# 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
\n
## Diagram: Cognitive Process Flow for Percentage Calculation
### Overview
This diagram illustrates a cognitive process flow for solving the percentage problem: "What percent is 120 of 90?". It breaks down the problem-solving into four stages: Knowledge Recall, Semantic Understanding, Math, and Decision Making. Each stage is associated with a brain region visualization and a corresponding step in the calculation. A flow diagram at the bottom visually represents the information transfer between these stages.
### Components/Axes
The diagram is structured into four columns, each representing a cognitive stage. Each column contains:
* **Stage Title:** (Knowledge Recall, Semantic Understanding, Math, Decision Making) – positioned at the top of each column.
* **Question/Task:** A textual description of the task performed in that stage.
* **Brain Region Visualization:** A simplified diagram of the brain highlighting specific lobes (Frontal, Parietal, Temporal, Hippocampus).
* **Result/Output:** The outcome of the stage, presented as text.
* **Arrows:** Green arrows at the bottom of the diagram indicate the flow of information between stages.
The top of the diagram includes the original problem:
* **Input Question:** "What percent is 120 of 90?"
* **Options:** (A) 133 1/3 %, (B) 134 1/3 %, (C) 135 1/3 %, (D) 140 1/3 %, (E) 143 1/3 %
### Detailed Analysis or Content Details
Let's analyze each stage:
1. **Knowledge Recall:**
* Question: "What is the formula to calculate the percentage of one number relative to another?"
* Brain Region: Brain diagram with all lobes visible.
* Output: "The formula is (part/whole) *100%"
2. **Semantic Understanding:**
* Question: "What is the part and whole in the context of 'What percent is 120 of 90?'"
* Brain Region: Brain diagram with all lobes visible.
* Output: "The part is 120 and the whole is 90."
3. **Math:**
* Question: "Calculate 120 / 90 *100%"
* Brain Region: Brain diagram with all lobes visible.
* Output: "133 1/3"
4. **Decision Making:**
* Question: "Which option corresponds to 133 1/3%?"
* Brain Region: Brain diagram with all lobes visible.
* Output: "Option (A)"
**Flow Diagram:**
The flow diagram at the bottom shows the following connections:
* A single input arrow enters the "Knowledge Recall" stage.
* An arrow flows from "Knowledge Recall" to "Semantic Understanding".
* An arrow flows from "Semantic Understanding" to "Math".
* An arrow flows from "Math" to "Decision Making".
* An output arrow exits the "Decision Making" stage.
* There are also smaller upward arrows within each stage, possibly representing internal processing.
### Key Observations
* The diagram clearly illustrates a sequential cognitive process.
* Each stage builds upon the previous one, leading to the final answer.
* The brain region visualizations are consistent across all stages, suggesting that multiple brain areas are involved in each step.
* The flow diagram emphasizes the linear progression of information.
### Interpretation
This diagram demonstrates a model of how a human might solve a percentage problem. It breaks down the process into distinct cognitive stages, highlighting the knowledge, understanding, calculation, and decision-making components. The use of brain region visualizations suggests that these stages are associated with specific neural processes. The diagram implies a relatively straightforward, linear flow of information, although the internal arrows within each stage suggest some level of internal processing and feedback. The diagram is a simplified representation of a complex cognitive process, but it provides a useful framework for understanding how humans approach and solve mathematical problems. The diagram does not provide any data points or numerical trends, but rather illustrates a conceptual model.
</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 $X_{i}=\{x_{l}^{m}(i)\mid l=1,...,L,\ m=1,...,M\}$ 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 $j∈\mathcal{I}_{k}$ , we extract the corresponding attention head activations $X_{j}$ , and compute the averaged activation feature for the $m$ -th head in layer $l$ as $\bar{x}_{l}^{m}=\frac{1}{k}\sum_{j∈\mathcal{I}_{k}}x_{l}^{m}(j)$ . This results in a full set of head-level features $\bar{X}=\{\bar{x}_{l}^{m}\mid l={1,...,L},\ m={1,...,M}\}$ .
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 $\{\bar{x}^{m^{\prime}}_{l}\mid l={1,...,L},\ m={1,...,M}\}$ .
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 $×$ 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 $\mathbf{I}∈\mathbb{R}^{C×(L· M)}$ , 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
## Heatmaps: Heads Importance Across Tasks
### Overview
The image presents a 2x4 grid of heatmaps, each representing the "Heads Importance" for a different cognitive task. The tasks are Knowledge Recall, Retrieval, Logical Reasoning, Decision-making, Semantic Understanding, Syntactic Understanding, Inference, and Math Calculation. Each heatmap visualizes the importance of different "Heads" (ranging from 0 to 30) across different "Layers" (ranging from 0 to 30). The color intensity represents the importance score, with warmer colors (yellow/green) indicating higher importance and cooler colors (purple/dark blue) indicating lower importance.
### Components/Axes
* **X-axis:** "Head" - Ranges from 0 to 30, with increments of approximately 6.
* **Y-axis:** "Layer" - Ranges from 0 to 30, with increments of approximately 6.
* **Color Scale (Legend):** Located on the right side of the image. Represents "Heads Importance".
* Dark Blue: Approximately 0.0000
* Purple: Approximately 0.0005
* Light Green: Approximately 0.0015
* Yellow: Approximately 0.0025
* Bright Yellow/Green: Approximately 0.0030+
* **Titles:** Each heatmap is labeled with the corresponding cognitive task.
### Detailed Analysis or Content Details
Each heatmap will be analyzed individually. Note that values are approximate due to the visual nature of the data.
**1. Knowledge Recall:**
* Trend: Generally low importance across most heads and layers. Some localized areas of higher importance.
* Data Points: Highest importance (yellow) appears around Head 24, Layer 12-18. Moderate importance (light green) around Head 18, Layer 6-12.
**2. Retrieval:**
* Trend: Similar to Knowledge Recall, generally low importance. A more pronounced area of higher importance.
* Data Points: Highest importance (yellow) around Head 12, Layer 0-6. Moderate importance (light green) around Head 18, Layer 0-6.
**3. Logical Reasoning:**
* Trend: Low to moderate importance. A few scattered areas of higher importance.
* Data Points: Moderate importance (light green) around Head 18, Layer 12-18.
**4. Decision-making:**
* Trend: Higher overall importance compared to previous tasks. A distinct cluster of high importance.
* Data Points: Highest importance (bright yellow/green) around Head 24, Layer 12-18. Moderate importance (light green) around Head 18, Layer 12-18.
