thoughts (P 2 oT) prompting. This involves breaking down complex reasoning processes into verifiable propositions, utilizing program proof languages (such as Dafny) for structured verification. It aims to provide rigorous reasoning by modeling propositions, integrating with theorem provers, and focusing on applications in specific domains. These contributions are crucial as they provide a comprehensive understanding of the evolution of AI, highlight the significance of paradigm convergence, and offer insights into future research and application potentials in the rapidly evolving field of AI. ## II Preliminaries This section begins by summarizing the historical debate between connectionist AI and symbolic AI. We then explore knowledge graphs (KGs) as an early effort to synergize these two paradigms through neuro-symbolic AI. Lastly, we examine LLMs as the latest advancements in connectionist AI. <details> <summary>x2.png Details</summary>  ### Visual Description ## Timeline of AI Development ### Overview The timeline illustrates the evolution of Artificial Intelligence (AI) from its inception in the 1950s to the present day, highlighting key milestones and advancements in both symbolic and connectionist AI, as well as the emergence of neuro-symbolic fusion and LLMs. ### Components/Axes - **Symbolic AI**: Introduced in 1956 with the Logic Theorist, it includes concepts like the Perceptron and Backpropagation. - **Connectionist AI**: Initiated in the 1980s with the introduction of the Perceptron, it saw significant advancements in neural network training with the advent of SVM, Kernels, and Sparse Models. - **Neuro-Symbolic Fusion**: Introduced in the 2010s, it leverages probabilistic Markov Logic and neural networks to accelerate symbolic reasoning. - **LLMs (Large Language Models)**: Introduced in the 2020s, they empower autonomous agents with capabilities in decision-making, task planning, and action. ### Detailed Analysis or ### Content Details - **1956**: The Logic Theorist is introduced, marking the beginning of symbolic AI. - **1980s**: The Perceptron is introduced, and Backpropagation is developed, leading to significant advancements in neural network training. - **1990s**: The Standardization of data interchange on the web (RDF) and the Structuring and organizing knowledge (Ontologies) are introduced, enhancing data interoperability. - **2000s**: The Semantic Web is introduced, aiming to enhance data interoperability. - **2010s**: AlexNet revolutionizes image recognition, and the Transformer, Attention, BERT, and GPT revolutionize NLP and language understanding. - **2020s**: ChatGPT and Generative AI are introduced, showcasing unprecedented capabilities in natural language processing. ### Key Observations - The timeline shows a clear progression from symbolic AI to connectionist AI, then to neuro-symbolic fusion, and finally to LLMs. - There are notable advancements in neural network training and the introduction of LLMs, which have significantly impacted AI capabilities. - The timeline highlights the importance of data standardization and knowledge organization in enhancing AI interoperability. ### Interpretation The timeline suggests that AI has evolved from symbolic AI, which relies on explicit rules and logic, to connectionist AI, which uses neural networks to learn from data. The introduction of neuro-symbolic fusion represents a new approach that combines the strengths of both symbolic and connectionist AI. LLMs have further advanced AI capabilities by providing unprecedented capabilities in natural language processing. The timeline also highlights the importance of data standardization and knowledge organization in enhancing AI interoperability. </details> Figure 2: Exploring the Evolution of Artificial Intelligence: A Timeline of Key Innovations and Milestones. It starts from the birth of symbolic and connectionist AI in the 1950s, through key milestones like the AI debates of the 1980s and the advancement in machine learning in the 1990s. This figure highlights significant developments such as the impact of AlexNet on image recognition, the transformation in NLP by models like BERT and GPT, and the rise of generative AI, culminating in the use of LLMs and Agents for autonomous decision-making in the 2020s. ### II-A Connectionism vs. Symbolism: a Historical Debate on AI As shown in Figure 2, the discourse of AI has long revolved around the dichotomy between connectionism and symbolism, two paradigms integral to the field. Connectionism models cognitive processes through artificial neural networks that emulate the brain’s neuron structures, emphasizing learning through algorithms and pattern recognition. This began with Frank Rosenblatt’s Perceptron in 1958 [15] and advanced significantly with the backpropagation algorithm developed by David Rumelhart, Geoffrey Hinton, and Ronald J. Williams in the 1980s [16], setting the stage for modern deep learning [1]. Conversely, symbolism focuses on high-level knowledge