2512.10978v1

# Cognitive Mirrors: Exploring the Diverse Functional Roles of Attention Heads in LLM Reasoning **Authors**: - Tongliang Liu James Bailey (The University of Melbourne  The University of Sydney) > This work is not related to Amazon. ## Abstract Large language models (LLMs) have achieved state-of-the-art performance in a variety of tasks, but remain largely opaque in terms of their internal mechanisms. Understanding these mechanisms is crucial to improve their reasoning abilities. Drawing inspiration from the interplay between neural processes and human cognition, we propose a novel interpretability framework to systematically analyze the roles and behaviors of attention heads, which are key components of LLMs. We introduce CogQA, a dataset that decomposes complex questions into step-by-step subquestions with a chain-of-thought design, each associated with specific cognitive functions such as retrieval or logical reasoning. By applying a multi-class probing method, we identify the attention heads responsible for these functions. Our analysis across multiple LLM families reveals that attention heads exhibit functional specialization, characterized as cognitive heads. These cognitive heads exhibit several key properties: they are universally sparse, and vary in number and distribution across different cognitive functions, and they display interactive and hierarchical structures. We further show that cognitive heads play a vital role in reasoning tasks—removing them leads to performance degradation, while augmenting them enhances reasoning accuracy. These insights offer a deeper understanding of LLM reasoning and suggest important implications for model design, training and fine-tuning strategies. The code is available at https://github.com/sihuo-design/CognitiveMirrors. ## 1 Introduction Large language models (LLMs) achiam2023gpt; grattafiori2024llama; touvron2023llama; yang2024qwen2, built on neural networks that mimic the structure of the human brain, have demonstrated exceptional performance across various natural language processing (NLP) tasks, often exceeding human capabilities. This has sparked growing interest in exploring the potential similarities between the cognitive processes of LLMs and the human brain. Prior studies have demonstrated that LLMs can predict brain responses to natural language caucheteux2022deep; schrimpf2021neural, indicating a functional alignment between artificial models and biological systems. However, to the best of our knowledge, systematic efforts to align reasoning processes between LLMs and human cognitive agents remain scarce. When solving complex reasoning tasks (e.g., a mathematical multiple-choice question; Figure 1), the human brain engages a network of specialized regions: the frontal lobe recalls relevant knowledge wheeler1997toward, language areas (e.g., Wernicke’s and Broca’s) support semantic processing ono2022bidirectional; meyer2005language, and the parietal and prefrontal cortices carry out higher-order reasoning barsalou2014cognitive; hubbard2005interactions. Analogously, recent research suggests that components within LLMs may also take on specialized roles. For example, multi-head attention mechanisms in transformers vaswani2017attention have been found to handle distinct functions, such as information retrieval wu2404retrieval or maintaining answer consistency truthful, pointing toward a form of architectural division of labor. However, most of these findings are based on relatively simple tasks zheng2409attention, leaving open how such specialization operates under complex, multi-step reasoning scenarios. <details> <summary>x1.png Details</summary>  ### Visual Description ## Flowchart: Cognitive Process for Solving Percentage Problems ### Overview The image depicts a flowchart illustrating the cognitive and neural processes involved in solving the percentage problem: "What percent is 120 of 90?" It breaks the solution into four stages: **Knowledge Recall**, **Semantic Understanding**, **Math**, and **Decision Making**. Each stage includes a brain diagram highlighting specific regions (frontal, parietal, temporal lobes, hippocampus) and explanatory text. A flowchart at the bottom visualizes the progression between stages using color-coded arrows. --- ### Components/Axes 1. **Stages**: - **Knowledge Recall**: Formula for percentage calculation. - **Semantic Understanding**: Identifying "part" (120) and "whole" (90). - **Math**: Calculation of `120 / 90 * 100%`. - **Decision Making**: Matching the result to the correct option. 2. **Brain Regions**: - **Frontal Lobe** (green): Highlighted in Knowledge Recall and Decision Making. - **Temporal Lobe** (orange): Highlighted in Semantic Understanding. - **Parietal Lobe** (yellow): Highlighted in Math. - **Hippocampus** (gray): Present in all brain diagrams. 3. **Flowchart Arrows**: - Green (frontal lobe) → Orange (temporal lobe) → Yellow (parietal lobe) → Green (frontal lobe). --- ### Detailed Analysis #### Knowledge Recall - **Text**: "The formula is (part/whole)×100%." - **Brain Diagram**: Frontal lobe highlighted. - **Hippocampus**: Labeled in the diagram. #### Semantic Understanding - **Text**: "The part is 120 and the whole is 90." - **Brain Diagram**: Temporal lobe highlighted. - **Hippocampus**: Labeled in the diagram. #### Math - **Text**: "Calculate 120 / 90 * 100% = 133 1/3%." - **Brain Diagram**: Parietal lobe highlighted. - **Hippocampus**: Labeled in the diagram. #### Decision Making - **Text**: "Option (A) corresponds to 133 1/3%." - **Brain Diagram**: Frontal lobe highlighted. - **Hippocampus**: Labeled in the diagram. #### Flowchart - **Arrows**: - Green (frontal lobe) → Orange (temporal lobe): Knowledge Recall → Semantic Understanding. - Orange (temporal lobe) → Yellow (parietal lobe): Semantic Understanding → Math. - Yellow (parietal lobe) → Green (frontal lobe): Math → Decision Making. --- ### Key Observations 1. **Correct Answer**: Option (A) 133 1/3% is selected in the Decision Making stage. 2. **Cognitive Flow**: The problem-solving process progresses sequentially from recalling the formula to applying it and making a decision. 3. **Brain Region Roles**: - Frontal lobe: Involved in formula recall and final decision. - Temporal lobe: Processes semantic understanding of "part" and "whole." - Parietal lobe: Handles mathematical computation. - Hippocampus: Consistently present, suggesting memory integration across stages. --- ### Interpretation The flowchart demonstrates how solving a percentage problem engages distributed neural networks: - **Frontal Lobe**: Critical for both retrieving prior knowledge (formula) and making final decisions. - **Temporal Lobe**: Specializes in contextual understanding of numerical relationships. - **Parietal Lobe**: Dedicated to arithmetic operations. - **Hippocampus**: Acts as a hub for integrating memory across stages. The color-coded arrows in the flowchart reinforce the hypothesis that problem-solving is a modular process, with distinct brain regions handling specific cognitive tasks. The correct answer (A) emerges from this coordinated neural activity, emphasizing the interplay between memory, comprehension, computation, and decision-making. </details> Figure 1: To solve a complex question, the human brain engages multiple regions to perform distinct cognitive functions necessary for generating a response. We explore whether there are specific attention heads in LLM play functional roles in producing answers. In parallel, prompting techniques like chain-of-thought (CoT) cot have been shown to improve LLM performance by decomposing complex problems into intermediate steps, a strategy reminiscent of human problem-solving, like the example in Figure 1. We hypothesize that such prompting may activate and coordinate specialized components within the model. Thus, analyzing the behavior of attention heads under CoT reasoning could contribute insights for a deeper understanding of the internal workings of LLMs and how they process complex tasks. In this work, we present a novel interpretability framework to systematically analyze the cognitive roles of attention heads during complex reasoning. To facilitate this, we introduce Cognitive Question&Answering (CogQA), a benchmark dataset that decomposes natural language questions into structured subquestions annotated with fine-grained cognitive functions, such as retrieval, logical inference, and knowledge recall. Leveraging CogQA, we develop a multi-class probing method to identify and characterize attention heads responsible for distinct cognitive operations within the transformer architecture. We conduct extensive experiments on three major LLM families, including LLaMA (touvron2023llama), Qwen (yang2024qwen2), and Yi (young2024yi). Our results reveal the existence of cognitive heads that consistently exhibit universality, sparsity, and layered functional organization across architectures. Further analysis of the correlations among these cognitive heads reveals clear functional clustering, with heads grouping based on cognitive roles, and uncovers a hierarchical structure in which lower-level heads modulate higher-level ones—mirroring the modular and distributed processing observed in the human cortex (barsalou2014cognitive; ono2022bidirectional). Furthermore, we validate the functional importance of these heads by showing that their removal degrades performance on complex tasks and leads to specific error patterns, while their enhancement improves reasoning capabilities. Our findings shed light on the structured cognitive architecture embedded in LLMs and open avenues for function-aware model design and analysis. ## 2 CogQA In this section, we present a detailed account of our benchmark dataset CogQA’s construction and key characteristics. Although extensive existing benchmark collections span a wide array of NLP tasks, to our knowledge no resource explicitly evaluates LLM reasoning across diverse cognitive functions. To address this, we introduce CogQA, a dataset containing 570 main questions and 3,402 subquestions. Each example comprises a question, its answer, and an annotation specifying the cognitive function required for resolution. ### 2.1 Cognitive Function To systematically capture the cognitive processes involved in complex reasoning tasks, we categorize cognitive functions into two groups: low-level functions and high-order functions, inspired by established frameworks in cognitive science anderson2014rules; diamond2013executive. Low-level functions primarily involve information retrieval and linguistic analysis, while high-order functions engage more abstract reasoning, problem-solving, and decision-making. Detailed descriptions of these cognitive functions are provided in Appendix A.4. The low-level cognitive functions include: - Retrieval: locating relevant information from an external source or prior context. - Knowledge Recall: accessing stored factual or procedural knowledge from memory. - Semantic Understanding: interpreting the meaning of words, phrases, or concepts. - Syntactic Understanding: analyzing the grammatical structure of a sentence. The high-order cognitive functions include: - Mathematical Calculation: performing arithmetic or numerical operations. - Logical Reasoning: drawing conclusions based on formal logical relationships. - Inference: deriving implicit information that is not directly stated. - Decision-Making: selecting the best outcome among alternatives based on reasoning. This categorization reflects a natural progression from basic information processing to complex cognitive integration. Both the human brain and LLMs encompass a wide range of functional modules. Our focus in this work is specifically on reasoning-related cognitive functions. By identifying and organizing these eight core reasoning functions, we can more clearly examine how LLMs handle different types of thinking steps, in a way that is both systematic and easy to interpret. ### 2.2 Data Collections Based on our categorization of cognitive functions, we sampled 750 diverse questions from NLP reasoning benchmarks, selecting 150 examples from each of AQuA aqua, CREAK creak, ECQA ecqa, e-SNLI esnli, and GSM8K gsm8k. These datasets cover a range of reasoning types, including logical, mathematical, and commonsense reasoning. Using the CoT paradigm, we prompted GPT-4o hurst2024gpt to decompose each question into subquestions, each targeting a single cognitive function. The prompt encourages structured, step-by-step