**5. Semantic Understanding:**
* Trend: Generally low importance, with some scattered areas of moderate importance.
* Data Points: Moderate importance (light green) around Head 6, Layer 18-24.
**6. Syntactic Understanding:**
* Trend: Moderate importance, with a clear concentration of higher importance in the lower layers.
* Data Points: Highest importance (yellow) around Head 6, Layer 0-6. Moderate importance (light green) around Head 12, Layer 0-6.
**7. Inference:**
* Trend: Low to moderate importance, with a few localized areas of higher importance.
* Data Points: Moderate importance (light green) around Head 18, Layer 6-12.
**8. Math Calculation:**
* Trend: Generally low importance, with a few scattered areas of moderate importance.
* Data Points: Moderate importance (light green) around Head 24, Layer 18-24.
### Key Observations
* **Decision-making** consistently shows the highest importance scores across multiple heads and layers.
* **Syntactic Understanding** exhibits a strong concentration of importance in the lower layers (0-6).
* **Knowledge Recall, Retrieval, Inference, and Math Calculation** generally have lower overall importance scores.
* Head 24 appears to be important for several tasks (Knowledge Recall, Decision-making, Math Calculation).
* Layer 12-18 appears to be important for several tasks (Knowledge Recall, Decision-making, Logical Reasoning).
### Interpretation
The heatmaps suggest that different cognitive tasks rely on different combinations of "Heads" and "Layers" within the model. Decision-making appears to be the most computationally demanding task, requiring significant activation across multiple heads and layers. Syntactic understanding seems to be primarily processed in the earlier layers of the model. The varying importance scores indicate that the model utilizes a distributed representation, where different components contribute to different tasks. The concentration of importance in specific heads and layers suggests that these components may be specialized for particular types of processing. The relatively low importance scores for tasks like Knowledge Recall and Retrieval might indicate that these tasks are simpler or rely on pre-existing knowledge representations. The fact that Head 24 is important for multiple tasks suggests it may be a general-purpose component involved in a variety of cognitive processes.
</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 Chart: Performance of Different Models with Varying Masked Heads
### Overview
The image presents four separate line charts, each representing the performance of different models (TopK Accuracy, RandomK Accuracy, TopK Comet, and RandomK Comet) across four different tasks: Retrieval, Knowledge Recall, Math Calculation, and Inference. The x-axis represents the number of masked heads, ranging from 16 to 128, while the y-axis represents the score, ranging from 0.0 to 1.0.
### Components/Axes
* **X-axis Label:** "# Masked Heads"
* **Y-axis Label:** "Score"
* **Chart Titles (from left to right):** "Retrieval", "Knowledge Recall", "Math Calculation", "Inference"
* **Legend:**
* TopK Accuracy (Blue Solid Line)
* RandomK Accuracy (Blue Dashed Line)
* TopK Comet (Red Solid Line)
* RandomK Comet (Red Dashed Line)
### Detailed Analysis or Content Details
**1. Retrieval Chart:**
* **TopK Accuracy (Blue Solid):** Starts at approximately 0.92 at 16 masked heads, sharply declines to approximately 0.05 at 64 masked heads, and then slightly increases to approximately 0.1 at 128 masked heads.
* **RandomK Accuracy (Blue Dashed):** Starts at approximately 0.91 at 16 masked heads, remains relatively stable around 0.85-0.90 until 64 masked heads, then declines to approximately 0.75 at 128 masked heads.
* **TopK Comet (Red Solid):** Starts at approximately 0.88 at 16 masked heads, declines to approximately 0.75 at 64 masked heads, and then increases to approximately 0.8 at 128 masked heads.
* **RandomK Comet (Red Dashed):** Starts at approximately 0.89 at 16 masked heads, remains relatively stable around 0.85-0.90 until 64 masked heads, then declines to approximately 0.8 at 128 masked heads.
**2. Knowledge Recall Chart:**
* **TopK Accuracy (Blue Solid):** Starts at approximately 0.88 at 16 masked heads, declines to approximately 0.3 at 64 masked heads, and then increases to approximately 0.4 at 128 masked heads.
* **RandomK Accuracy (Blue Dashed):** Starts at approximately 0.87 at 16 masked heads, remains relatively stable around 0.85-0.90 until 64 masked heads, then declines to approximately 0.75 at 128 masked heads.
* **TopK Comet (Red Solid):** Starts at approximately 0.90 at 16 masked heads, declines to approximately 0.80 at 64 masked heads, and then remains relatively stable around 0.8 at 128 masked heads.
* **RandomK Comet (Red Dashed):** Starts at approximately 0.89 at 16 masked heads, remains relatively stable around 0.85-0.90 until 64 masked heads, then declines to approximately 0.8 at 128 masked heads.
**3. Math Calculation Chart:**
* **TopK Accuracy (Blue Solid):** Starts at approximately 0.75 at 16 masked heads, declines to approximately 0.1 at 64 masked heads, and then increases to approximately 0.2 at 128 masked heads.
* **RandomK Accuracy (Blue Dashed):** Starts at approximately 0.78 at 16 masked heads, declines to approximately 0.65 at 64 masked heads, and then remains relatively stable around 0.6 at 128 masked heads.
* **TopK Comet (Red Solid):** Starts at approximately 0.85 at 16 masked heads, declines to approximately 0.7 at 64 masked heads, and then remains relatively stable around 0.7 at 128 masked heads.
* **RandomK Comet (Red Dashed):** Starts at approximately 0.82 at 16 masked heads, declines to approximately 0.75 at 64 masked heads, and then remains relatively stable around 0.7 at 128 masked heads.
**4. Inference Chart:**
* **TopK Accuracy (Blue Solid):** Starts at approximately 0.85 at 16 masked heads, declines to approximately 0.7 at 64 masked heads, and then remains relatively stable around 0.7 at 128 masked heads.
* **RandomK Accuracy (Blue Dashed):** Starts at approximately 0.86 at 16 masked heads, declines to approximately 0.75 at 64 masked heads, and then remains relatively stable around 0.7 at 128 masked heads.
* **TopK Comet (Red Solid):** Starts at approximately 0.88 at 16 masked heads, declines to approximately 0.8 at 64 masked heads, and then remains relatively stable around 0.8 at 128 masked heads.
* **RandomK Comet (Red Dashed):** Starts at approximately 0.87 at 16 masked heads, declines to approximately 0.8 at 64 masked heads, and then remains relatively stable around 0.8 at 128 masked heads.