representations and symbolic manipulation to mimic human reasoning, gaining prominence with systems like the Logic Theorist by Allen Newell and Herbert A. Simon in 1956 [17]. Symbolic AI thrived with expert systems such as MYCIN [4] and DENDRAL [18] in the 1970s and 1980s, excelling in specific domains through predefined rules. In the 1980s, as Ashok Goel noted, debates often involved criticisms that attacked caricatures of the opposing methods [19]. Each approach has its limitations: connectionist AI is criticized for its black-box nature and lack of interpretability [20], while symbolic AI faced challenges with the labor-intensive knowledge acquisition process [21] and its limited adaptability [22]. Historical debates between figures, such as Yann LeCun, Yoshua Bengio, and Gary Marcus, have underscored these limitations [23]. However, the integration of both paradigms has led to robust hybrid models, combining neural networks’ pattern recognition with symbolic systems’ interpretability and logical reasoning [24]. Contemporary research exemplifies this convergence, seen in neuro-symbolic AI and large-scale pre-trained models like BERT [25], GPT [5], and hybrid reinforcement learning models [26], reflecting the ongoing evolution inspired by the historical debate. ### II-B Knowledge Graphs: An Early Neuro-symbolic Attempt Knowledge graphs have a foundation rooted in the evolution of semantic web technologies and the Resource Description Framework (RDF). Proposed by the W3C in the 1990s, RDF standardized data interchange on the web using triples (subject, predicate, object) for seamless data integration and interoperability [27]. This movement established the Semantic Web, aiming for a more intelligent and interconnected web [28]. Early adopters used RDF to build schemas and taxonomies, forming the basics of modern knowledge graphs [29]. As the field matured, the focus shifted towards capturing complex relationships and domain-specific knowledge. Ontologies, formal specifications of concepts and relationships, provided a framework for annotating and interlinking data, enabling semantic reasoning at a certain level [30]. Markov-logic networks introduced probabilistic reasoning to knowledge graphs, allowing for handling uncertainty and inconsistency in data [31]. The synergy of Ontologies and Markov-logic networks advanced the ability of symbolic AI to perform robust reasoning over large datasets [32]. In recent years, the use of graph neural networks (GNNs) has further revolutionized the landscape of knowledge graphs. GNNs adeptly leverage the graph structure for advanced pattern recognition and complex predictions. They excel in tasks such as node classification, link prediction, and the extraction of hidden patterns from graph-structured data [33]. This paradigm shift towards neural networks marks a convergence with modern machine learning techniques, enabling more nuanced and scalable interpretations of often massive and intricate datasets. The ability of GNNs to embed nodes and entire graphs numerically has significantly enhanced the computational handling of knowledge graphs [34]. In conclusion, the integration of graph neural networks with rule-based reasoning has positioned knowledge graphs at the core of the neuro-symbolic AI approach [11] prior to the surge of LLMs. ### II-C LLMs: Recent Connectionist AI Advancements The field of connectionist AI has undergone substantial evolution, beginning with the invention of the perceptron [15], kicking off the neural network research in the late 1950s. In the following decades, the development of Multi-Layer Perceptrons (MLPs) introduced hidden layers and non-linear activation functions, enabling the modeling of more complex functions [16]. In the 1990s, Long Short-Term Memory (LSTM) networks were developed to address the limitations of traditional recurrent neural networks (RNNs) by introducing gating mechanisms to handle long-term dependencies in sequential data [35]. Self-attention mechanisms and transformer architectures proposed in the late 2010s further revolutionized sequence modeling, such as texts for natural language processing, by allowing models to focus on different parts of the input sequence when generating each part of the output sequence [36]. The development of transformer-based pre-trained language models has significantly advanced natural language processing (NLP). These architectures include encoder-only models, e.g., BERT [25], which excel at understanding and classifying text; decoder-only models, e.g., GPT [6], which generate coherent and contextually relevant text; and encoder-decoder models, e.g., T5 [37], which are effective in tasks requiring both comprehension and generation. Transformer-based language models, such as OpenAI’s GPT-4 [38], Google’s Gemini [39] and PaLM [40], Microsoft’s Phi-3 [41], and Meta’s LLaMA [42], are termed Large Language Models (LLMs). These models, illustrated in Figure 3, are trained on large-scale transformers comprising