reasoning, with each subquestion being clear, answerable, and sequentially dependent. This yields a set of subquestion-answer-cognitive function (subQAC) triples for each QA pair: $\operatorname{subQACs}=\left\{\left(q_{i},a_{i},c_{i}\right)\right\}_{i=1}^{k}$ , where each contains a subquestion $q_{i}$ , its concise answer $a_{i}$ , and the corresponding cognitive function label $c_{i}$ . The prompt for generating subquestions and examples are list in Appendix A.4 and Appendix A.6, respectively. ### 2.3 Data Filtering and Annotation Recent advances have made it increasingly feasible to use LLMs for dataset construction, owing to their strong reasoning abilities and capacity to generate high-quality annotations at scale llm_annotate. Although our dataset is constructed automatically using an LLM to reduce manual effort, we implement a strict two-stage human verification pipeline to ensure data quality and mitigate hallucinations. In the first stage, three expert annotators independently assess whether the subquestions are logically structured and align with natural human reasoning. QA pairs with inconsistent or incoherent decompositions are filtered out. In the second stage, annotators verify and, if necessary, relabel the cognitive function associated with each subquestion to ensure alignment with the intended mental process. Finally, we validate the subanswers by cross-checking them using the GPT-o4-mini model o4mini2024, followed by human adjudication where discrepancies arise. Details of the annotation process and rubric can be found in Appendix A.5. This multi-step filtering ensures that each retained subQAC triple reflects a coherent, interpretable reasoning step grounded in core cognitive functions. After this refinement, our final dataset contains 570 main QA and 3,402 validated subQAC triplets. ## 3 Cognitive Function Detections Given the CogQA dataset, we aim to identify which attention heads in LLMs are associated with specific cognitive functions. We adopt a probing-based framework, a widely used interpretability technique in which an auxiliary classifier is trained to predict properties from intermediate model representations alain2016understanding; belinkov2022probing; tenney2019bert. We frame this as a multi-class classification task: for each cognitively annotated subquestion, we extract head activations (see Section 3.1), train classifier and compute importance scores to identify contributing heads (see Section 3.2). Unlike prior work focusing on a single-class, our method captures many-to-many relationships between heads and functions, enabling a more detailed analysis of functional specialization and overlap compared to prior single-class approaches. ### 3.1 Head Feature Extraction Given a large language model $\mathcal{M}$ , we generate an answer $a_{i}^{\mathcal{M}}$ for each subquestion $q_{i}$ derived from a main question $Q_{i}$ . To support coherent multi-step reasoning, we include preceding subquestions and their answers as contextual input, emulating the incremental reasoning process observed in human cognition. During inference, input tokens are embedded and processed through successive transformer layers. At each layer, attention and feedforward operations update the residual stream, which is ultimately decoded into token predictions. For each generated token $i$ , we extract attention head outputs $X_{i}=\{x_{l}^{m}(i)\mid l=1,\dots,L,\ m=1,\dots,M\}$ across all layers, where $x^{m}_{l}$ denotes the value vector from the $m$ -th head in layer $l$ projected into the residual stream, with $M$ the number of heads per layer and $L$ the total number of layers. Let $N_{t}$ denote the number of tokens in the generated answer $a_{i}^{\mathcal{M}}$ . To isolate semantically informative content relevant to reasoning, we select the top- $k$ most important tokens, We include an ablation study in Appendix A.9 to analyze the impact of using alternative token positions. determined by prompting GPT-o4-mini o4mini2024 (skilled in reasoning), yielding an index set $\mathcal{I}_{k}$ with $|\mathcal{I}_{k}|=k$ (Top- $k$ ( $k=5$ ) token examples are in Appendix A.10). For each index $j\in\mathcal{I}_{k}$ , we extract the corresponding attention head activations $X_{j}$ , and compute the averaged activation feature for the $m$ -th head in layer $l$ as $\bar{x}_{l}^{m}=\frac{1}{k}\sum_{j\in\mathcal{I}_{k}}x_{l}^{m}(j)$ . This results in a full set of head-level features $\bar{X}=\{\bar{x}_{l}^{m}\mid l={1,\ldots,L},\ m={1,\ldots,M}\}$ . Given prior findings suggesting that cognitive functions may vary by layer depth zheng2409attention, we incorporate layer-wise information by computing the average activation $\bar{x}_{l}=\frac{1}{M}\sum_{m=1}^{M}\bar{x}_{l}^{m}$ for each layer. We then augment each head-level vector with its corresponding layer summary, resulting in enriched features $\bar{x}^{m^{\prime}}_{l}=[\bar{x}^{m}_{l};\bar{x}_{l}]$ . For each subQA triplet $(q_{i},\ a_{i},\ c_{i})$ , the final input to the probing classifier is given by $\{\bar{x}^{m^{\prime}}_{l}\mid l={1,\ldots,L},\ m={1,\ldots,M}\}$ . ### 3.2 Heads Importance For the CogQA dataset with $N$ subQA pairs, we collect all activations to construct the probing dataset: $$ \mathcal{D}_{\text{probe}}=\left\{(\bar{x}^{m^{\prime}}_{l},\ c)_{i}\right\}_{i=1}^{N},l\in\{1,\ldots,L\},\ m\in\{1,\ldots,M\} \tag{1} $$ We split the dataset into training and validation sets with a $4{:}1$ ratio. Each attention head feature is first passed through a trainable linear projection for dimensionality reduction, followed by a two-layer MLP that performs multi-class classification over cognitive functions (training details are provided in Appendix A.3). To interpret the contribution of individual heads to each function, we use a gradient-based attribution method. Specifically, for each function class $c$ , we compute the contribution of each head feature via the gradient $\times$ activation technique: $$ I^{(c)}_{j}=\mathbb{E}_{(\bar{x},c)\sim\mathcal{D}_{\text{probe}}}\left[\frac{\partial\hat{y}_{c}}{\partial\bar{x}_{j}}\cdot\bar{x}_{j}\right], \tag{2} $$ where $\bar{x}_{j}$ is the $j$ -th head input feature, and $\hat{y}_{c}$ is the classifier’s predicted logit for class $c$ . This yields an importance score for each attention head with respect to each cognitive function. We aggregate the scores into a matrix $\mathbf{I}\in\mathbb{R}^{C\times(L\cdot M)}$ , where each row corresponds to a function class and each column to a specific head in a specific layer. We hypothesize that attention heads with higher importance scores contribute more significantly to each cognitive function. By ranking heads according to their importance, we can identify which heads and layers are specialized for specific functions. Subsequent targeted interventions on these heads validate the effectiveness of this approach. ## 4 Experiments We conduct a series of experiments on three LLM families across various model scales, including LLaMA touvron2023llama (Llama3.1-8B-instruct and Llama3.2-3B-instruct), Qwen yang2024qwen2 (Qwen3-8B and Qwen3-4B), and Yi young2024yi (Yi1.5-9B and Yi1.5-6B). Our goal is to identify cognitive attention heads associated with specific reasoning functions and evaluate their roles via targeted interventions. By selectively masking these heads, we assess their functional significance in supporting downstream performance. We evaluate our method in terms of functional alignment, consistency across models, and causal impact on reasoning tasks. Results confirm the existence of sparse, function-specific heads and highlight their critical contribution to structured cognitive processing within LLMs. ### 4.1 Properties of Cognitive Heads <details> <summary>x2.png Details</summary>  ### Visual Description ## Heatmap: Neural Network Head Importance Across Cognitive Tasks ### Overview The image displays a composite heatmap visualization of neural network head importance across 30 layers and 30 heads for eight cognitive tasks. Each panel represents a different task (e.g., Knowledge Recall, Logical Reasoning), with color intensity indicating the magnitude of head importance (0.0000 to 0.0030+). The visualization reveals spatial patterns of activation across layers and heads for each task. ### Components/Axes - **X-axis (Head)**: 0–30 heads, labeled sequentially - **Y-axis (Layer)**: 0–30 layers, labeled sequentially - **Legend**: Color scale from dark purple (0.0000) to bright yellow (0.0030+) - **Panels**: 8 task-specific heatmaps arranged in 2 rows (4 per row) - Top row: Knowledge Recall, Retrieval, Logical Reasoning, Decision-making - Bottom row: Semantic Understanding, Syntactic Understanding, Inference, Math Calculation ### Detailed Analysis 1. **Knowledge Recall** (Top-left) - Bright yellow spots (0.0025–0.0030+) concentrated in: - Layers 12–18, Heads 6–12 - Layer 24, Heads 18–24 - Gradual darkening toward layer 30 2. **Retrieval** (Top-center) - High importance (0.0020–0.0025) in: - Layers 15–20, Heads 9–15 - Layer 25, Heads 12–18 - Faint diagonal gradient from top-left to bottom-right 3. **Logical Reasoning** (Top-right) - Clustered activation (0.0020–0.0025) in: - Layers 10–15, Heads 3–9 - Layer 22, Heads 15–21 - Sparse activation in lower layers (<5) 4. **Decision-making** (Top-rightmost) - Broad activation (0.0015–0.0020) across: - Layers 18–25, Heads 10–20 - Notable outlier: Layer 6, Head 24 (0.0028) 5. **Semantic Understanding** (Bottom-left) - Diffuse activation (0.0010–0.0015) in: - Layers 8–20, Heads 5–15 - Weakest signal in layer 30 (all <0.0005) 6. **Syntactic Understanding** (Bottom-center) - Concentrated activation (0.0018–0.0022) in: - Layers 12–18, Heads 7–13 - Layer 24, Heads 16–22 - Layer 30 shows sporadic activation (0.0010–0.0015) 7. **Inference** (Bottom-rightmost) - High importance (0.0025–0.0030) in: - Layers 15–20, Heads 10–16 - Layer 27, Heads 18–24 - Layer 5 shows unexpected activation (0.0018) 8. **Math Calculation** (Bottom-right) - Clustered activation (0.0020–0.0025) in: - Layers 10–15, Heads 4–10 - Layer 22, Heads 14–20 - Layer 30 shows minimal activation (<0.0005) ### Key Observations - **Layer-specific patterns**: Higher layers (20–30) show stronger activation for complex tasks (Logical Reasoning, Decision-making) - **Head specialization**: Heads 6–12 and 15–21 consistently show higher importance across multiple tasks - **Task differentiation**: Math Calculation and Logical Reasoning show more localized activation than Semantic Understanding - **Anomalies**: - Layer 6 Head 24 in Decision-making (0.0028) exceeds general trend - Layer 5 Head 10 in Inference (0.0018) appears out of pattern ### Interpretation The heatmaps suggest a hierarchical organization of cognitive processing: 1. **Lower layers** (0–10) show broad activation for basic tasks (Retrieval, Semantic Understanding) 2. **Mid-layers** (10–20) demonstrate specialized activation for complex tasks (Logical Reasoning, Inference) 3. **Higher layers** (20–30) show concentrated activation for advanced tasks (Decision-making, Math Calculation) The spatial patterns indicate that specific heads develop specialized roles across layers, with some heads (e.g., 6–12, 15–21) showing cross-task importance. The anomaly in Layer 6 Head 24 for Decision-making suggests either an outlier in training data or a unique neural pathway for rapid decision processes. The gradual darkening in higher layers for basic tasks implies efficient resource allocation, with complex tasks requiring deeper network engagement. </details> Figure 2: The existence of cognitive heads in Llama3.1-8B-instruct responsible for eight distinct functions in complex reasoning tasks. The x-axis represents the head index, while the y-axis indicates the layer index. Our analysis reveals that cognitive head importance in large language models exhibits three key properties: sparsity and universality, and layered functional organization. To illustrate these characteristics, we present the heatmap of attention head importance scores across eight cognitive functions in Llama3.1-8B-instruct (Figure 2). Sparsity and Universality: As shown in Figure 2, each cognitive function activates only a small number of high-importance attention heads, revealing a strikingly sparse pattern. In Llama3.1-8B-instruct, fewer than 7% of all heads have importance scores above 0.001 across the eight functions, suggesting that only a compact subset of heads meaningfully contribute to task performance. This sparsity is not uniform: Retrieval contains the highest proportion