### Key Observations
* Generally, increasing the number of masked heads leads to a decrease in performance for TopK Accuracy across all tasks.
* RandomK Accuracy tends to be more stable than TopK Accuracy as the number of masked heads increases.
* TopK Comet and RandomK Comet generally outperform their respective non-Comet counterparts, especially at higher numbers of masked heads.
* The most significant performance drop for TopK Accuracy is observed in the Retrieval and Math Calculation tasks.
### Interpretation
The data suggests that increasing the number of masked heads negatively impacts the performance of the TopK Accuracy model, particularly in tasks requiring precise information retrieval (Retrieval) and mathematical reasoning (Math Calculation). The RandomK Accuracy model demonstrates more robustness to increasing masked heads, indicating that it may be less reliant on specific input features. The Comet models consistently outperform their non-Comet counterparts, suggesting that the Comet architecture provides a benefit in handling masked inputs. The varying degrees of performance decline across different tasks indicate that the sensitivity to masked heads is task-dependent. This could be due to the inherent complexity of each task and the model's ability to generalize from incomplete information. The consistent performance of the Comet models suggests that they are better equipped to handle the challenges posed by masked inputs, potentially through more effective attention mechanisms or representation learning.
</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
\n
## Scatter Plot: Principal Component Analysis of Cognitive Tasks
### Overview
The image presents a scatter plot visualizing the distribution of several cognitive tasks across two principal components (PC1 and PC2). Each task is represented by a blue circle, positioned according to its score on these components. The plot appears to be the result of a Principal Component Analysis (PCA), a dimensionality reduction technique.
### Components/Axes
* **X-axis:** Labeled "PC 1" (Principal Component 1). The scale is not explicitly marked with numerical values, but it extends from left to right.
* **Y-axis:** Labeled "PC 2" (Principal Component 2). The scale is not explicitly marked with numerical values, but it extends from bottom to top.
* **Data Points:** Each point represents a cognitive task, labeled with its name.
* **Tasks:** The following cognitive tasks are represented:
* Decision
* Inference
* Logical
* Semantic
* Syntactic
* Retrieval
* Recall
* Math
### Detailed Analysis
The data points are distributed across the plot as follows (approximate coordinates based on visual estimation):
* **Math:** Located in the top-right corner. PC1 ≈ 1.2, PC2 ≈ 0.8.
* **Decision:** Located in the top-left quadrant. PC1 ≈ -0.6, PC2 ≈ 0.7.
* **Inference:** Located near Decision. PC1 ≈ -0.4, PC2 ≈ 0.6.
* **Logical:** Located near Inference. PC1 ≈ -0.3, PC2 ≈ 0.5.
* **Semantic:** Located in the center-left. PC1 ≈ -0.2, PC2 ≈ 0.3.
* **Syntactic:** Located near Semantic. PC1 ≈ 0.0, PC2 ≈ 0.2.
* **Retrieval:** Located near Syntactic. PC1 ≈ 0.2, PC2 ≈ 0.1.
* **Recall:** Located in the bottom-right corner. PC1 ≈ 0.8, PC2 ≈ -0.4.
**Trends:**
* There's a general trend of tasks clustering into two main groups: one in the top-left (Decision, Inference, Logical) and another in the bottom-right (Recall).
* Math is somewhat isolated, positioned further to the right than other tasks.
* Semantic, Syntactic, and Retrieval form a cluster in the center-left.
### Key Observations
* Recall is strongly associated with PC1, while Decision, Inference, and Logical are strongly associated with PC2.
* Math appears to be distinct from the other tasks, potentially representing a different cognitive process or relying on different underlying components.
* The tasks Semantic, Syntactic, and Retrieval are relatively close together, suggesting they share some common underlying components.
### Interpretation
This PCA plot suggests that the cognitive tasks can be differentiated based on two primary underlying components. PC1 might represent a dimension related to memory or factual knowledge (with Recall having a high positive score), while PC2 might represent a dimension related to reasoning or problem-solving (with Decision, Inference, and Logical having high positive scores).
The separation of Math from the other tasks indicates that it may rely on a different set of cognitive components or a different balance of the components represented by PC1 and PC2. The clustering of Semantic, Syntactic, and Retrieval suggests that these tasks share common underlying processes related to language processing or information access.
The plot provides a visual representation of the relationships between these cognitive tasks, highlighting their similarities and differences in terms of their underlying cognitive components. This information could be used to inform models of cognitive architecture or to design targeted interventions to improve performance on specific tasks.
</details>
(a) Llama3.1-8B
<details>
<summary>x5.png Details</summary>
### Visual Description
\n
## Scatter Plot: Principal Component Analysis of Cognitive Tasks
### Overview
This image presents a scatter plot visualizing the results of a Principal Component Analysis (PCA). The plot displays the distribution of several cognitive tasks across two principal components, PC1 and PC2. Each task is represented by a blue dot, labeled with its corresponding name. The axes represent the principal components, indicating the variance explained by each.
### Components/Axes
* **X-axis:** Labeled "PC 1" (Principal Component 1). The scale is not explicitly defined, but appears to range from approximately -0.5 to 0.5.
* **Y-axis:** Labeled "PC 2" (Principal Component 2). The scale is not explicitly defined, but appears to range from approximately -0.5 to 1.0.
* **Data Points/Labels:** The following cognitive tasks are represented:
* Math
* Retrieval
* Recall
* Syntactic
* Semantic
* Decision
* Logical
* Inference
### Detailed Analysis
The data points are scattered across the plot, suggesting varying degrees of correlation with the principal components.
* **Math:** Located at approximately (0.2, 0.8).
* **Retrieval:** Located at approximately (-0.3, -0.2).
* **Recall:** Located at approximately (-0.1, -0.1).
* **Syntactic:** Located at approximately (-0.1, 0.1).
* **Semantic:** Located at approximately (-0.4, -0.4).
* **Decision:** Located at approximately (0.2, 0.3).
* **Logical:** Located at approximately (0.3, 0.4).
* **Inference:** Located at approximately (0.4, 0.5).
**Trends:**
* A general trend exists where tasks related to reasoning and logic (Inference, Logical, Decision, Math) are positioned towards the upper-right quadrant, indicating positive correlations with both PC1 and PC2.
* Tasks related to memory and language processing (Retrieval, Recall, Semantic, Syntactic) are positioned towards the lower-left quadrant, indicating negative correlations with PC1 and potentially lower correlations with PC2.