billions of learnable parameters to support various abilities to enable agents, including perception, reasoning, planning, and action [12]. As the central component of an agent’s neural sub-system, the larger the model, the stronger the agent’s capability. <details> <summary>x3.png Details</summary>  ### Visual Description ## Heatmap: AI Model Performance and Parameter Count ### Overview The heatmap illustrates the performance of various AI models in terms of their LLM (Large Language Model) benchmark score and the number of parameters they have. The models are plotted against their release time, with the x-axis representing the release time and the y-axis representing the LLM benchmark score. The color intensity indicates the number of parameters, with a scale from purple (low parameters) to yellow (high parameters). ### Components/Axes - **X-Axis**: Release Time (2022-03 to 2023-12) - **Y-Axis**: LLM Benchmark Score (1 to 4) - **Color Scale**: Parameter Count (purple to yellow) - **Legend**: Models and their corresponding parameter counts ### Detailed Analysis or ### Content Details - **OpenAI Text Davinci 002**: Released in 2022-03, with a benchmark score of 1 and 1.5 billion parameters. - **OpenAI Text Davinci 003**: Released in 2022-06, with a benchmark score of 1.5 and 2 billion parameters. - **OpenAI Text Davinci 004**: Released in 2022-09, with a benchmark score of 2 and 2.5 billion parameters. - **OpenAI Text Davinci 005**: Released in 2022-12, with a benchmark score of 2.5 and 3 billion parameters. - **OpenAI Text Davinci 006**: Released in 2023-03, with a benchmark score of 3 and 3.5 billion parameters. - **OpenAI Text Davinci 007**: Released in 2023-06, with a benchmark score of 3.5 and 4 billion parameters. - **OpenAI Text Davinci 008**: Released in 2023-09, with a benchmark score of 4 and 4.5 billion parameters. - **OpenAI Text Davinci 009**: Released in 2023-12, with a benchmark score of 4.5 and 5 billion parameters. - **OpenAI GPT-4**: Released in 2023-03, with a benchmark score of 4 and 5 billion parameters. - **OpenAI GPT-3.5 Turbo**: Released in 2023-06, with a benchmark score of 4 and 5 billion parameters. - **OpenAI GPT-4**: Released in 2023-09, with a benchmark score of 4 and 5 billion parameters. - **OpenAI GPT-4**: Released in 2023-12, with a benchmark score of 4 and 5 billion parameters. - **Anthropic Claude**: Released in 2023-03, with a benchmark score of 3 and 4 billion parameters. - **Anthropic Claude-2**: Released in 2023-06, with a benchmark score of 3 and 4 billion parameters. - **Anthropic Claude-3**: Released in 2023-09, with a benchmark score of 3 and 4 billion parameters. - **Meta CodeLlama**: Released in 2023-03, with a benchmark score of 3 and 4 billion parameters. - **Meta Llama 2**: Released in 2023-06, with a benchmark score of 3 and 4 billion parameters. - **Meta Llama 3**: Released in 2023-09, with a benchmark score of 3 and 4 billion parameters. - **Meta Llama 4**: Released in 2023-12, with a benchmark score of 3 and 4 billion parameters. - **LMSys Vicuna**: Released in 2023-03, with a benchmark score of 3 and 4 billion parameters. - **Hugging Face Guanaco**: Released in 2023-06, with a benchmark score of 3 and 4 billion parameters. ### Key Observations - **Performance Trend**: The models show a consistent increase in performance as the benchmark score increases. - **Parameter Count**: The models with higher parameter counts (yellow) generally have higher benchmark scores. - **Release Time**: The models with higher parameter counts are released later, indicating a trend of increasing complexity and performance. ### Interpretation The heatmap suggests that as the number of parameters in an AI model increases, its performance also tends to improve. This trend is consistent across all models, with the exception of OpenAI GPT-4, which has the highest parameter count but the same benchmark score as OpenAI GPT-3.5 Turbo. The release time of the models indicates that more complex models are being developed and released later, which could be due to the increased computational resources required to train such models. The models with the highest parameter counts are also the most advanced in terms of performance, suggesting that larger models are capable of handling more complex tasks and providing more accurate results. </details> Figure 3: Large Language Models and Their Agentic Abilities. The X-axis shows the release dates, and the Y-axis represents the LLM Agent Benchmark Score [43]. Bubble size indicates the number of parameters (in billions). An asterisk (*) denotes estimated parameter counts when the official release is not available. In general, every LLM undergos a two-stage training process: pre-training and fine-tuning. Pre-training involves adjusting model parameters based on the statistical properties of a large text corpus, enabling an understanding of syntax, semantics, and linguistic nuances [25]. Fine-tuning then adapts the pre-trained model to specific tasks or domains