of salient heads (6.45% exceeding 0.01), while Inference has the fewest (3.42%). These results highlight that LLMs rely on highly specialized, localized components for different cognitive abilities. Importantly, we observe that this sparse functional organization is consistent across different model architectures and sizes. Additional heatmaps for five other models are provided in Appendix A.1, supporting the universality of this phenomenon. Layered Functional Organization: In addition to sparsity, attention heads show a structured distribution across model layers. Retrieval-related heads cluster primarily in the middle layers, while math-related heads appear more frequently in higher layers. This structured, task-dependent localization points to an emergent modular organization, where different layers support distinct cognitive operations. Further, we identify cognitive heads by selecting those before the elbow point of each function’s descending importance curve (Appendix A.2), and find notable variation in head counts across functions (Appendix A.8). For example, in the LLaMA family, mathematical calculation requires fewer heads (59 in Llama3.1-8B-Instruct, 35 in Llama3.2-3B-Instruct), while inference draws on substantially more (139 and 98, respectively), reflecting differences in representational and computational complexity. Table 1: Intervention results (%) of cognitive heads vs. random heads across 8 cognitive functions: Retrieval, Knowledge Recall, Semantic Understanding, Syntax Understanding, Math Calculation, Inference, Logic Reasoning, and Decision Making. Lower values indicate more effective intervention outcomes, suggesting that the corresponding heads play a greater role in the cognitive function. | Model | Inter_Head | Information Extraction and Analysis Functions | Higher-Order Processing Functions | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Retrieval | Recall | Semantic | Syntactic | Math | Inference | Logic | Decision | | | | | | | | | | | | comet | acc | comet | acc | comet | acc | comet | acc | comet | acc | comet | acc | comet | acc | comet | acc | | | | Llama3.1-8B | random | 90.83 | 84.71 | 87.85 | 83.84 | 91.44 | 97.50 | 87.81 | 66.17 | 94.25 | 83.08 | 91.90 | 70.18 | 91.39 | 54.69 | 97.64 | 90.91 | | cognitive | 44.96 | 8.24 | 56.93 | 38.38 | 81.98 | 75.00 | 69.20 | 40.00 | 87.81 | 66.17 | 76.65 | 52.63 | 52.07 | 4.69 | 56.02 | 4.55 | | | Llama3.2-3B | random | 87.89 | 86.47 | 76.35 | 68.69 | 90.54 | 90.00 | 75.82 | 40.00 | 94.98 | 69.65 | 95.66 | 85.96 | 92.75 | 76.56 | 93.30 | 81.82 | | cognitive | 49.47 | 17.06 | 49.69 | 13.13 | 52.29 | 10.00 | 43.62 | 0.00 | 92.01 | 80.10 | 53.60 | 7.02 | 46.69 | 0.00 | 49.25 | 0.00 | | | Qwen3-8B | random | 92.81 | 75.29 | 89.90 | 53.54 | 92.73 | 42.50 | 88.60 | 80.00 | 92.69 | 60.20 | 94.45 | 24.56 | 94.15 | 20.31 | 96.52 | 31.82 | | cognitive | 59.19 | 38.24 | 64.81 | 30.30 | 85.95 | 47.50 | 46.26 | 0.00 | 89.29 | 53.23 | 72.77 | 35.09 | 87.61 | 21.88 | 83.17 | 54.55 | | | Qwen3-4B | random | 94.17 | 84.71 | 84.61 | 77.78 | 86.91 | 77.50 | 98.15 | 80.00 | 87.15 | 44.78 | 96.89 | 87.72 | 92.00 | 75.00 | 94.79 | 72.73 | | cognitive | 80.13 | 64.71 | 63.10 | 35.35 | 65.95 | 60.00 | 46.25 | 0.00 | 82.40 | 46.27 | 84.88 | 64.91 | 82.79 | 39.06 | 45.49 | 13.64 | | | Yi-1.5-9B | random | 86.83 | 79.41 | 82.02 | 54.55 | 77.40 | 35.00 | 81.53 | 60.00 | 76.04 | 36.32 | 89.83 | 36.84 | 87.53 | 42.19 | 86.27 | 63.64 | | cognitive | 52.76 | 21.76 | 45.99 | 9.09 | 47.25 | 2.50 | 48.10 | 40.00 | 54.22 | 16.92 | 52.41 | 15.79 | 82.75 | 26.56 | 62.85 | 18.18 | | | Yi-1.5-6B | random | 80.64 | 69.41 | 68.82 | 38.38 | 77.83 | 55.00 | 69.61 | 60.00 | 73.33 | 43.78 | 77.71 | 22.81 | 81.65 | 29.69 | 88.54 | 72.73 | | cognitive | 49.90 | 15.29 | 68.23 | 41.41 | 49.54 | 2.50 | 42.92 | 0.00 | 76.64 | 43.78 | 68.53 | 14.04 | 44.94 | 0.00 | 86.28 | 50.00 | | <details> <summary>x3.png Details</summary>  ### Visual Description ## Line Graphs: Accuracy Metrics vs. Masked Heads ### Overview The image contains four line graphs comparing accuracy metrics across four tasks (Retrieval, Knowledge Recall, Math Calculation, Inference) as the number of masked heads increases (16, 32, 64, 128). Each graph tracks four metrics: TopK Accuracy (solid blue), RandomK Accuracy (dashed blue), TopK Comet (solid red), and RandomK Comet (dashed red). Scores range from 0 to 1.0. ### Components/Axes - **X-axis**: "# Masked Heads" (16, 32, 64, 128) - **Y-axis**: "Score" (0.0 to 1.0) - **Legends**: - Top-left: TopK Accuracy (solid blue), RandomK Accuracy (dashed blue), TopK Comet (solid red), RandomK Comet (dashed red) - **Subplots**: - Top-left: Retrieval - Top-right: Knowledge Recall - Bottom-left: Math Calculation - Bottom-right: Inference ### Detailed Analysis #### Retrieval - **TopK Accuracy**: Starts at ~0.95 (16 masked heads), drops sharply to ~0.8 (32), ~0.6 (64), and ~0.2 (128). - **RandomK Accuracy**: Remains stable (~0.8) across all masked heads. - **TopK Comet**: Declines gradually from ~0.95 to ~0.75. - **RandomK Comet**: Stable (~0.85) with minor fluctuations. #### Knowledge Recall - **TopK Accuracy**: Starts at ~0.9, drops to ~0.7 (32), ~0.5 (64), and ~0.3 (128). - **RandomK Accuracy**: Stable (~0.8) with a slight dip at 64 (~0.75). - **TopK Comet**: Declines from ~0.9 to ~0.6. - **RandomK Comet**: Stable (~0.85). #### Math Calculation - **TopK Accuracy**: Starts at ~0.95, drops to ~0.8 (32), ~0.6 (64), and ~0.4 (128). - **RandomK Accuracy**: Stable (~0.85) with a minor dip at 64 (~0.8). - **TopK Comet**: Declines from ~0.95 to ~0.75. - **RandomK Comet**: Stable (~0.85). #### Inference - **TopK Accuracy**: Starts at ~0.9, drops to ~0.7 (32), ~0.6 (64), and ~0.4 (128). - **RandomK Accuracy**: Stable (~0.85) with a slight dip at 64 (~0.8). - **TopK Comet**: Declines from ~0.9 to ~0.75. - **RandomK Comet**: Stable (~0.85). ### Key Observations 1. **TopK metrics degrade sharply** as masked heads increase, especially in Retrieval and Math Calculation. 2. **RandomK metrics remain stable** across all tasks and masked heads, suggesting robustness. 3. **TopK Comet** consistently outperforms RandomK Comet in Retrieval and Math Calculation but underperforms in Knowledge Recall and Inference. 4. **RandomK Comet** maintains near-constant performance (~0.85) across all tasks. ### Interpretation The data suggests that **TopK methods are sensitive to masked heads**, with performance collapsing as masking increases. In contrast, **RandomK methods show resilience**, maintaining stable scores regardless of masking. The Comet metrics (TopK/RandomK) appear more robust than Accuracy metrics, particularly in Knowledge Recall and Inference. This implies that Comet-based evaluations might better capture task-specific nuances under varying masking conditions. The sharp decline in TopK Accuracy for Retrieval and Math Calculation at 128 masked heads highlights a critical vulnerability in these methods when extensive masking is applied. </details> Figure 3: The performance of Llama3.1-8B-instruct by masking out top K cognitive heads vs K random heads on retrieval, knowledge recall, math calculation, and inference. ### 4.2 Functional Contributions of Cognitive Heads After identifying the cognitive heads associated with each function, we examine their functional roles by evaluating the model’s behavior on the CogQA test set under targeted interventions. We perform head ablation by scaling the output of a specific attention head with a small factor $\epsilon$ (e.g., 0.001), effectively suppressing its contribution: $$ x_{i}^{\text{mask}}=\operatorname{Softmax}\left(\frac{W_{q}^{i}W_{k}^{iT}}{\sqrt{d_{k}/n}}\right)\cdot\epsilon W_{v}^{i} \tag{3} $$ Specifically, we compare model performance when masking identified cognitive heads versus masking an equal number of randomly selected heads. To quantify the impact of masking, we use several standard evaluation metrics including COMET rei2020comet, BLEU papineni2002bleu, ROUGE chin2004rouge, and semantic similarity to compare the model’s outputs before and after intervention. We define an output as unaffected if the BLEU score exceeds 0.8, or either the ROUGE or semantic similarity scores surpass 0.6, and compute accuracy accordingly. As shown in Table 1, masking cognitive heads leads to a significant decline in performance, whereas masking an equal number of random heads results in only marginal degradation across all LLMs. In some cases, masking the identified cognitive heads causes the accuracy to drop to zero, indicating that the model cannot execute the corresponding function without them. This sharp contrast highlights the essential role cognitive heads play in enabling specific reasoning capabilities. To further validate the functional specialization, we conduct experiments where we mask the retrieval heads during the evaluation of knowledge recall (Recall), and conversely, mask knowledge recall heads during the evaluation of retrieval performance. The results in Table 2 show that masking the corresponding cognitive heads causes a significantly larger performance drop than masking others. Table 2: Intervention results (%) of different cognitive heads and random heads across Retrieval and Knowledge Recall functions. | Llama3.1-8B Llama3.1-8B Llama3.1-8B | random retrieval recall | 90.83 44.96 86.79 | 84.71 8.24 75.29 | 87.85 72.05 56.93 | 83.84 33.33 38.38 | | --- | --- | --- | --- | --- | --- | | Qwen3-8B | random | 92.81 | 75.29 | 89.90 | 53.54 | | Qwen3-8B | retrieval | 59.19 | 38.24 | 79.26 | 57.58 | | Qwen3-8B | recall | 83.31 | 71.18 | 64.81 | 30.30 | We further investigate the performance of model under different numbers of masked attention heads. As shown in Figure 3, increasing the number of randomly masked heads has minimal impact on overall performance of Llama3.1-8B-instruct. In contrast, masking cognitive heads results in a significant drop in performance across various functions. Notably, masking heads associated with Retrieval and Knowledge Recall causes a pronounced degradation in their respective functions, whereas functions such as Math Calculation and Inference exhibit more resilience. This suggests that certain cognitive functions depend more heavily on specific, distinguishable attention heads, while others are distributed more broadly across the model. ### 4.3 Relationship Among Cognitive Heads While cognitive heads are specialized for distinct functions, understanding their relationships is crucial for revealing how complex reasoning emerges from their cooperation. Functional Clustering: Inspired by neuroscience findings that related cognitive functions localize in overlapping brain regions (e.g., prefrontal cortex for reasoning and inference barsalou2014cognitive), we investigate whether LLM attention heads show similar patterns. We rank each head’s importance across eight cognitive functions, form ranking vectors, and apply principal component analysis (PCA) to visualize their organization (Figure 4). The results reveal clear clustering: heads linked to reasoning, inference, and decision-making group closely, while those related to mathematical computation form a distinct cluster in Llama and Qwen, and lie adjacent to reasoning heads in Yi. Lower-level functions also show moderate clustering. These patterns suggest a modular functional architecture in LLMs akin to that in the human brain. <details> <summary>x4.png Details</summary>  ### Visual Description ## Scatter Plot: Principal Component Analysis of Cognitive Tasks ### Overview The image is a scatter plot visualizing the distribution of cognitive tasks across two principal components (PC1 and PC2). Points are labeled with task names, and their positions reflect their relative scores on the principal components. The plot uses a grid of dotted lines for spatial reference. ### Components/Axes - **X-axis (PC1)**: Labeled "PC 1" with no numerical scale. - **Y-axis (PC2)**: Labeled "PC 2" with no numerical scale. - **Data Points**: Blue circular markers with labels for each task. - **Grid**: Dotted lines forming a Cartesian coordinate system. ### Detailed Analysis 1. **Task Labels and Positions**: - **Math**: Top-right quadrant (high PC1, high PC2). - **Decision**: Upper-middle quadrant (moderate PC1, high PC2). - **Inference**: Left-middle quadrant (low PC1, high PC2). - **Logical**: Left-middle quadrant (low PC1, moderate PC2). - **Semantic**: Lower-left quadrant (low PC1, low PC2). - **Retrieval**: Lower-left quadrant (moderate PC1, low PC2). - **Syntactic**: Center-left quadrant (moderate PC1, moderate PC2). - **Recall**: Bottom-right quadrant (high PC1, low PC2). 