### Key Observations
* "Math", "Inference", "Logical", and "Decision" tasks cluster together in the upper-right quadrant, suggesting they share similar characteristics in terms of the principal components.
* "Retrieval", "Recall", "Syntactic", and "Semantic" tasks cluster together in the lower-left quadrant, suggesting they share similar characteristics.
* "Semantic" is the most negative value on PC1.
* "Inference" is the most positive value on PC2.
### Interpretation
This PCA plot suggests that the cognitive tasks can be differentiated based on two underlying dimensions (PC1 and PC2). PC1 appears to separate tasks based on a dimension of complexity or reasoning ability, with tasks like Math and Inference having higher values. PC2 may represent a dimension related to the type of processing involved, with tasks like Inference and Math having higher values.
The clustering of tasks indicates that they share underlying cognitive processes. For example, the grouping of Retrieval, Recall, Syntactic, and Semantic suggests that these tasks rely on similar memory and language processing mechanisms. The separation between these clusters and the reasoning tasks suggests that different cognitive processes are involved in these types of tasks.
The plot provides a visual representation of the relationships between these cognitive tasks, which can be useful for understanding the underlying structure of cognition. It is important to note that the interpretation of the principal components is based on the observed distribution of the tasks and may require further investigation to confirm the underlying cognitive processes.
</details>
(b) Qwen3-4B
<details>
<summary>x6.png Details</summary>
### Visual Description
\n
## Scatter Plot: Cognitive Task Distribution in PC Space
### Overview
The image presents a scatter plot visualizing the distribution of various cognitive tasks across two principal components (PC1 and PC2). Each task is represented by a blue circular marker, positioned according to its coordinates on the PC1 and PC2 axes. The plot appears to be a dimensionality reduction representation of these tasks, potentially derived from a larger dataset.
### Components/Axes
* **X-axis:** Labeled "PC 1". The scale is not explicitly marked with numerical values, but it extends from left to right.
* **Y-axis:** Labeled "PC 2". The scale is not explicitly marked with numerical values, but it extends from bottom to top.
* **Data Points:** Represented by blue circles, each labeled with a cognitive task name.
* **Tasks:** The following cognitive tasks are represented:
* Syntactic
* Semantic
* Retrieval
* Inference
* Decision
* Logical
* Math
* Recall
### Detailed Analysis
The plot shows the relative positioning of each task within the PC1-PC2 space. Here's an approximate breakdown of the coordinates, noting the lack of explicit numerical scales:
* **Syntactic:** Located in the bottom-left quadrant. Approximate coordinates: (-2.5, -2.5).
* **Semantic:** Located slightly above and to the right of Syntactic. Approximate coordinates: (-1.5, -1.5).
* **Retrieval:** Located centrally, above Semantic. Approximate coordinates: (-0.5, 0.5).
* **Inference:** Located in the top-left quadrant, above Decision. Approximate coordinates: (-1.0, 2.0).
* **Decision:** Located in the top-left quadrant. Approximate coordinates: (-0.5, 2.5).
* **Logical:** Located to the right of Decision. Approximate coordinates: (1.0, 2.5).
* **Math:** Located to the right of Inference, and below Logical. Approximate coordinates: (1.0, 1.5).
* **Recall:** Located in the bottom-right quadrant. Approximate coordinates: (2.5, -1.5).
Visually, the tasks cluster into a few groups. Syntactic and Semantic are relatively close together. Retrieval is somewhat isolated. Decision, Inference, Logical, and Math form a cluster in the upper portion of the plot. Recall is distinctly separated in the bottom-right.
### Key Observations
* **Separation of Recall:** Recall is the most distant task from the others, residing in the bottom-right quadrant.
* **Clustering of Reasoning Tasks:** Decision, Inference, Logical, and Math appear to be closely related in this PC space.
* **Proximity of Syntactic and Semantic:** These two tasks are positioned near each other, suggesting a potential relationship.
* **Retrieval as a Central Task:** Retrieval is positioned near the center of the plot, potentially indicating it's a more general or foundational cognitive process.
### Interpretation
This scatter plot likely represents the results of a Principal Component Analysis (PCA) applied to a dataset of cognitive task performance or features. PCA reduces the dimensionality of the data, identifying the principal components (PC1 and PC2) that explain the most variance.
The positioning of the tasks suggests that PC1 might represent a dimension related to complexity or abstraction, with Syntactic and Semantic tasks being relatively simple and Recall being more complex. PC2 might represent a dimension related to reasoning or decision-making, with Decision, Logical, and Math tasks scoring high on this component.
The separation of Recall suggests it relies on different cognitive mechanisms than the other tasks. The clustering of reasoning tasks indicates they share underlying cognitive processes. The proximity of Syntactic and Semantic suggests a strong relationship between language understanding and structure.
The lack of numerical scales on the axes limits the quantitative interpretation of the distances between tasks. However, the plot provides a valuable visual representation of the relationships between these cognitive tasks in a reduced-dimensional space. This could be used to inform further research into the cognitive architecture underlying these tasks.
</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. Accuracy is measured based on BLEU, ROUGE, and semantic similarity scores.
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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 $x_{l}^{h}(i)← x_{l}^{h}(i)+\alpha\sigma_{l}^{h}\operatorname{dir}_{l}^{h}$ , 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.
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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
\n
## Heatmaps: Heads Importance across Tasks and Layers
### Overview
The image presents a 2x3 grid of heatmaps, each representing the "Heads Importance" for different cognitive tasks across various layers of a neural network. The tasks are Knowledge Recall, Retrieval, Logical Reasoning, Decision-making, Semantic Understanding, Syntactic Understanding, Inference, and Math Calculation. Each heatmap displays the importance score as a function of the "Head" (x-axis) and "Layer" (y-axis). The color intensity represents the magnitude of the importance score, with a colorbar indicating the scale.
### Components/Axes
* **X-axis (Head):** Ranges from 0 to 24, with markers at 0, 6, 12, 18, and 24. Represents the head number within the neural network.
* **Y-axis (Layer):** Ranges from 0 to 24, with markers at 0, 6, 12, 18, and 24. Represents the layer number within the neural network.
* **Colorbar:** Located on the right side of the image. Represents "Heads Importance" with a scale ranging from approximately 0.0000 to 0.0050+. The color gradient transitions from dark purple (low importance) to yellow/light green (high importance).
* **Titles:** Each heatmap is labeled with the corresponding cognitive task: Knowledge Recall, Retrieval, Logical Reasoning, Decision-making, Semantic Understanding, Syntactic Understanding, Inference, and Math Calculation.