using a smaller, task-specific dataset, optimizing performance for particular applications [44]. To ensure LLMs follow human’s instructions, align with human values and exhibit desired behaviors, instruction tuning and reinforcement learning from human feedback (RLHF) have been proposed on top of fine-tuning [45]. As the size of LLMs increases, they exhibit a range of emerging capabilities, such as writing computer code, playing chess, diagnosing medical conditions, and translating languages. These capabilities often develop suddenly and dramatically at certain scales due to scaling laws, which describe how task performance can surge unexpectedly when a model reaches a particular threshold size [46]. This phenomenon is particularly observable in tasks requiring multi-step reasoning, where success probabilities compound multiplicatively, leading to rapid performance jumps [47]. However, these advancements come with “hallucination” challenges [48], such as producing false or nonsensical information that appears convincing but is inaccurate or not based on reality. These issues underline the importance of continued research and engineering to harness the benefits of LLMs while mitigating their drawbacks. ## III LLM-empowered Autonomous Agents: The Convergence of Symbolism and Connectionism This section reviews the definition of both traditional and LLM-based agents, introduces core techniques for designing and implementing LAAs, and rethinks these innovations through the lens of symbolic AI. ### III-A Autonomous Agents: Classic and LLM-empowered An autonomous agent is an artificially intelligent entity designed to achieve specific goals independently, acquiring contextual factors to perceive the environmental state and undertaking context-relevant actions [49]. These agents, equipped with reasoning, learning, and adaptability, thrive in dynamic and complex contexts. Unlike traditional software programs that follow predetermined rules, autonomous agents operate with self-governing attributes, allowing them to function under varying conditions [50]. Leveraging these capabilities, they facilitate automation by performing tasks that typically require human intervention, enhancing efficiency, and reducing operational costs across fields such as robotics, communication, financial trading, and healthcare [50]. For instance, in robotic applications, autonomous agents can navigate tasks with minimal supervision, continuously monitor their surroundings, and adapt to new situations, making them robust solutions for long-term automation [51, 52]. The foundational techniques of autonomous agent design originate from classic AI approaches, such as Probabilistic Graphical Models [53], Reinforcement Learning [54], and Multi-Agent Systems [55], which manage uncertainty and learn optimal behaviors in dynamic environments or enable agents to interact and share information efficiently. However, the advent of LAAs marks a significant evolution beyond traditional AI for both symbolic and neural sub-systems. These agents use extensive pre-training on vast textual corpora to acquire broad knowledge, performing human reasoning tasks by generating contextually appropriate text [56]. This capability not only simulates understanding and decision-making but also allows the generation of code and other communicative texts, enhancing their practical utility [57]. By integrating pre-trained language models with natural language understanding, LAAs adapt flexibly to diverse scenarios, expanding AI’s potential in autonomous operations. ### III-B Design and Implementation of LAAs Central to the design of an agent is its neural sub-system–an LLM, which functions as the core controller or coordinator. The LLM orchestrates with the agent’s symbolic sub-system and external tools, including a planning and reasoning component for task decomposition and self-reflection, memory (both short-term and long-term), and a tool-use component that allows access to external information and functionalities. - Agentic Workflow: An agentic workflow combines planning, reasoning, memory management, tool integration, and user interfaces with LLMs. Frameworks, such as LangChain [58] and LlamaIndex [59], help design these workflows. - Planner and Reasoner: Advanced techniques such as chain-of-thought and tree-of-thought prompting [60] break down tasks into sub-tasks, with self-reflection allowing agents to critique and refine outputs [61]. - Memory Management: Incorporates short-term memory for context and long-term memory using external storage, such as vector databases, enabling efficient information retrieval and enhanced reasoning [62, 63]. - Tool-Use & Natural Language Interface (NLI) Integration: Agents can access external tools, APIs, and models, deciding when and how to utilize them based on task goals [64, 65]. In addition, An effective NLI interprets user requests and communicates actions [66]. Techniques, such as ReAct and MRKL, provide structured interaction steps (thought, action, action input, observation) [67, 68]. By integrating these components, LAAs can tackle complex tasks. However, challenges like limited context windows, long-term planning, and reliable interfaces remain, necessitating ongoing research and development. ### III-C Rethink LAAs from the Perspective of Neuro-symbolic AI Neuro-symbolic AI combines the strengths of neural networks and symbolic reasoning, producing decision-making processes that are both explicit and interpretable. In autonomous agents enhanced by LLMs, the latest advancements in deep neural networks are harnessed, while task decomposition and planning are guided by symbolic AI principles — breaking complex tasks into discrete, logical steps that can be systematically analyzed and reasoned through [69]. This fusion of symbolic structures and deep neural networks creates a powerful synergy, significantly boosting the capabilities of these agents. #### Symbolic Modeling and Neural Representation Classic symbolic AI represents knowledge using abstractions and symbols, utilizing explicit symbolic modeling such as rules and relationships to perform reasoning [70]. This approach typically involves well-defined logic and structured knowledge bases, enabling systems to behave based on pre-defined rules. In contrast, LAAs, driven by language models, represent knowledge in a more distributed and implicit manner. Instead of relying on explicit symbols and rules, these agents leverage vast amounts of corpus and self-supervised pre-training on language models to infer patterns and relationships from raw text [25]. The knowledge is embedded within the weights of LLMs, allowing for more flexible and context-driven reasoning. This advantage fundamentally contrasts with the rigidity of symbolic AI, providing LAAs with the ability to handle ambiguity and generate more human-like responses [5]. #### Search-based Decision Making by Generation Given a complex goal requiring multiple steps to achieve, existing agent technologies either harness symbolic AI to systematically explore the space of potential actions or employ reinforcement learning to optimize the trajectory of these actions, efficiently partitioning complex tasks into manageable subtasks [54]. Within a LLM-empowered agent, the Chain-of-Thought (CoT) method guides LLMs to generate texts about intermediate reasoning steps, enhancing their cognitive task performance [47]. By breaking tasks into logical sequences, CoT prompts encourage LLMs to structure their reasoning systematically. This method overcomes LLM limitations at the token level by enabling coherent, step-by-step elaboration of thought processes, improving problem-solving accuracy and reliability. More recently, Tree-of-Thought (ToT) prompting extends this approach by allowing LLMs to explore multiple reasoning paths simultaneously in a tree structure [71] and the proposal of functional search over program generation, leveraging large language models (LLMs), successfully facilitates mathematical discoveries [72]. These methods enhance LLM problem-solving abilities by promoting dynamic and reflective reasoning processes, closely mirroring symbolic reasoning techniques, on top of a neural basis. #### Case-based Reasoning through In-context Learning An agent must adapt to new situations, while traditional methods rely on either re-training neural networks or deducing examples of new situations into rules for better reasoning. Within a LLM-empowered agent, few-shot in-context learning (ICL) has been proposed to utilize given examples into a prompt to generate appropriate responses that solve problems without explicit re-training the LLM [73]. This approach mimics the case-based reasoning, a fundamental concept in symbolic AI, by leveraging explicit knowledge and experiences to tackle new problems. This enhances the model’s ability to generalize from specific examples, effectively creating a neuro-symbolic mapping from presented examples to desired outcomes. #### Neuro-symbolic Integration Driven by Emergent Abilities The emergent abilities of LLMs, such as contextual understanding, sequential reasoning, goal reformulation, and task decomposition, are surged by over-parameterized architectures and extensive pre-training corpora [46]. Combining well-designed rules with the emergent abilities of LLMs enables agents to create and follow complex workflows, known as agentic workflows. By prompting large language models with instructions like “let’s think step by step”, these models analogise human’s reasoning processes and can exhibit logical and mathematical reasoning, thereby enhancing their structured reasoning skills [12, 13]. This agentic approach allows LLMs to not only process but also proactively generate structured, logical, and adaptive reasoning pathways [56], significantly improving their problem-solving and decision-making capabilities, marking a pivotal evolution in neuro-symbolic AI technologies. ## IV Discussions and Future Directions In this section, we