2. **Spatial Distribution**: - Points are spread across the plot, with no strict clustering. - "Math" and "Decision" occupy the upper-right region, suggesting higher scores on both PC1 and PC2. - "Recall" is isolated in the bottom-right, indicating high PC1 but low PC2. - "Inference" and "Logical" cluster in the upper-left, sharing high PC2 but lower PC1. - "Semantic" and "Retrieval" are in the lower-left, with lower scores on both axes. - "Syntactic" is centrally located, reflecting moderate values on both components. ### Key Observations - **Outliers**: "Recall" is the only point in the bottom-right quadrant, distinct from other tasks. - **Trends**: - Tasks like "Math" and "Decision" show elevated scores on both principal components. - "Inference" and "Logical" share high PC2 but differ in PC1. - "Semantic" and "Retrieval" cluster in the lower-left, suggesting similar underlying factors. - **Grid Alignment**: All points align with the grid, but no numerical values are provided for PC1/PC2. ### Interpretation This scatter plot likely represents a Principal Component Analysis (PCA) of cognitive or linguistic tasks, reducing multidimensional data to two axes. The positions of labeled points suggest: - **PC1** may capture factors like computational complexity or memory demand (e.g., "Math" and "Recall" have high PC1). - **PC2** might reflect aspects like reasoning or syntactic processing (e.g., "Inference" and "Logical" have high PC2). - The distribution implies that tasks like "Math" and "Decision" share overlapping characteristics in both dimensions, while "Recall" is distinct in its PC1 dominance. The lack of numerical scales limits precise quantification, but the relative positions highlight potential groupings or contrasts among tasks. </details> (a) Llama3.1-8B <details> <summary>x5.png Details</summary>  ### Visual Description ## Scatter Plot: Principal Component Analysis of Cognitive/Linguistic Categories ### Overview The image is a 2D scatter plot visualizing the distribution of cognitive/linguistic categories across two principal components (PC1 and PC2). Eight labeled data points are plotted, with positions indicating their relative relationships in the reduced-dimensional space. ### Components/Axes - **X-axis (PC1)**: Represents the first principal component, capturing the greatest variance in the data. - **Y-axis (PC2)**: Represents the second principal component, capturing the second greatest variance. - **Data Points**: Labeled directly on the plot (no separate legend). Colors are uniform (blue), with no gradient or categorical differentiation. ### Detailed Analysis 1. **Math**: Positioned at the top-left quadrant (high PC2, low PC1). 2. **Retrieval**: Located at the bottom-left (low PC2, low PC1). 3. **Syntactic**: Clustered near the center-left (moderate PC1, moderate PC2). 4. **Recall**: Slightly above Syntactic (moderate PC1, slightly higher PC2). 5. **Decision**: Positioned mid-right (higher PC1, moderate PC2). 6. **Semantic**: Near the bottom-right (high PC1, low PC2). 7. **Logical**: Top-right quadrant (high PC1, high PC2). 8. **Inference**: Furthest top-right (highest PC1 and PC2). ### Key Observations - **Clustering**: - "Logical" and "Inference" dominate the top-right, suggesting strong alignment with both PC1 and PC2. - "Retrieval" and "Math" occupy extreme left positions, indicating low PC1 but differing PC2 values. - "Semantic" and "Decision" form a mid-right cluster, emphasizing PC1 dominance. - **Spread**: - PC1 ranges from ~-3 (Retrieval) to ~+3 (Inference). - PC2 ranges from ~-2 (Semantic) to ~+3 (Math/Inference). - **Outliers**: - "Math" is isolated in the top-left, distinct from other categories. - "Semantic" is the only point in the bottom-right quadrant. ### Interpretation The plot suggests that the first principal component (PC1) primarily distinguishes between **logical/reasoning-oriented categories** (e.g., Logical, Inference) and **memory/retrieval-focused categories** (e.g., Retrieval, Recall). The second principal component (PC2) appears to separate **analytical categories** (Math, Inference) from **semantic/linguistic categories** (Semantic, Syntactic). Notably, "Decision" bridges the mid-right cluster, potentially indicating a hybrid role in both logical reasoning and semantic processing. The isolation of "Math" in the top-left may reflect its unique relationship to abstract reasoning (high PC2) while remaining distinct from other categories in PC1. This visualization highlights how cognitive tasks vary along orthogonal dimensions of processing, with potential implications for understanding task-specific neural or computational mechanisms. </details> (b) Qwen3-4B <details> <summary>x6.png Details</summary>  ### Visual Description ## Scatter Plot: Cognitive Function Distribution in Principal Component Space ### Overview The image depicts a 2D scatter plot visualizing the distribution of cognitive functions across two principal components (PC1 and PC2). The plot uses blue circular markers to represent labeled cognitive functions, with a dotted grid overlay for reference. No explicit legend is present, but labels are directly annotated on the data points. ### Components/Axes - **X-axis (PC1)**: Principal Component 1, ranging approximately from -10 to +10 (inferred from grid spacing). - **Y-axis (PC2)**: Principal Component 2, ranging approximately from -10 to +10. - **Grid**: Dotted lines at regular intervals (likely 2-unit increments) for spatial reference. - **Labels**: Directly placed on data points, representing cognitive functions (see "Content Details" below). ### Detailed Analysis #### Labeled Data Points and Positions 1. **Syntactic**: Bottom-left quadrant (PC1 ≈ -8, PC2 ≈ -8). 2. **Semantic**: Slightly right and above Syntactic (PC1 ≈ -6, PC2 ≈ -6). 3. **Retrieval**: Middle-left quadrant (PC1 ≈ -4, PC2 ≈ 4). 4. **Inference**: Upper-left quadrant (PC1 ≈ -2, PC2 ≈ 8). 5. **Decision**: Near Inference but slightly rightward (PC1 ≈ 0, PC2 ≈ 10). 6. **Logical**: Top-right quadrant (PC1 ≈ 8, PC2 ≈ 10). 7. **Math**: Middle-right quadrant (PC1 ≈ 6, PC2 ≈ 6). 8. **Recall**: Bottom-right quadrant (PC1 ≈ 10, PC2 ≈ -8). #### Spatial Distribution - **Upper-left cluster**: Inference, Decision, and Retrieval form a diagonal band from bottom-left to top-right. - **Lower-right cluster**: Recall and Syntactic occupy the lower-left and lower-right corners. - **Upper-right outlier**: Logical is isolated in the top-right quadrant. - **Middle-right**: Math sits between Retrieval and Recall. ### Key Observations 1. **Dimensional Spread**: PC1 and PC2 capture significant variance, with cognitive functions distributed across the full range of both axes. 2. **Clustering Patterns**: - **Left-side dominance**: Syntactic, Semantic, and Retrieval cluster in the left half (PC1 < 0). - **Right-side diversity**: Math, Logical, and Recall occupy the right half (PC1 > 0). 3. **Vertical Extremes**: - Highest PC2 value: Decision (PC2 ≈ 10). - Lowest PC2 value: Recall (PC2 ≈ -8). 4. **Diagonal Relationships**: - Inference → Decision → Logical follows a northeast trajectory. - Syntactic → Semantic → Retrieval follows a northwest trajectory. ### Interpretation This PCA plot reveals how cognitive functions vary along two orthogonal dimensions of cognitive processing: 1. **Horizontal Axis (PC1)**: Likely represents a spectrum from **analytical/abstract** (right: Logical, Math) to **contextual/linguistic** (left: Syntactic, Semantic). 2. **Vertical Axis (PC2)**: Appears to distinguish **procedural/executive functions** (top: Decision, Inference) from **memory/retrieval processes** (bottom: Recall, Retrieval). The diagonal clusters suggest interrelated cognitive processes: - **Top-left to bottom-right**: Functions like Inference and Decision may share procedural/executive components but differ in memory integration (Retrieval vs. Recall). - **Bottom-left to top-right**: Syntactic processing may evolve into higher-order functions like Decision through semantic integration. Notably, **Logical** stands apart in the top-right, indicating it may represent a unique cognitive domain combining analytical reasoning (high PC1) with executive control (high PC2). The plot underscores the multidimensional nature of cognition, with no single axis capturing all variance. </details> (c) Yi-1.5-6B Figure 4: PCA visualization of the 8 function heads’ clustering in three models. Table 3: Study on the influence of low-level cognitive heads for high-order function on Llama3.1-8B-instruct. 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}\pgfsys@transformcm{1.0}{0.0}{0.0}{1.0}{2.84526pt}{3.36821pt}\pgfsys@invoke{ }\hbox{{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}\hbox{\minipage[b]{22.76222pt}\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}\ignorespaces\centering\ignorespaces{\text{ 0.00}}\@add@centering\endminipage}}}\pgfsys@invoke{ }\pgfsys@endscope}\pgfsys@invoke{ }\pgfsys@endscope{}{}{}\hss}\pgfsys@discardpath\pgfsys@invoke{ }\pgfsys@endscope\hss}}\endpgfpicture}}\par}$ | Hierarchical Structure: Human problem solving often involves hierarchical reasoning, where lower-level functions such as retrieval and comprehension support higher-level inference and decision-making. The CogQA dataset captures this structure through subquestions progressing from simple information extraction to complex reasoning. We test if LLMs reflect this hierarchy by masking attention heads tied to early-stage functions and measuring the effect on later tasks. For instance, to assess how Retrieval affects Math Calculation, we suppress Retrieval-related heads throughout the subquestions. Answers from earlier Retrieval are used as priors for later math reasoning, allowing us to observe how disrupting low-level functions can propagate and impair higher-level reasoning along the chain. As Table 3 shows, masking retrieval or knowledge recall heads causes significant performance drops in subsequent decision-making steps, whereas masking syntactic understanding heads has minimal impact. This provides evidence for an emergent hierarchical organization in LLMs, where foundational cognitive functions underpin advanced reasoning. ### 4.4 Influence of Cognitive Heads on Downstream Tasks In this section, we investigate how cognitive heads influence downstream tasks through both negative interventions (masking out cognitive function heads) and positive interventions (shifting heads toward specific functions). We conduct experiments on two tasks: a math task using 100 GSM8K samples (GSM8K_100) and a retrieval task with 49 samples from an extractive_QA dataset. The Extractive_QA pairs are generated by GPT-4o, with answers extracted directly from the source paragraph. Negative Intervention: We perform negative intervention by masking corresponding cognitive heads (Math Calculation heads for GSM8K_100 and Retrieval heads for Extractive_QA), effectively suppressing their activations. As shown in Table 4, this causes significant performance drops across models, confirming these heads’ functional roles. Notably, after masking, performance converges to a similarly low level across different LLMs, regardless of model size or original accuracy. This is expected, as the crucial cognitive heads responsible for specific functions are disabled, making it difficult for the model to arrive at correct answers. For math, the remaining 30% accuracy likely stems from two factors: (1) memorized answers in the base model, and (2) simple questions not requiring actual computation. For retrieval, masking Retrieval heads almost completely abolishes the model’s retrieval ability across all scales. This indicates that cognitive functions are indeed localized in a subset of heads, and masking them leads to a systematic degradation, irrespective of model capacity. The negative intervention example further shows that, masking the Math Calculation heads leads to errors in arithmetic tasks, while retrieval and language functions remain largely unaffected. This confirms that these cognitive heads are crucial for specific functions and highlights the robustness and generalizability of our method. Positive Intervention: We calculate the activation directions of different cognitive functions using the CogQA dataset. For each function, the activation direction of a head at layer $l$ and index $h$ is computed as: $$ \operatorname{dir}_{l}^{h}=\mathbb{E}_{i\in\mathcal{D}_{\text{correct }}}\left[x_{l}^{h}(i)\right]-\mathbb{E}_{i\in\mathcal{D}_{\text{incorrect }}}\left[x_{l}^{h}(i)\right] \tag{4} $$ where $x_{l}^{h}(i)$ denotes the activation of head at layer $l$ and index $h$ , and $\mathcal{D}_{\text{correct }}$ and $\mathcal{D}_{\text{incorrect }}$ represent the sets of samples answered correctly and incorrectly, respectively. Then we estimate the standard deviation of activations truthful along the cognitive function direction to be $\sigma_{l}^{h}$ , and shift original head activation as $x_{l}^{h}(i)\leftarrow x_{l}^{h}(i)+\alpha\sigma_{l}^{h}\operatorname{dir}_{l}^{h}$ , where $\alpha$ is a parameter. The experimental results in Table 4 show that enhancing the activation of retrieval heads along their corresponding functional directions leads to improved performance on the retrieval task. For the math task, questions often engage multiple cognitive functions. We observe cases where computations are correct but semantic understanding fails. By positively intervening on either Math Calculation or Semantic Understanding heads, performance consistently improves, highlighting the collaborative nature of cognitive functions in complex reasoning and the need for joint interventions—a direction we leave for future work. The example below illustrates a positive intervention on Math Calculation heads in Qwen3-4B: the model initially produces an incorrect answer (red) but generates the correct one (blue) after intervention. This demonstrates that adjusting cognitive head activations along their functional directions reliably enhances performance on complex reasoning tasks. Negative Intervention Case Query: Question: Solve -42*r + 27*c = -1167 and 130*r + 4*c = 372 for r. Original Output: Okay, so I need to solve this system of equations: -42r + 27c = -1167 and 130r + 4c = 372 … First equation: -42*4 + 27*(-37) = -168 - 999 = -1167. Correct. Second equation: 130*4 + 4*(-37) = 520 - 148 = 372. Correct. Yes, that’s right. So everything checks out. So I think that’s the correct answer. Therefore, r is 4. Negative Intervention (Math) Output: … To eliminate $c$ , I need the coefficients of $c$ in both equations to be the same (or negatives). The coefficients are 27 and 4. The least common multiple of 27 and 4 is 100? Wait, 27 is $3^{3}$ , and 4 is $2^{2}$ , so LCM is $2^{2}*3^{3}={\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}4*27=100}$ . So if I can make the coefficients of $c$ to be 100 and 100, or 27 and 4. Wait, but 27 and 4. So if I multiply the first equation by 4 and the second equation by 27, then the coefficients of $c$ would be 27*4 = 100 and 4*27 = 100. Then, if I subtract the equations, the $c$ terms would be 100 and 100, but since they are both positive, subtracting the equations would eliminate $c$ . … Positive Intervention Case Query: On a school trip to the seashore, Alan and his friends collected shells. Alan collected four times as many shells as Ben did. Ben got a late start and only collected a third of what Laurie did. If Laurie collected 36 shells how many did Alan collect? Original Output: Alan collected four times as many shells as Ben did, and Ben collected a third of what Laurie did. Since Laurie collected 36 shells, Ben collected 36 / 3 = 12 shells. Therefore, Alan collected 4 * 12 = 48 shells. However, the question asks for the number of shells Alan collected, and it is given that Alan collected four times as many shells as Ben did. Therefore, the correct answer is 4 * 12 = 48 * 4 / 3 = 72. Positive Intervention (Math) Output : …Since Ben collected a third of what Laurie did, he collected 36 / 3 = 12 shells. Alan collected four times as many shells as Ben did, so he collected 4 * 12 = 48 shells …The correct answer is 48 Table 4: The LLM performance on GSM8k_100 and Extractive_QA by Negative and Positive Intervention (Inter.). Math accuracy (%) is measured by exact answer match; Extractive_QA accuracy checks if the original paragraph answer appears in the response. | Dataset | Method | Head | Llama3.1-8B | Llama3.2-3B | Qwen3-8B | Qwen3-4B | | --- | --- | --- | --- | --- | --- | --- | | Extractive_QA | Base | - | 57.14 | 36.73 | 57.14 | 51.02 | | Negative Inter. | Retrieval | 0 | 0 | 14.29 | 12.24 | | | Positive Inter. | Retrieval | 63.26 | 44.90 | 61.22 | 69.38 | | | GSM8K_100 | Base | - | 82 | 64 | 94 | 91 | | Negative Inter. | Math | 38 | 34 | 34 | 37 | | | Positive Inter. | Math | 84 | 66 | 94 | 92 | | | Positive Inter. | Semantic | 84 | 65 | 94 | 93 | | ## 5 Related Works #### Neural Networks and the Brain Neural networks have long been studied as computational models of the brain, with early work linking artificial neurons to the biological mechanisms of perception and learning McCullochP90. Convolutional neural networks (CNNs), in particular, have been shown to capture representations similar to those in the visual cortex yamins2014performance, and more recent studies suggest that the functional modularity observed in deep networks gives rise to brain-like specialization (dobs2022brain) in vision task. More recently, LLMs have exhibited striking parallels with human brain activity during language processing. In particular, transformer-based models, such as GPT-2, produce internal representations that align with neural responses in language-selective brain regions caucheteux2022deep; schrimpf2021neural. However, prior work mostly focuses on perception and language representations, with limited study on higher-level cognitive functions like reasoning. We instead analyze LLMs’ behavior in complex reasoning tasks to explore their alignment with human cognitive functions and functional specialization. #### Functional Specialization of Attention Heads Recent years have witnessed growing interest in understanding the functional roles of attention heads in Transformer-based models, forming a core component of mechanistic interpretability research. Early work by clark2019does demonstrated that individual heads in BERT capture specific linguistic phenomena such as syntactic dependencies and coreference, indicating a degree of functional specialization. Building on this, voita2019analyzing proposed a pruning-based approach to identify important heads by measuring their contribution to downstream performance, showing that many heads are redundant. Subsequent studies extended this analysis to decoder-only large language models (LLMs). michel2019sixteen explored functional decomposition in such models, leading to the identification of distinct attention heads responsible for tasks such as pattern induction (induction), truthfulness (truthful), information retrieval (wu2404retrieval), and safety alignment (safety). For a broader survey, see zheng2409attention. Despite these advances, most prior work focuses on isolated heads and evaluates them in relatively simple or synthetic tasks. In contrast, we investigate functionally specialized heads under more complex reasoning settings by aligning attention head behavior with human cognitive functions. ## 6 Limitations and Future works While our study provides an initial framework for analyzing the cognitive functions of attention heads, several limitations remain. First, we focus on eight predefined cognitive functions, which, though representative, may not capture the full spectrum of LLM capabilities; future work could extend this taxonomy with finer-grained or emergent functions. Each subquestion in CogVision is annotated with a single cognitive function, though real reasoning may engage multiple functions. Similarly, we assume one head corresponds to one function, while in practice a head may support multiple functions, vary with context, or reflect hierarchical compositions. These complexities are not fully addressed in our current framework. Excluding subquestions with incorrect subanswers could improve multi-class probing, and further investigation is needed to understand heads serving multiple functions. Finally, our work emphasizes analysis over application, but identifying cognitively relevant heads could inform model design, including dynamic head activation, improved chain-of-thought prompting, targeted fine-tuning, or modular architectures—directions we leave for future exploration. ## 7 Conclusions We propose an interpretability framework that connects attention heads in large language models (LLMs) to human cognitive functions involved in reasoning. To support this, we introduce CogQA, a cognitively grounded dataset, along with a multi-class classification approach to identify specialized heads associated with specific reasoning tasks. Our analysis across multiple LLM families and scales demonstrates that attention heads exhibit universality, sparsity, intrinsic roles, and dynamic, hierarchical organization. These findings indicate that LLMs internally organize reasoning processes in a manner akin to human cognition, laying the groundwork for more interpretable and cognitively informed language models. ## Acknowledgements This work is partially supported by the following Australian Research Council (ARC) projects: FT220100318, DP220102121, LP220100527, LP220200949, DP230101534. ## NeurIPS Paper Checklist 1. Claims 1. Question: Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? 1. Answer: [Yes] 1. Justification: Yes, the main claims in the abstract and introduction accurately reflect the paper’s contributions and scope. 1. Guidelines: - The answer NA means that the abstract and introduction do not include the claims made in the paper. - The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. 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Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required. 1. Answer: [Yes] 1. Justification: We used LLMs as an integral part of our dataset construction process. Specifically, LLMs were used to generate intermediate reasoning steps and candidate answers under controlled prompting. All prompts, generation procedures, and filtering steps are clearly documented in the main paper and supplementary materials to ensure transparency and reproducibility. 1. Guidelines: - The answer NA means that the core method development in this research does not involve LLMs as any important, original, or non-standard components. - Please refer to our LLM policy (https://neurips.cc/Conferences/2025/LLM) for what should or should not be described. ## Appendix A Appendix ### A.1 The cognitive function distribution of other models We present the heatmaps for the remaining five models in this section. The results reveal a notable universality in the sparsity patterns of attention heads across different architectures. Moreover, models within the same family tend to exhibit similar sparsity distributions. For instance, Llama3.2-3B (Figure 5) and Llama3.1-8B (Figure 2) share comparable patterns, as do Qwen3-4B (Figure 7) and Qwen3-8B (Figure 6), as well as Yi-1.5-6B (Figure 9) and Yi-1.5-9B (Figure 8). This consistency is likely due to the shared architectural design and similar pretraining data within each model family. <details> <summary>x7.png Details</summary>  ### Visual Description ## Heatmap: Head Importance Across Cognitive Tasks ### Overview The image displays a composite heatmap visualization comparing neural activation patterns (measured by "Head Importance") across eight cognitive tasks. The visualization is organized into two rows of four panels, each representing a distinct cognitive domain. Color intensity (from dark purple to yellow) indicates the magnitude of head importance, with a logarithmic scale provided on the right. ### Components/Axes - **X-axis (Horizontal)**: "Head" (0-18), representing individual neural processing units - **Y-axis (Vertical)**: "Layer" (0-24), representing hierarchical processing depth - **Legend**: Color scale from 0.0000 (dark purple) to 0.0050+ (bright yellow), indicating head importance magnitude - **Panel Titles**: Eight cognitive tasks organized in two rows: - Top Row: Knowledge Recall, Retrieval, Logical Reasoning, Decision-making - Bottom Row: Semantic Understanding, Syntactic Understanding, Inference, Math Calculation - **Spatial Layout**: - Legend positioned right-aligned - Panels arranged in 2x4 grid (top row: cognitive tasks A-D, bottom row: E-H) - Color scale occupies 5% of total width on the right ### Detailed Analysis 1. **Knowledge Recall** (Top-Left): - Yellow squares concentrated at layers 6-12 and heads 6-12 - Peak importance: 0.0045 at layer 9, head 9 - Gradual decline to 0.0012 at layer 18, head 18 2. **Retrieval** (Top-Second): - Similar pattern to Knowledge Recall but with additional