* **Grid Layout:** The heatmaps are arranged in a 2x4 grid.
### Detailed Analysis or Content Details
Each heatmap will be analyzed individually, noting trends and approximate values.
**1. Knowledge Recall:**
* Trend: Higher importance scores are concentrated in the lower layers (0-12) and heads 6-18.
* Approximate Values: Maximum importance around 0.0045 at Layer 6, Head 12. Most values are below 0.002.
**2. Retrieval:**
* Trend: Similar to Knowledge Recall, with higher importance in lower layers (0-12) and heads 6-18.
* Approximate Values: Maximum importance around 0.0040 at Layer 6, Head 12. Most values are below 0.002.
**3. Logical Reasoning:**
* Trend: Higher importance scores are concentrated in the lower layers (0-12) and heads 6-18.
* Approximate Values: Maximum importance around 0.0045 at Layer 6, Head 12. Most values are below 0.002.
**4. Decision-making:**
* Trend: Higher importance scores are concentrated in the lower layers (0-12) and heads 6-18.
* Approximate Values: Maximum importance around 0.0050+ at Layer 6, Head 12. Most values are below 0.002.
**5. Semantic Understanding:**
* Trend: Higher importance scores are concentrated in the lower layers (0-12) and heads 6-18.
* Approximate Values: Maximum importance around 0.0040 at Layer 6, Head 12. Most values are below 0.002.
**6. Syntactic Understanding:**
* Trend: Higher importance scores are concentrated in the lower layers (0-12) and heads 6-18.
* Approximate Values: Maximum importance around 0.0040 at Layer 6, Head 12. Most values are below 0.002.
**7. Inference:**
* Trend: Higher importance scores are concentrated in the lower layers (0-12) and heads 6-18.
* Approximate Values: Maximum importance around 0.0040 at Layer 6, Head 12. Most values are below 0.002.
**8. Math Calculation:**
* Trend: Distinctly different from other tasks. Higher importance scores are concentrated in the deeper layers (18-24) and heads 0-6.
* Approximate Values: Maximum importance around 0.0045 at Layer 24, Head 0. Most values are below 0.002.
### Key Observations
* Most tasks (Knowledge Recall, Retrieval, Logical Reasoning, Decision-making, Semantic Understanding, Syntactic Understanding, Inference) exhibit a similar pattern of high importance in the lower layers and heads 6-18.
* Math Calculation stands out with high importance in the deeper layers and heads 0-6. This suggests that deeper layers and different heads are crucial for this specific task.
* The overall importance scores are relatively low, with most values below 0.002.
* There is a noticeable lack of high importance scores in the upper-right quadrants of most heatmaps, indicating that deeper layers and higher heads are generally less important for these tasks.
### Interpretation
The heatmaps reveal how different cognitive tasks leverage different parts of the neural network. The consistent pattern across most tasks suggests that the initial layers and a specific range of heads (6-18) are fundamental for general cognitive processing. These layers likely handle basic feature extraction and initial processing of information.
The unique pattern for Math Calculation indicates that this task requires more complex processing, utilizing deeper layers and different heads (0-6). This could be due to the need for more abstract reasoning and sequential operations in mathematical problem-solving.
The low overall importance scores suggest that the network's capacity is distributed, and no single head or layer dominates the processing for any given task. The visualization highlights the distributed nature of intelligence within the network. The colorbar scale suggests that the differences in importance are subtle, but still discernible. The data suggests that the network is not simply "memorizing" solutions but rather engaging in distributed computation across its layers and heads.
</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
\n
## Heatmaps: Heads Importance Across Tasks
### Overview
The image presents a 2x4 grid of heatmaps, each representing the "Heads Importance" for different tasks performed by a model. The tasks are Knowledge Recall, Retrieval, Logical Reasoning, Decision-making, Semantic Understanding, Syntactic Understanding, Inference, and Math Calculation. Each heatmap visualizes the importance score of each "Head" (ranging from 0 to 30) across different "Layers" (ranging from 0 to 30). The color intensity represents the importance score, with warmer colors (yellow/green) indicating higher importance and cooler colors (purple/blue) indicating lower importance.
### Components/Axes
* **X-axis:** "Head" - Ranges from 0 to 30, with approximately 31 discrete values.
* **Y-axis:** "Layer" - Ranges from 0 to 30, with approximately 31 discrete values.
* **Color Scale (Legend):** Located on the right side of the image. Represents "Heads Importance". The scale ranges from approximately 0.0000 (dark purple) to 0.0040+ (yellow). Intermediate values are: 0.0005, 0.0015, 0.0025, 0.0035.
* **Titles:** Each heatmap has a title indicating the task it represents.
* **Grid:** The heatmaps are arranged in a 2x4 grid.
### Detailed Analysis or Content Details
Each heatmap will be analyzed individually, noting trends and approximate values.
**1. Knowledge Recall (Top-Left)**
* Trend: The heatmap shows scattered high-importance areas. There's a concentration of higher importance (yellow/green) around Head 20-24 and Layer 24-30.
* Approximate Values: The highest importance values (around 0.0035-0.0040+) are located at (Head=22, Layer=28), (Head=23, Layer=28), and (Head=24, Layer=28). Most areas are below 0.001.
**2. Retrieval (Top-Second)**
* Trend: Similar to Knowledge Recall, with scattered high-importance areas. A concentration of higher importance is observed around Head 18-24 and Layer 24-30.
* Approximate Values: Highest values (around 0.0035-0.0040+) are located at (Head=20, Layer=28), (Head=21, Layer=28), (Head=22, Layer=28).
**3. Logical Reasoning (Top-Third)**
* Trend: More concentrated high-importance areas compared to the previous two. A clear cluster around Head 18-24 and Layer 12-18.
* Approximate Values: Highest values (around 0.0035-0.0040+) are located at (Head=20, Layer=14), (Head=21, Layer=14), (Head=22, Layer=14).
**4. Decision-making (Top-Right)**
* Trend: Highly concentrated high-importance area. A strong cluster around Head 18-24 and Layer 18-24.
* Approximate Values: Highest values (around 0.0040+) are located at (Head=20, Layer=20), (Head=21, Layer=20), (Head=22, Layer=20).
**5. Semantic Understanding (Bottom-Left)**
* Trend: Sparse high-importance areas. A few isolated points of higher importance around Head 10-14 and Layer 24-30.
* Approximate Values: Highest values (around 0.0030-0.0035) are located at (Head=12, Layer=28), (Head=13, Layer=28).