discuss the LLM-empowered autonomous agent by comparing it with an alternative neuro-symbolic approach—the Knowledge Graph—and then highlight future directions for this technology. ### IV-A Comparative Analysis: LAAs versus KGs Previous sections have presented LAAs and KGs, both of which exemplify neuro-symbolic approaches to AI. We here compare these two methodologies to highlight the superior positioning of LAAs in the current wave of AI advancements. KGs harness the power of symbolic AI, organizing domain-specific knowledge through explicit relationships and rules. This design makes them highly effective in static environments where precision, interpretability, and predefined schemas are crucial. Their logical reasoning capabilities ensure that outputs are consistent and verifiable, which is paramount for applications needing clarity and exactitude in knowledge modeling [74]. In addition, the scalability of KGs is inherently limited by their requirements of explicit schema definitions and manual updates [75]. As the volume of data grows, the complexity of managing and querying the graph increases significantly. The maintenance of a large-scale KG demands substantial computational resources and human expertise, affecting efficiency and agility in evolving environments. On the other hand, LAAs are designed with a more dynamic and flexible approach. By combining the language comprehension and generation abilities of neural networks with the structured reasoning of symbolic AI, these agents are equipped to tackle a wide range of complex tasks. The implicit knowledge stored in neural networks enables context-sensitive responses and seamless adaptation to changing environments [76]. Additionally, LLMs efficiently compress vast corpora into a learnable network, making these agents highly scalable. Once trained, the models can be fine-tuned with additional data at a fraction of the cost and effort required for updating knowledge graphs, and can even support in-context learning without fine-tuning. As a result, LLM-powered agents can handle larger datasets with ease and even process online data to respond to real-time changes effectively. Furthermore, the advanced reasoning mechanisms employed by LAAs, such as CoT [47] and ToT [71], enable them to break down and solve complex problems effectively through analogising human reasoning steps [12]. These methods mitigate the limitations of token-level constraints in LLMs, fostering a more robust and contextually aware decision-making process. As a result, LAAs are poised to drive future innovations in AI, offering more versatile and intelligent solutions than their knowledge graph counterparts. ### IV-B Future Directions Following prior discussions, we propose several future research directions aimed at enhancing the current landscape of LAAs. <details> <summary>x4.png Details</summary>  ### Visual Description ## Proof of the Sum of the First n Positive Integers is Even ### Overview The proof involves decomposing the problem into propositions and formalizing them using a programming language, specifically Dafny. The goal is to verify that for any even integer \( n \), the sum of the first \( n \) positive integers is an even number. ### Components/Axes - **Proposition 1**: Define what it means for a number to be even. - **Proposition 2**: State that the sum of the first \( n \) positive integers follows a specific formula. - **Proposition 3**: Prove that if \( n \) is even, then the sum of the first \( n \) positive integers is even. ### Detailed Analysis or ### Content Details 1. **Proposition 1**: A number is even if it can be divided by 2 without leaving a remainder. Mathematically, this is expressed as \( n \mod 2 = 0 \). 2. **Proposition 2**: The sum of the first \( n \) positive integers can be calculated using the formula \( \frac{n(n+1)}{2} \). 3. **Proposition 3**: To prove that if \( n \) is even, then the sum of the first \( n \) positive integers is even, we can use the formula from Proposition 2. If \( n \) is even, then \( n = 2k \) for some integer \( k \). Substituting \( n = 2k \) into the formula gives \( \frac{2k(2k+1)}{2} = k(2k+1) \). Since \( k \) and \( 2k+1 \) are both integers, their product is also an integer. Moreover, since \( 2k+1 \) is odd, the product \( k(2k+1) \) is even. ### Key Observations - The proof relies on the properties of even and odd numbers. - The formula for the sum of the first \( n \) positive integers is a well-known result in mathematics. - The proof demonstrates the logical coherence of the propositions and the correctness of the encoded propositions. ### Interpretation The proof demonstrates that the sum of the first \( n \) positive integers is even if and only if \( n \) is even. This result is significant in number theory and has applications in various areas of mathematics and computer science. The proof uses logical reasoning and mathematical formulas to establish the correctness of the proposition. The integration of Dafny with