activation at layer 15, head 15 (0.0038) - Notable cluster at layers 12-18, heads 6-12 3. **Logical Reasoning** (Top-Third): - Sparse yellow squares at layers 8-10, heads 6-8 (0.0031) - Single outlier at layer 14, head 10 (0.0027) 4. **Decision-making** (Top-Right): - Broad activation across layers 6-12 and heads 6-18 - Peak at layer 9, head 12 (0.0041) - Extended tail to layer 15, head 15 (0.0023) 5. **Semantic Understanding** (Bottom-Left): - Minimal activation: single yellow square at layer 12, head 6 (0.0018) - Faint activation at layer 18, head 12 (0.0011) 6. **Syntactic Understanding** (Bottom-Second): - Concentrated activation at layers 6-8, heads 6-10 (0.0033) - Secondary cluster at layer 14, head 8 (0.0025) 7. **Inference** (Bottom-Third): - Diffuse activation across layers 10-16, heads 4-14 - Peak at layer 12, head 10 (0.0039) - Multiple secondary peaks at 0.0022-0.0028 8. **Math Calculation** (Bottom-Right): - Strong activation at layers 18-24, heads 6-12 - Peak at layer 21, head 9 (0.0047) - Secondary cluster at layer 19, head 12 (0.0035) ### Key Observations 1. **Task-Specific Activation**: - Math Calculation shows highest importance in upper layers (18-24) - Decision-making demonstrates broad mid-layer activation (6-12) - Semantic Understanding exhibits minimal activation overall 2. **Head-Layer Correlation**: - Strong diagonal patterns in Knowledge Recall and Retrieval suggest coordinated head-layer interactions - Math Calculation shows vertical columnar activation (fixed heads, varying layers) 3. **Importance Thresholds**: - 80% of yellow squares exceed 0.0020 importance - Only 5% reach the 0.0040+ threshold (bright yellow) ### Interpretation The visualization reveals distinct neural signatures for different cognitive tasks. Math Calculation and Decision-making demonstrate the most pronounced activation patterns, suggesting specialized neural circuitry for these functions. The diagonal activation patterns in Knowledge Recall and Retrieval imply distributed processing across both heads and layers. Notably, Semantic Understanding shows the least activation, potentially indicating either efficient processing or different neural representation strategies. The logarithmic scale emphasizes that even "low" importance values (0.0010-0.0020) represent significant neural activity when compared to baseline. These patterns align with theories of hierarchical neural processing, where complex tasks engage deeper layers and specialized head populations. </details> Figure 5: The existence of cognitive heads in Llama3.2-3B-instruct responsible for eight distinct functions in complex reasoning tasks. The x-axis represents the head index, while the y-axis indicates the layer index. <details> <summary>x8.png Details</summary>  ### Visual Description ## Heatmap: Cognitive Task Processing Across Neural Heads and Layers ### Overview The image displays eight heatmaps arranged in a 2x4 grid, each representing the importance of neural heads across layers for different cognitive tasks. Color intensity (purple to yellow) indicates head importance, with a legend on the right quantifying values from 0.0000 (dark purple) to 0.0040+ (bright yellow). Each panel corresponds to a specific cognitive function, with axes labeled "Layer" (y-axis) and "Head" (x-axis). ### Components/Axes - **X-axis (Head)**: 0–30, labeled "Head" - **Y-axis (Layer)**: 0–30, labeled "Layer" - **Legend**: Right-aligned, color scale from dark purple (0.0000) to yellow (0.0040+), labeled "Heads Importance" - **Panels**: 1. Knowledge Recall 2. Retrieval 3. Logical Reasoning 4. Decision-making 5. Semantic Understanding 6. Syntactic Understanding 7. Inference 8. Math Calculation ### Detailed Analysis - **Knowledge Recall**: Yellow spots (0.0035–0.0040+) cluster in layers 12–18 and heads 6–12. Lower importance (purple) dominates outer regions. - **Retrieval**: Yellow highlights appear in layers 18–24 and heads 12–18, with sparse yellow in layer 0, head 0. - **Logical Reasoning**: Yellow regions concentrate in layers 18–24 and heads 12–18, with a notable yellow spot at layer 24, head 24. - **Decision-making**: Yellow clusters in layers 24–30 and heads 18–24, with a bright yellow at layer 30, head 30. - **Semantic Understanding**: Yellow spots in layers 6–12 and heads 0–6, with a dense yellow region at layer 12, head 6. - **Syntactic Understanding**: Yellow highlights in layers 12–18 and heads 12–18, with a bright yellow at layer 18, head 18. - **Inference**: Yellow regions in layers 18–24 and heads 12–18, with a yellow spot at layer 30, head 24. - **Math Calculation**: Yellow clusters in layers 24–30 and heads 18–24, with a bright yellow at layer 30, head 24. ### Key Observations 1. **Task-Specific Clustering**: Each cognitive task shows distinct clusters of high-importance heads (yellow), suggesting specialized neural circuitry for different functions. 2. **Layer Depth Correlation**: Higher layers (24–30) show increased importance for decision-making and math calculation, while lower layers (0–12) dominate semantic and syntactic tasks. 3. **Head Specialization**: Heads 12–18 and 18–24 are consistently critical across multiple tasks, indicating overlapping functional roles. 4. **Outliers**: - Layer 0, head 0 in Retrieval (0.0015) - Layer 30, head 24 in Inference (0.0030) - Layer 30, head 30 in Decision-making (0.0040+) ### Interpretation The heatmaps reveal that neural heads exhibit task-specific activation patterns, with higher layers (24–30) specializing in complex tasks like decision-making and math calculation. The clustering of high-importance heads (e.g., heads 12–18 across multiple tasks) suggests shared processing mechanisms for related cognitive functions. The bright yellow spots (0.0040+) in Decision-making and Math Calculation at layer 30 indicate these heads may play a critical role in advanced reasoning. The sparse yellow in lower layers for semantic tasks implies early-stage processing of basic meaning, while syntactic understanding relies on mid-layer heads (12–18). The outlier at layer 30, head 24 in Inference (0.0030) may represent a unique pathway for integrating information across modalities. </details> Figure 6: The existence of cognitive heads in Qwen3-8B responsible for eight distinct functions in complex reasoning tasks. The x-axis represents the head index, while the y-axis indicates the layer index. <details> <summary>x9.png Details</summary>  ### Visual Description ## Heatmap: Neural Head Importance Across Cognitive Tasks ### Overview The image displays an 8-panel heatmap visualizing neural head importance across cognitive tasks. Each panel represents a specific cognitive function (e.g., Knowledge Recall, Retrieval) with Layer (0-30) on the y-axis and Head (0-30) on the x-axis. Color intensity indicates importance magnitude, with a legend mapping colors to values (dark purple = 0.0000, yellow = 0.0040+). ### Components/Axes - **Axes**: - **Vertical (Layer)**: 0-30 (discrete intervals) - **Horizontal (Head)**: 0-30 (discrete intervals) - **Legend**: Right-aligned, color gradient from dark purple (low importance) to yellow (high importance), labeled "Heads Importance" with values 0.0000 to 0.0040+. - **Panels**: 8 cognitive tasks: 1. Knowledge Recall 2. Retrieval 3. Logical Reasoning 4. Decision-making 5. Semantic Understanding 6. Syntactic Understanding 7. Inference 8. Math Calculation ### Detailed Analysis - **Color Distribution**: - **Knowledge Recall**: Yellow squares concentrated in lower layers (0-10) and heads (0-10). - **Retrieval**: Yellow squares in mid-layers (10-20) and heads (10-20). - **Logical Reasoning**: Scattered yellow squares across mid-layers (10-20) and heads (10-20). - **Decision-making**: Yellow squares in mid-layers (10-20) and heads (10-20). - **Semantic Understanding**: Yellow squares in lower layers (0-10) and heads (0-10). - **Syntactic Understanding**: Yellow squares in mid-layers (10-20) and heads (10-20). - **Inference**: Yellow squares in upper layers (20-30) and heads (20-30). - **Math Calculation**: Yellow squares in lower layers (0-10) and heads (0-10), with the highest intensity (brightest yellow) at Layer 0, Head 0. ### Key Observations 1. **Task-Specific Patterns**: - Math Calculation shows the most concentrated importance (brightest yellow) in Layer 0, Head 0. - Inference and Decision-making exhibit broader, less intense distributions. 2. **Layer-Head Correlation**: - Lower layers (0-10) dominate for Knowledge Recall, Semantic Understanding, and Math Calculation. - Mid-layers (10-20) are critical for Retrieval, Syntactic Understanding, and Logical Reasoning. - Upper layers (20-30) are most active for Inference. 3. **Color Consistency**: - All yellow squares align with the legend’s high-importance range (0.0035-0.0040+). - Dark purple dominates most panels, indicating low importance in most head-layer combinations. ### Interpretation The heatmap reveals distinct neural activation patterns for different cognitive tasks: - **Specialized Processing**: Math Calculation’s peak at Layer 0, Head 0 suggests a dedicated neural circuit for arithmetic. - **Distributed Processing**: Tasks like Retrieval and Logical Reasoning show dispersed importance, implying parallel processing across multiple heads/layers. - **Hierarchical Engagement**: Lower layers dominate for foundational tasks (e.g., Math Calculation), while upper layers (Inference) handle complex, abstract reasoning. - **Overlap and Specialization**: Overlapping yellow regions (e.g., Retrieval and Syntactic Understanding in mid-layers) may indicate shared neural resources for related tasks. This visualization supports hypotheses about modular yet interconnected neural architectures for cognitive functions, with Math Calculation exhibiting the most localized activation. </details> Figure 7: The existence of cognitive heads in Qwen3-4B responsible for eight distinct functions in complex reasoning tasks. The x-axis represents the head index, while the y-axis indicates the layer index. <details> <summary>x10.png Details</summary>  ### Visual Description ## Heatmap: Cognitive Task Processing Across Neural Layers and Heads ### Overview The image displays a matrix of 8 heatmaps arranged in two rows (4 top, 4 bottom), each representing neural activity patterns for different cognitive tasks. The heatmaps visualize the importance of specific "heads" (neurons) across "layers" (depth) in processing tasks like knowledge recall, logical reasoning, and math calculation. Color intensity indicates head importance, with yellow representing highest values (0.0020+) and purple the lowest (0.0000). ### Components/Axes - **X-axis (Horizontal)**: "Head" (0-30), incrementing by 6 - **Y-axis (Vertical)**: "Layer" (0-42), incrementing by 6 - **Legend**: Right-aligned colorbar (purple→yellow) labeled "Heads Importance" - **Panel Titles**: - Top row: Knowledge Recall, Retrieval, Logical Reasoning, Decision-making - Bottom row: Semantic Understanding, Syntactic Understanding, Inference, Math Calculation ### Detailed Analysis 1. **Knowledge Recall** (Top-left) - Yellow spots concentrated in layers 12-18 and heads 6-12 - Gradual transition to green in layers 24-30 2. **Retrieval** (Top-center-left) - Yellow clusters in layers 18-24 and heads 12-18 - Green dominance in upper layers (30-42) 3. **Logical Reasoning** (Top-center-right) - Yellow in layers 18-24 and heads 12-18 - Green in layers 24-30 across heads 6-24 4. **Decision-making** (Top-right) - Yellow in layers 24-30 and heads 18-24 - Green in layers 18-24 across heads 12-24 5. **Semantic Understanding** (Bottom-left) - Yellow in layers 12-18 and heads 6-12 - Green in layers 24-30 across heads 0-30 6. **Syntactic Understanding** (Bottom-center-left) - Yellow in layers 18-24 and heads 12-18 - Green in layers 24-30 across heads 6-24 7. **Inference** (Bottom-center-right) - Yellow in layers 24-30 and heads 18-24 - Green in layers 18-24 across heads 12-24 8. **Math Calculation** (Bottom-right) - Yellow in layers 24-30 and heads 18-24 - Green in layers 18-24 across heads 12-24 ### Key Observations - **Layer Specialization**: Higher layers (24-30) show increased importance for complex tasks (logical reasoning, math calculation) - **Head Activation Patterns**: - Heads 12-18 dominate in middle layers (18-24) - Heads 18-24 activate in upper layers (24-30) - **Task-Specific Patterns**: - Math Calculation and Logical Reasoning show strongest yellow in upper-right quadrant - Knowledge Recall shows distributed activity across middle layers - **Color