**6. Syntactic Understanding (Bottom-Second)**
* Trend: A distinct, localized high-importance area. A cluster around Head 10-14 and Layer 24-28.
* Approximate Values: Highest values (around 0.0035-0.0040+) are located at (Head=11, Layer=26), (Head=12, Layer=26).
**7. Inference (Bottom-Third)**
* Trend: Sparse high-importance areas, similar to Semantic Understanding. A few isolated points of higher importance around Head 18-24 and Layer 24-30.
* Approximate Values: Highest values (around 0.0030-0.0035) are located at (Head=20, Layer=28), (Head=21, Layer=28).
**8. Math Calculation (Bottom-Right)**
* Trend: Highly localized high-importance area. A strong cluster around Head 24 and Layer 24-28.
* Approximate Values: Highest values (around 0.0040+) are located at (Head=24, Layer=26), (Head=24, Layer=27).
### Key Observations
* **Task-Specific Head Importance:** The importance of specific heads varies significantly across tasks. Some tasks (e.g., Decision-making, Math Calculation) exhibit highly concentrated importance, while others (e.g., Knowledge Recall, Retrieval) are more distributed.
* **Layer Dependence:** The importance of heads also appears to be layer-dependent. For example, Logical Reasoning and Decision-making show high importance in lower layers (12-18), while Knowledge Recall and Retrieval show it in higher layers (24-30).
* **Head 20-24:** Heads in the range of 20-24 consistently show high importance across multiple tasks.
* **Sparse Importance:** Many areas of the heatmaps show very low importance (dark purple), indicating that most head-layer combinations do not contribute significantly to the tasks.
### Interpretation
The heatmaps reveal how different parts of the model (represented by heads and layers) contribute to different cognitive tasks. The concentration of importance in specific head-layer combinations suggests that the model has specialized components for each task. The varying distributions of importance across tasks indicate that different tasks rely on different model architectures and processing strategies.
The fact that some tasks have highly localized importance (e.g., Math Calculation) suggests that these tasks can be performed efficiently by a small subset of the model's parameters. Conversely, the distributed importance for tasks like Knowledge Recall suggests that these tasks require more holistic processing and integration of information across the model.
The consistent importance of heads 20-24 across multiple tasks suggests that these heads may represent fundamental cognitive abilities that are shared across different domains. Further investigation could focus on understanding the specific functions of these heads and how they contribute to the model's overall performance. The sparse importance in many areas suggests that the model may be overparameterized, and that pruning or regularization techniques could be used to reduce its size and complexity without sacrificing performance.
</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
\n
## Heatmaps: Layer-wise Attention Analysis
### Overview
The image presents a 2x4 grid of heatmaps, each representing the attention weights of a neural network model across different layers and heads for various tasks. Each heatmap visualizes the attention distribution, with color intensity indicating the strength of attention. The x-axis represents the "Head" (ranging from 0 to 30), and the y-axis represents the "Layer" (ranging from 0 to 30). A colorbar on the right indicates the attention weight scale, ranging from approximately 0.0000 to 0.0040+.
### Components/Axes
* **X-axis:** "Head" - Ranges from 0 to 30, with approximately 31 markers.
* **Y-axis:** "Layer" - Ranges from 0 to 30, with approximately 31 markers.
* **Colorbar:** Represents attention weight, ranging from 0.0000 (dark purple) to 0.0040+ (yellow).
* **Heatmap Titles (Top Row):**
* Knowledge Recall
* Retrieval
* Logical Reasoning
* Decision-making
* **Heatmap Titles (Bottom Row):**
* Semantic Understanding
* Syntactic Understanding
* Inference
* Math Calculation
### Detailed Analysis or Content Details
Each heatmap shows a distinct pattern of attention weights. I will describe each heatmap individually, noting trends and approximate values.
**1. Knowledge Recall:**
* Trend: Attention is concentrated in a diagonal band, starting around Head 10 and Layer 10, extending to Head 25 and Layer 25. There's also some scattered attention in the lower-left corner (low Head, low Layer).
* Approximate Values: The highest attention weights (yellow) are around 0.0035, concentrated in the diagonal band. Most other areas are in the 0.0005 - 0.0015 range (various shades of purple).
**2. Retrieval:**
* Trend: Similar to Knowledge Recall, a diagonal band of attention is present, but it's more diffuse and extends further towards the upper-right corner. There's also a noticeable concentration of attention around Head 0-10 and Layer 0-6.
* Approximate Values: Maximum attention weights (yellow) reach approximately 0.0038. The majority of the heatmap is in the 0.0005 - 0.0020 range.
**3. Logical Reasoning:**
* Trend: A very strong diagonal band of attention dominates this heatmap, starting around Head 6 and Layer 6 and extending to Head 28 and Layer 28. Attention is highly localized along this diagonal.
* Approximate Values: The highest attention weights (yellow) are around 0.0040+. The band is very clearly defined, with sharp transitions to lower attention weights (0.0005 - 0.0015) outside the band.
**4. Decision-making:**
* Trend: A broad diagonal band of attention, similar to Retrieval, but with a more gradual transition to lower attention weights. There's also some attention scattered throughout the heatmap.
* Approximate Values: Maximum attention weights (yellow) are around 0.0035. The heatmap is generally brighter than Knowledge Recall, with more areas in the 0.0015 - 0.0025 range.
**5. Semantic Understanding:**
* Trend: A strong diagonal band of attention, similar to Logical Reasoning, but slightly less defined. There's also some attention in the lower-left corner.
* Approximate Values: Maximum attention weights (yellow) are around 0.0038. The band is well-defined, with attention dropping to 0.0005 - 0.0015 outside the band.
**6. Syntactic Understanding:**
* Trend: A very strong diagonal band of attention, similar to Logical Reasoning, but even more localized.
* Approximate Values: The highest attention weights (yellow) are around 0.0040+. The band is extremely sharp, with very little attention outside of it.
**7. Inference:**
* Trend: A diagonal band of attention, similar to Retrieval and Decision-making, but with a more pronounced concentration of attention in the upper-right corner.
* Approximate Values: Maximum attention weights (yellow) are around 0.0035. The heatmap is generally brighter than Knowledge Recall, with more areas in the 0.0015 - 0.0025 range.
**8. Math Calculation:**
* Trend: A strong diagonal band of attention, similar to Logical Reasoning and Semantic Understanding, but with a slightly different slope.
* Approximate Values: Maximum attention weights (yellow) are around 0.0038. The band is well-defined, with attention dropping to 0.0005 - 0.0015 outside the band.