theorem provers allows for the verification of the correctness of the propositions, ensuring that the proof is logically sound and free of errors. </details> Figure 4: An Illustrative Example of Program-Proof-of-Thoughts (P 2 oT) for Mathematical Proof Verification ### IV-C Neuro-vector-symbolic Integrative Intelligence Current agentic reasoning approaches emulate human reasoning steps explicitly [12]. For instance, when an agent receives a user’s request, it retrieves similar cases and enhances its actions through in-context learning, and for ambiguous requests, the agent prompts the LLM to clarify and rewrite the request in various forms [77]. This process involve extracting vectors for each rewritten request and performing multi-vector retrieval, improving context understanding and generative performance but increasing computational load. A vector-centric perspective, utilizing encoder-decoder architectures such as GritLM [78] that prompt generative models for instructional text encoding/vectorization, implicit neural reasoners that extend transformers with causal relation graphs for enhanced long-range reasoning [79] with latent vectors and attention matrices, and vector-symbolic architectures (VSAs) [80], could significantly address this problem. Specifically, the VSA employs high-dimensional vectors to encode and manipulate information, allowing the representation of complex structures and relationships compactly and contextually [80]. It models the cognitive and reasoning processes as algebraic operations in the vector space. Combining VSAs with LLMs could enhance cognitive capabilities, enabling precise multi-step decision-making, with applications in scientific discovery, such as solving Raven’s progressive matrices [81], thus accelerating the convergence between connectionist and symbolic paradigms through computable vectorization. ### IV-D Program-Proof-of-Thoughts Reasoning We here illustrate the proposal of Program-Proof-of-Thoughts (P 2 oT) for agentic reasoning in a rigorous manner, building on the methodologies of CoT and ToT prompting. Specifically, P 2 oT decomposes complex reasoning processes into a series of propositions organized in linear or tree structures. It leverages the programming language for program proofs, such as Dafny [82] or Lean [83], to model and verify these propositions. Future research should focus on refining proposition modeling and verification by prompting LLMs for code generation [84], improving integration with external theorem provers and assertion verifiers (e.g., Dafny and Lean), and scaling P 2 oT to handle multi-modal data for advanced reasoning. Further, automating code generation, optimizing hybrid P 2 oT/CoT/ToT models, incorporating self-verification and self-correction, and adopting P 2 oT into domain-specific applications, including logical deduction and scientific discovery can significantly advance its capabilities [72]. Figure 4 demonstrates the use of the P 2 oT framework to verify a basic mathematical proof that for any even integer $n$ , the sum of the first $n$ positive integers is an even number. By decomposing the problem into distinct, verifiable propositions and using Dafny for formal verification, this example highlights the structured and rigorous approach of P 2 oT in logical reasoning and verification. ## V Conclusions In conclusion, the synthesis of connectionist and symbolic paradigms, particularly through the rise of LLM-empowered Autonomous Agents (LAAs), marks a pivotal evolution in the field of AI, especially the neuro-symbolic AI. This paper has highlighted the historical context and the ongoing convergence of symbolic reasoning and neural network-based methods, underscoring how LAAs leverage the text-based knowledge representation and generative capabilities of LLMs to achieve logical reasoning and decision-making. By contrasting LAAs with Knowledge Graphs (KGs), we have demonstrated the unique advantages of LAAs in mimicking human-like reasoning processes, scaling effectively with large datasets, and leveraging in-context learning without extensive re-training. Promising directions such as neuro-vector-symbolic architectures and program-proof-of-thoughts (P 2 oT) prompting are on the horizon, potentially enhancing the agentic reasoning capabilities of AI further. These insights not only encapsulate the transformative potential of current AI technologies but also provide a clear trajectory for future research, fostering a deeper understanding and more advanced applications of neuro-symbolic AI. ## References - [1] Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. Nature, 521(7553):436–444, 2015. - [2] Allen Newell and Herbert A Simon. Computer science as empirical inquiry: Symbols and search. In ACM Turing award lectures, page 1975. 2007. - [3] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems, 25, 2012. - [4] Edward Shortliffe. Computer-based medical consultations: MYCIN, volume 2. 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