Consistency**: All yellow regions align with legend's 0.0020+ threshold ### Interpretation The heatmaps reveal a clear hierarchical processing structure: 1. **Lower Layers (0-12)**: Primarily handle basic knowledge recall and semantic understanding 2. **Middle Layers (12-24)**: Specialized for syntactic processing and intermediate reasoning 3. **Upper Layers (24-30)**: Critical for complex tasks requiring integration (logical reasoning, math calculation) Notable anomalies include the strong yellow concentration in layers 18-24 for Retrieval and Syntactic Understanding, suggesting these tasks require distributed processing across multiple heads. The consistent yellow in upper layers for Math Calculation implies specialized neural circuitry for numerical processing. The spatial distribution patterns indicate that cognitive tasks are processed through distinct but interconnected neural pathways, with higher layers showing increased specialization for complex cognitive functions. This aligns with theories of neural network architecture where deeper layers handle abstract representations. </details> Figure 8: The existence of cognitive heads in Yi-1.5-9B responsible for eight distinct functions in complex reasoning tasks. The x-axis represents the head index, while the y-axis indicates the layer index. <details> <summary>x11.png Details</summary>  ### Visual Description ## Heatmap: Cognitive Task Activation Across Neural Layers and Heads ### Overview The image displays a heatmap visualization of neural activation patterns across 30 layers and 30 heads for eight cognitive tasks: Knowledge Recall, Retrieval, Logical Reasoning, Decision-making, Semantic Understanding, Syntactic Understanding, Inference, and Math Calculation. Each panel uses a color gradient (purple to yellow) to represent "Heads Importance" values, with a legend on the right indicating importance levels from 0.0000 (purple) to 0.0030+ (yellow). ### Components/Axes - **X-axis (Head)**: Labeled "Head" with values 0–30 in increments of 6. - **Y-axis (Layer)**: Labeled "Layer" with values 0–30 in increments of 6. - **Legend**: Positioned on the right, showing a vertical color bar with values 0.0000 (dark purple) to 0.0030+ (bright yellow). - **Panel Titles**: Eight subplots arranged in two rows, each labeled with a cognitive task (e.g., "Knowledge Recall," "Math Calculation"). ### Detailed Analysis #### Panel Trends 1. **Knowledge Recall**: - Yellow spots (high importance) concentrated at Layer 30, Heads 0–6. - Lower importance (blue/purple) dominates other regions. 2. **Retrieval**: - Yellow clusters at Layer 18–24, Heads 12–18. - Additional yellow spots at Layer 30, Heads 0–6. 3. **Logical Reasoning**: - Yellow spots at Layer 24–30, Heads 0–6. - Sparse yellow in Layer 12–18, Heads 12–18. 4. **Decision-making**: - Yellow at Layer 30, Heads 18–24. - Yellow at Layer 12, Heads 24–30. 5. **Semantic Understanding**: - Yellow spots at Layer 6–12, Heads 6–12. - Scattered yellow in Layer 18–24, Heads 18–24. 6. **Syntactic Understanding**: - Yellow clusters at Layer 12–18, Heads 12–18. - Yellow at Layer 24, Heads 6–12. 7. **Inference**: - Yellow at Layer 18–24, Heads 12–18. - Yellow at Layer 30, Heads 0–6. 8. **Math Calculation**: - Bright yellow at Layer 30, Head 30. - Yellow at Layer 24, Heads 18–24. #### Key Observations - **High Importance Clusters**: - Math Calculation shows the strongest activation (bright yellow) at the deepest layer (30) and head (30). - Retrieval and Decision-making exhibit concentrated yellow regions in mid-layers (18–24) and specific heads. - **Layer Depth Correlation**: - Tasks like Math Calculation and Logical Reasoning show higher importance in deeper layers (24–30), suggesting complex processing in later layers. - **Head-Specific Activation**: - Retrieval and Inference show strong activation in Heads 12–18, while Decision-making peaks in Heads 18–24. - **Sparsity**: - Most panels have low importance (purple) in the majority of layers/heads, indicating sparse neural engagement for these tasks. ### Interpretation The heatmaps reveal task-specific neural activation patterns, suggesting that different cognitive processes rely on distinct subsets of neural resources: - **Math Calculation** and **Logical Reasoning** activate deeper layers (24–30), possibly reflecting hierarchical processing of abstract concepts. - **Retrieval** and **Inference** show mid-layer activation (18–24), aligning with memory and reasoning tasks requiring intermediate abstraction. - **Decision-making** and **Knowledge Recall** involve both deep and shallow layers, indicating integration of stored knowledge with real-time processing. - The sparsity of yellow regions across most panels implies that only a small fraction of neural heads/layers are critical for each task, highlighting the efficiency of neural resource allocation. The data supports the hypothesis that cognitive tasks are modularly represented in neural networks, with specific layers and heads specializing in particular functions. The brightest activations (e.g., Math Calculation at Layer 30, Head 30) may represent bottlenecks or hubs for complex computations. </details> Figure 9: The existence of cognitive heads in Yi-1.5-6B responsible for eight distinct functions in complex reasoning tasks. The x-axis represents the head index, while the y-axis indicates the layer index. ### A.2 Importance curve We ranked the importance scores and identified the elbow point, as illustrated in Figure 10. <details> <summary>x12.png Details</summary>  ### Visual Description ## Line Graphs: Cognitive Process Importance Across Heads ### Overview The image displays eight line graphs arranged in a 2x4 grid, each representing a cognitive process (e.g., Decision-making, Inference, Knowledge Recall). All graphs share identical axes: - **X-axis**: "Heads" (logarithmic scale: 1, 256, 512, 7681024) - **Y-axis**: "Importance" (linear scale: 0.00e+00 to 6.00e-03) Each graph features a black line and a single red data point at the first x-axis value (1 head). The lines exhibit a sharp decline in importance after the initial head, with values approaching zero for subsequent heads. --- ### Components/Axes 1. **X-axis (Heads)**: - Values: 1, 256, 512, 7681024 (logarithmic spacing). - Position: Bottom of all graphs. 2. **Y-axis (Importance)**: - Values: 0.00e+00 to 6.00e-03 (linear scale). - Position: Left of all graphs. 3. **Graph Titles**: - Top row: Decision-making, Inference, Knowledge Recall, Logical Reasoning. - Bottom row: Math Calculation, Retrieval, Semantic Understanding, Syntactic Understanding. 4. **Data Points**: - Red dots at (1, ~1.5e-3 to 4.5e-3) for all graphs. - Black lines drop sharply after x=1, flattening near y=0. --- ### Detailed Analysis 1. **Trends**: - All graphs show a **steep decline** in importance after the first head. - Importance at x=1 ranges from **1.5e-3 to 4.5e-3** (red dots). - For x > 1, importance values are **effectively zero** (black lines collapse to the baseline). 2. **Data Points**: - Red dots are consistently positioned at the far left (x=1) across all graphs. - No additional markers or annotations are present. 3. **Scale Observations**: - The logarithmic x-axis emphasizes the vast difference between 1 and 7681024 heads. - Y-axis values are uniformly small, suggesting importance is inherently low except at the first head. --- ### Key Observations 1. **Dominance of Initial Heads**: - Importance is **orders of magnitude higher** at the first head (1) compared to all subsequent heads. - Example: At x=256, importance drops to ~0.000001 (1e-6), a 1000x reduction from x=1. 2. **Consistency Across Processes**: - All cognitive processes exhibit identical patterns, indicating a universal trend. 3. **Logarithmic Scale Impact**: - The x-axis compression visually exaggerates the drop-off, emphasizing the insignificance of additional heads. --- ### Interpretation The data suggests that cognitive processes (e.g., decision-making, semantic understanding) are **highly sensitive to initial inputs** (first head) but **insensitive to incremental information** (additional heads). This could imply: - **Primacy Effect**: Early information dominates cognitive outcomes. - **Diminishing Returns**: Adding more data beyond the first head provides negligible value. - **Potential Bottlenecks**: Systems relying on these processes may prioritize initial inputs over comprehensive data. The logarithmic x-axis underscores the scale disparity, reinforcing that even small increases in heads (e.g., 1 → 256) lead to catastrophic drops in importance. This pattern may reflect computational efficiency strategies or cognitive heuristics favoring simplicity over complexity. </details> Figure 10: Importance curve for eight functions, Llama3.1-8B-instruct. ### A.3 MLP We train a two-layer multi-class MLP for cognitive function classification. The first layer applies a shared linear projection to each multi-head representation vector, reducing each to a 64-dimensional embedding. These embeddings are then flattened and concatenated into a single vector of size $64\times numberofheads$ . This vector is fed into a hidden layer with 512 units, followed by a ReLU activation and a dropout with a rate of 0.3. The final output layer maps the 512-dimensional hidden representation to the set of cognitive function labels. The model is trained using the Adam optimizer with a learning rate of $10^{-4}$ and a cross-entropy loss. Training proceeds for 100 epochs. The test accuracy of our classification method across all LLM models is summarized in the Table 5. Table 5: The test accuracy (%) of probing method on different LLMs. | Dataset CogQA | Llama3.1-8B-instruct 83.73 | Llama3.2-3B-instruct 79.80 | Qwen3-8B 84.71 | Qwen3-4B 80.79 | Yi-1.5-9B 77.56 | Yi-1.5-6B 75.18 | | --- | --- | --- | --- | --- | --- | --- | ### A.4 Prompt for Generating CogQA Prompt Prompt: You are an expert in analytical logical reasoning. You will be given a question along with its chain-of-thought process. Your task is to break the question down into subquestions based on the chain-of-thought process, ensuring that all necessary steps for solving the problem and constructing the logical chain are included to simulate critical thinking. Decompose the Question: Identify and formulate the key subquestions required to solve the main question logically. Fill in Missing Steps: Ensure that all essential reasoning steps are explicitly stated. NOTE: The information of chain-of-thought cannot be used directly if it doesn’t exist in main query. Each subquestion should be derived solely from the main query and the preceding subquestion. Answer the Subquestions: Provide clear, step-by-step solutions for each subquestion. Annotate Cognitive Skills: Identify and label the specific cognitive abilities required to answer each subquestion. If you believe other cognitive skills are relevant, you may also consider incorporating them. You will be given predefined labels along with their descriptions. Your goal is to enhance the logical reasoning process by making it explicit and structured. <cognitive_skills> **Retrieval**: Refers to the process of fetching relevant information from input text, typically involving the extraction of specific words, phrases, or sentences directly from the original text. **Knowledge Recall**: Involves the storage and recall of domain-specific knowledge, such as concepts from math, physics, biology, etc. This is typically the internal knowledge base of a language model. (Corresponding to the memory head) **Semantic Understanding**: Refers to the ability to comprehend and extract meaning from text or symbols by recognizing relationships between words, phrases, and concepts. It goes beyond syntactic understanding by grasping context, intent, and underlying knowledge. **Syntactic Understanding*: Involves the ability to analyze and interpret the grammatical structure of sentences, including the roles and relationships of words, phrases, and clauses within the language. **Math Calculation**: Refers to the process of performing arithmetic or mathematical operations to obtain a result. It involves applying mathematical concepts, such as addition, subtraction, multiplication, division, and more complex operations (e.g., algebra, calculus), to solve problems or derive values from given inputs. **Inference**: Involves drawing conclusions based on existing evidence or information. It follows logical rules to deduce new statements or decisions from given information. **Logical Reasoning**: The process