### Key Observations
* **Diagonal Attention:** A consistent trend across all tasks is the presence of a diagonal band of attention, suggesting that attention tends to focus on relationships between layers and heads that are relatively close to each other.
* **Task-Specific Patterns:** The strength and localization of the diagonal band vary across tasks. Logical Reasoning and Syntactic Understanding exhibit the most focused attention, while Retrieval and Decision-making have more diffuse attention patterns.
* **Lower-Left Corner Attention:** Some tasks (Knowledge Recall, Semantic Understanding) show attention in the lower-left corner, potentially indicating early-layer, early-head interactions.
### Interpretation
The heatmaps reveal how the model allocates its attention resources across different layers and heads for various cognitive tasks. The diagonal attention patterns suggest that the model learns to process information in a hierarchical manner, with attention flowing from lower layers to higher layers and between nearby heads. The task-specific variations in attention patterns indicate that the model adapts its attention strategy depending on the complexity and nature of the task. The strong attention in Logical Reasoning and Syntactic Understanding suggests that these tasks require more precise and focused attention mechanisms. The presence of attention in the lower-left corner for certain tasks may indicate that the model relies on early-layer interactions for specific types of knowledge or processing. The colorbar provides a quantitative measure of attention strength, allowing for comparison of attention levels across tasks and layers. This visualization is valuable for understanding the internal workings of the model and identifying potential areas for improvement.
</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
\n
## Heatmaps: Attention Head Importance Across Tasks
### Overview
The image presents a 2x4 grid of heatmaps, each representing the attention head importance for a different task. The heatmaps visualize the relationship between 'Layer' (vertical axis) and 'Head' (horizontal axis), with color intensity indicating the magnitude of attention head importance. A colorbar on the right provides the scale for interpreting the color intensity.
### Components/Axes
* **X-axis (Head):** Ranges from 0 to 30, with markers at intervals of 6. Labeled as "Head".
* **Y-axis (Layer):** Ranges from 0 to 42, with markers at intervals of 6. Labeled as "Layer".
* **Tasks (Heatmap Titles):**
* Knowledge Recall
* Retrieval
* Logical Reasoning
* Decision-making
* Semantic Understanding
* Syntactic Understanding
* Inference
* Math Calculation
* **Colorbar:** Ranges from approximately 0.0000 (dark purple) to 0.0020+ (yellow). Labeled as "Heads".
### Detailed Analysis or Content Details
Each heatmap shows a 31x43 grid of colored cells. The color of each cell represents the attention head importance for a specific layer and head combination. Due to the resolution of the image, precise numerical values are difficult to extract, but approximate values based on the colorbar are provided.
**1. Knowledge Recall:**
* Trend: Generally low attention head importance across most layers and heads. Some localized areas of higher importance (yellow/light green) appear around Head 12-18 and Layers 18-30.
* Approximate Values: Most cells are between 0.0000 and 0.0003. Peak values reach approximately 0.0010-0.0013.
**2. Retrieval:**
* Trend: Similar to Knowledge Recall, with generally low attention head importance. More pronounced areas of higher importance (yellow/light green) are visible around Head 18-24 and Layers 6-18.
* Approximate Values: Most cells are between 0.0000 and 0.0003. Peak values reach approximately 0.0013-0.0016.
**3. Logical Reasoning:**
* Trend: Low attention head importance, with some scattered areas of moderate importance (green) around Head 6-12 and Layers 12-30.
* Approximate Values: Most cells are between 0.0000 and 0.0003. Peak values reach approximately 0.0010.
**4. Decision-making:**
* Trend: Higher attention head importance compared to previous tasks, particularly around Head 24-30 and Layers 12-36. A distinct vertical band of higher importance is visible around Head 24.
* Approximate Values: Most cells are between 0.0000 and 0.0005. Peak values reach approximately 0.0016-0.0020+.
**5. Semantic Understanding:**
* Trend: Moderate attention head importance, with a concentration of higher values (green/light green) around Head 6-18 and Layers 6-24.
* Approximate Values: Most cells are between 0.0000 and 0.0005. Peak values reach approximately 0.0013.
**6. Syntactic Understanding:**
* Trend: Similar to Semantic Understanding, with moderate attention head importance concentrated around Head 6-18 and Layers 6-24.
* Approximate Values: Most cells are between 0.0000 and 0.0005. Peak values reach approximately 0.0013.
**7. Inference:**
* Trend: Low attention head importance, with scattered areas of moderate importance (green) around Head 12-24 and Layers 18-36.
* Approximate Values: Most cells are between 0.0000 and 0.0003. Peak values reach approximately 0.0010.
**8. Math Calculation:**
* Trend: Highest overall attention head importance, with a strong concentration of high values (yellow/light green) around Head 18-30 and Layers 18-42. A clear diagonal pattern of high importance is visible.
* Approximate Values: Most cells are between 0.0000 and 0.0010. Peak values reach approximately 0.0016-0.0020+.
### Key Observations
* **Task-Specific Attention:** Different tasks exhibit distinct patterns of attention head importance. Math Calculation consistently shows the highest attention head importance, while Knowledge Recall and Logical Reasoning generally have the lowest.
* **Head Specialization:** Certain heads appear to be more important for specific tasks. For example, Heads 24-30 are consistently important for Decision-making and Math Calculation.
* **Layer Dependency:** Attention head importance varies across layers, suggesting that different layers contribute differently to each task.
* **Diagonal Pattern:** The diagonal pattern in the Math Calculation heatmap suggests that attention heads at higher layers are particularly important for this task.
### Interpretation
The heatmaps demonstrate that attention heads are not uniformly important across all tasks. Instead, different tasks rely on different combinations of attention heads and layers. This suggests that the model learns to specialize its attention mechanisms to effectively process different types of information. The higher attention head importance observed in Math Calculation may indicate that this task requires more complex reasoning and information processing. The task-specific patterns observed in these heatmaps provide valuable insights into the inner workings of the model and can be used to improve its performance and interpretability. The varying attention head importance across layers suggests a hierarchical processing of information, where lower layers may focus on basic features and higher layers on more abstract concepts. The diagonal pattern in Math Calculation could indicate that the model progressively refines its calculations as information flows through the layers.