of drawing conclusions based on a set of premises, following established rules of logic, used to ensure that decisions of people are coherent, consistent, and based on sound principles. **Decision-making**: The process of making a choice in a selection task based on previous information or analysis. <cognitive_skills> Here is the question: <question> question <question> Here is the chain-of-thought: <chain-of-thought> cot <chain-of-thought> Note - Your task is to break the question down into detailed subquestions, ensuring each subquestion can be answered using only one specific cognitive skill. - You need to create a structured and explicit reasoning process that simulates critical thinking while maintaining clarity and precision. - The subquestion needs to be easy to answer and the answer needs to be concise - The information of chain-of-thought cannot be used directly if it doesn’t exist in main query. - Each subquestion should be derived solely from the main query and the preceding subquestion. - You CAN NOT retrieval information from chain-of-thought, but you can retrieval from question. - Your output should be formatted as a list of JSON objects, where each object represents a subquestion, its answer, and the required cognitive skill. - You should use the most efficient logic to analyze the problem and minimize the number of subquestions. Output format [ "subquestion": "<Subquestion text>", "answer": "<Concise answer>", "cognitive_skill": "<Assigned cognitive skill>" , "subquestion": "<Subquestion text>", "answer": "<Concise answer>", "cognitive_skill": "<Assigned cognitive skill>" ] Your answer: ### A.5 Annotations To ensure the quality and reliability of the decomposed subQAC triplets in the CogQA dataset, we design a rigorous multi-stage annotation pipeline, combining expert review and model-based verification. The goal is to verify the logical validity of subquestions, the correctness of their associated cognitive function labels, and the accuracy of the answers. #### Stage 1: Validating Subquestion Decomposition In the first stage, we evaluate whether the generated subquestions are logically sound and align with natural human reasoning. For each QA pair, three expert annotators (with backgrounds in linguistics or cognitive science) independently assess the validity of each subquestion. A subquestion is marked true if it meaningfully contributes to answering the main question and follows a logical reasoning trajectory. Otherwise, it is marked false. If a subquestion depends on prior information—such as the question text or the answer—from another subquestion, the subquestion order must reflect this dependency. While some subquestions can be answered in parallel and are order-independent, others have prerequisite relationships that require a specific sequence. As the overall reasoning structure often forms a graph, where both sequential and parallel dependencies coexist. During LLM inference, we include the previous subquestions and their corresponding subanswers in the prompt as prior information. Thus, the critical factor is not the ordering alone, but whether the prompt provides the necessary context to answer the current subquestion accurately. We apply the following filtering criteria: - AI-Human Agreement: If any annotator considers fewer than 60% of the subquestions valid, the entire QA decomposition is discarded. - Inter-Annotator Agreement: A subquestion is deemed invalid if at least two annotators mark it as false. If over 40% of the subquestions in a QA pair are invalid under this rule, the whole QA pair is removed. This filtering ensures that the retained QA decompositions follow coherent, cognitively plausible reasoning chains. #### Stage 2: Verifying Cognitive Function Labels In the second stage, annotators evaluate the correctness of the cognitive function label $c_{i}$ assigned to each subQAC triplet $(q_{i},a_{i},c_{i})$ . Three annotators independently mark each label as true or false. When discrepancies occur, annotators collaboratively reassign the correct cognitive label to ensure alignment with the underlying mental operation. This step ensures that the categorization of subquestions accurately reflects established distinctions between information retrieval, semantic understanding, logical reasoning, and other cognitive processes. #### Stage 3: Answer Verification via Model and Human Review In the final stage, we verify the correctness of each answer $a_{i}$ using both automated and manual procedures. We employ the o4-mini model [o4mini2024], known for its logical reasoning capabilities, to re-evaluate GPT-4o-generated answers. If o4-mini disagrees with GPT-4o, it provides an alternative answer. A human annotator then compares both answers and resolves discrepancies by supplying the correct one when necessary. Given the generally objective nature of answers, only one annotator is required for this task. #### Annotation Outcome Following this multi-stage process, we retain 570 validated QA pairs, yielding a total of 3,402 high-quality subQAC triplets. Notably, we augment certain cognitive functions to ensure balance across categories. As a result, the original 570 QA pairs were expanded to 720 (including some duplicates), with each duplicated pair potentially associated with distinct subquestions and cognitive functions. ### A.6 CogQA Example Table 6 presents illustrative examples from the CogQA dataset. The main question and its corresponding answer are taken from the original dataset. Based on an analysis of the main question, a sequence of sub-questions, their answers, and associated cognitive function labels are generated in order. Table 6: Two examples from the CogQA dataset showing a main question, its final answer, and a breakdown into subquestions with answers and their corresponding cognitive function labels. | Main Question | A one-year subscription to a newspaper is offered with a 45% discount. How much does the discounted subscription cost if a subscription normally costs $80? | | --- | --- | | Answer | We calculate first the discount: 80 $\times$ 45 / 100 = $36. So, the discounted subscription amounts to 80 – 36 = $44. | | 1. What is the normal cost of a one-year subscription to the newspaper? | $80 | Retrieval | | --- | --- | --- | | 2. What is the discount percentage offered on the subscription? | 45% | Retrieval | | 3. How much is the discount amount in dollars for the subscription? | $36 | Math Calculation | | 4. What is the cost of the subscription after applying the discount? | $44 | Math Calculation | | Main Question | What does every person talk out of? Options: - name - hide - mother and father - mouth - heart | | --- | --- | | Answer | By mouth, talking is done. Every person talk out of mouth. | | 1. What is the primary function of talking? | To communicate verbally. | Knowledge Recall | | --- | --- | --- | | 2. Which part of the human body is primarily used for verbal communication? | Mouth | Knowledge Recall | | 3. Based on the options provided, which option corresponds to the part used for verbal communication? | Mouth | Decision-making | ### A.7 Prompt for Question Asking Prompt Prompt: You are an expert in analytical and logical reasoning. You will be given a main question and prior knowledge in chain-of-thought (CoT) format. Your task is to answer a follow-up subquestion using the information provided. Here is the main question: <main_question> question </main_question> Here is the prior knowledge in chain-of-thought (CoT) format: <prior_knowledge> cot </prior_knowledge> Here is the subquestion: <subquestion> subquestion </subquestion> Instructions: - Answer the subquestion carefully. - You can use the information in the prior_knowledge to help you answer the subquestion. - Your response should be clear and concise. - Stick to factual reasoning based on provided CoT. - Do not include any explanation, commentary, or code. - Do not output anything after the closing square bracket ‘]‘. Only output your final answer using this format: [ "answer": "<Your answer here>" ] Your answer: ### A.8 The number of cognitive heads for different LLMs The number of cognitive heads for each model is shown in Table 7. Table 7: Count (C) and percentage (%) of attention heads exceeding elbow thresholds for each cognitive function across six models. | Llama3.1-8B-instruct Llama3.2-3B-instruct Qwen3-8B | 105 95 119 | 10.3 14.1 10.3 | 118 62 115 | 11.5 9.2 10.0 | 142 95 114 | 13.9 14.1 9.9 | 124 87 87 | 12.1 12.9 7.6 | 60 90 68 | 5.9 13.4 5.9 | 81 63 108 | 7.9 9.4 9.4 | 139 98 178 | 13.6 14.6 15.5 | 59 35 61 | 5.8 5.2 5.3 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Qwen3-4B | 115 | 10.0 | 94 | 8.2 | 120 | 10.4 | 170 | 14.8 | 143 | 12.4 | 106 | 9.2 | 109 | 9.5 | 99 | 8.6 | | Yi-1.5-9B | 200 | 13.0 | 134 | 8.7 | 134 | 8.7 | 174 | 11.3 | 218 | 14.2 | 140 | 9.1 | 173 | 11.3 | 167 | 10.9 | | Yi-1.5-6B | 118 | 11.5 | 90 | 8.8 | 200 | 19.5 | 93 | 9.1 | 99 | 9.7 | 142 | 13.9 | 146 | 14.3 | 67 | 6.5 | ### A.9 Ablation study - Different position of head activation In the main experiments, we use the top-k generated tokens and average their multi-head attention vectors. We also explore alternative strategies for extracting representations, including using the first generated token, the last generated token, the first meaningful token, and the average of all generated tokens. The corresponding results are shown in Table 8. Here, first is the first token, last is the last token, meaning_first is the first meaning token (excluding formatting), top-k is the top-k most semantically important tokens, full is all tokens in the answer.We observe that top-k token masking leads to the most significant performance drop when masking the top-30 identified heads, indicating higher precision in identifying retrieval-relevant heads. Interestingly, last, meaning_first, full, and top-k show similar performance trends. This is because different tokens in the output contribute to answering the question, and as the number of masked cognitive heads increases, the influence of token using decreases. Additionally, for Retrieval, the full answer is usually meaningful, whereas others like Math Calculation require semantically meaningful tokens. Based on these results, we choose top-k as our final setting. Table 8: Attention heads associated with cognitive functions are selected based on different token positions. Accuracy and COMET scores are evaluated after intervention; lower values indicate better outcomes. | Llama3.1-8B Llama3.1-8B Llama3.1-8B | 30 30 30 | first last meaning_first | 90.51 86.86 88.13 | 83.53 81.76 79.41 | 91.13 90.04 89.72 | 73.13 68.66 68.66 | | --- | --- | --- | --- | --- | --- | --- | | Llama3.1-8B | 30 | full | 73.93 | 47.06 | 89.92 | 69.15 | | Llama3.1-8B | 30 | top-k | 70.05 | 46.47 | 89.32 | 67.16 | | Llama3.1-8B | 50 | first | 93.28 | 89.41 | 94.46 | 89.57 | | Llama3.1-8B | 50 | last | 64.39 | 41.18 | 92.05 | 70.15 | | Llama3.1-8B | 50 | meaning_first | 62.90 | 34.12 | 84.60 | 60.69 | | Llama3.1-8B | 50 | full | 46.20 | 11.76 | 89.01 | 78.11 | | Llama3.1-8B | 50 | top-k | 65.64 | 47.76 | 89.65 | 70.15 | ### A.10 Examples of top- $k$ tokens The selected tokens are intended to semantically represent the generated answer. Below are examples for different cognitive functions for Llama3.1-8B-instruct: Table 9: Examples of question decomposition with cognitive functions and token selection. | Given the sentence "A surfboarder catches the waves." can we conclude that "A surfboarder in the water."? (Options: yes / it is not possible to tell / no) | What is typically required for a surfboarder to catch waves? | Knowledge Recall | The surfboarder needs to be in the water. | [’surfboarder’, ’needs’, ’be’, ’in’, ’water’] | | --- | --- | --- | --- | --- | | Is the following a factual statement? "Due to its high density, countries around the world use Palladium to mint coins." (Options: yes / no) | What is the statement in question? | Retrieval | The statement in question is: Due to its high density, countries around the world use Palladium to mint coins. | [’high’, ’density’, ’Palladium’, ’mint’, ’coins’] | | A one-year subscription to a newspaper is offered with a 45% discount. How much does the discounted subscription cost if a subscription normally costs $80? | How much is the discount amount in dollars for the subscription? | Math Calculation | 36 | [’36’] | We can see that the selected tokens semantically represent the answer. Note that we use all tokens when the number of tokens is fewer than 5.