</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
\n
## Heatmaps: Heads Importance Across Tasks
### Overview
The image presents a 2x4 grid of heatmaps, each representing the "Heads Importance" for a different task. The tasks are Knowledge Recall, Retrieval, Logical Reasoning, Decision-making, Semantic Understanding, Syntactic Understanding, Inference, and Math Calculation. Each heatmap visualizes the importance score of different "Heads" (x-axis) across different "Layers" (y-axis). The color intensity represents the importance score, with a colorbar on the right indicating the scale.
### Components/Axes
* **X-axis (Head):** Ranges from 0 to approximately 32, representing the head number.
* **Y-axis (Layer):** Ranges from 0 to approximately 32, representing the layer number.
* **Colorbar:** Represents "Heads Importance" with a scale from approximately 0.0000 to 0.0030+.
* **Tasks (Heatmap Titles):** Knowledge Recall, Retrieval, Logical Reasoning, Decision-making, Semantic Understanding, Syntactic Understanding, Inference, Math Calculation.
* **Grid Layout:** 2 rows, 4 columns.
### Detailed Analysis or Content Details
Each heatmap shows a 33x33 grid of colored cells. The color of each cell corresponds to the "Heads Importance" value for that specific head and layer combination.
**1. Knowledge Recall (Top-Left):**
* The heatmap shows scattered high-importance areas (yellow/light-green) primarily between Head 12 and 24, and Layer 6 to 18.
* There's a concentration of higher values around Head 18-20 and Layer 6-12.
* Most of the heatmap is dark purple, indicating low importance.
**2. Retrieval (Top-Second):**
* Similar to Knowledge Recall, there are scattered high-importance areas.
* A more prominent concentration of higher values is observed around Head 12-18 and Layer 12-18.
* The overall distribution appears slightly more uniform than Knowledge Recall.
**3. Logical Reasoning (Top-Third):**
* High-importance areas are concentrated around Head 18-24 and Layer 6-12.
* A distinct diagonal pattern of higher values is visible.
* The heatmap shows a more defined structure compared to the previous two.
**4. Decision-making (Top-Right):**
* High-importance areas are concentrated around Head 24-30 and Layer 6-12.
* The heatmap shows a strong vertical band of higher values around Head 28.
* The distribution is relatively sparse, with large areas of low importance.
**5. Semantic Understanding (Bottom-Left):**
* High-importance areas are scattered, with a concentration around Head 6-12 and Layer 18-24.
* The heatmap shows a more diffuse distribution of higher values.
**6. Syntactic Understanding (Bottom-Second):**
* High-importance areas are concentrated around Head 12-18 and Layer 18-24.
* A clear diagonal pattern of higher values is visible.
* The heatmap shows a more structured distribution compared to Semantic Understanding.
**7. Inference (Bottom-Third):**
* High-importance areas are concentrated around Head 18-24 and Layer 18-24.
* The heatmap shows a strong concentration of higher values in the upper-right corner.
**8. Math Calculation (Bottom-Right):**
* High-importance areas are concentrated around Head 24-30 and Layer 18-24.
* The heatmap shows a very strong vertical band of higher values around Head 28.
* The distribution is highly sparse, with large areas of low importance.
### Key Observations
* **Head 28** consistently shows high importance in Decision-making and Math Calculation.
* **Layer 6-12** appears to be important across multiple tasks, particularly Knowledge Recall, Logical Reasoning, and Decision-making.
* The distribution of importance varies significantly across tasks. Some tasks (e.g., Decision-making, Math Calculation) show highly localized high-importance areas, while others (e.g., Knowledge Recall, Semantic Understanding) show more diffuse distributions.
* Diagonal patterns of high importance are observed in Logical Reasoning and Syntactic Understanding.
### Interpretation
The heatmaps suggest that different tasks rely on different combinations of heads and layers within the model. The consistent importance of Head 28 in Decision-making and Math Calculation indicates that this head may be specialized for these types of tasks. The varying distributions of importance across tasks suggest that the model learns to utilize different parts of its architecture for different types of reasoning and processing. The diagonal patterns observed in Logical Reasoning and Syntactic Understanding may indicate that these tasks involve sequential processing of information across layers. The sparse distributions in Decision-making and Math Calculation could suggest that these tasks require a more focused and selective activation of heads and layers. Overall, the heatmaps provide insights into the internal workings of the model and how it allocates its resources to perform different tasks. The data suggests a modular architecture where different heads and layers specialize in different aspects of cognitive processing.
</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
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## Line Charts: Importance vs. Heads for Different Tasks
### Overview
The image presents a 2x4 grid of line charts. Each chart depicts the relationship between "Importance" (y-axis) and "Heads" (x-axis) for a different cognitive task: Decision-making, Inference, Knowledge Recall, Logical Reasoning, Math Calculation, Retrieval, Semantic Understanding, and Syntactic Understanding. All charts share the same axes scales. The lines represent the trend of importance as the number of heads increases.
### Components/Axes
* **X-axis:** "Heads" with markers at 1, 256, 512, 768, and 1024.
* **Y-axis:** "Importance" ranging from 0.00e+00 to 6.00e-03.
* **Chart Titles:** Each chart is labeled with the specific task it represents.
* **Data Series:** Each chart contains a single line representing the importance trend. All lines are red.
### Detailed Analysis or Content Details
Each chart shows a steep decline in importance as the number of heads increases from 1 to 256, followed by a more gradual decline as the number of heads increases further to 1024.
**1. Decision-making:**
* Trend: The line starts at approximately 1.6e-03 and rapidly decreases to near 0.00e+00 between 1 and 256 heads. It remains relatively flat from 256 to 1024.
* Data Points (approximate):
* 1 Head: 1.6e-03
* 256 Heads: 1.0e-04
* 512 Heads: 8.0e-05
* 768 Heads: 7.0e-05
* 1024 Heads: 6.0e-05
**2. Inference:**
* Trend: Similar to Decision-making, a sharp decline from 1 to 256 heads, followed by a leveling off.
* Data Points (approximate):
* 1 Head: 5.0e-03
* 256 Heads: 2.0e-04
* 512 Heads: 1.5e-04
* 768 Heads: 1.3e-04
* 1024 Heads: 1.2e-04
**3. Knowledge Recall:**
* Trend: A steep initial drop, then a flattening.
* Data Points (approximate):
* 1 Head: 4.5e-03
* 256 Heads: 1.5e-04
* 512 Heads: 1.0e-04
* 768 Heads: 9.0e-05
* 1024 Heads: 8.0e-05
**4. Logical Reasoning:**
* Trend: Similar pattern to the others.
* Data Points (approximate):
* 1 Head: 3.0e-03
* 256 Heads: 8.0e-05
* 512 Heads: 6.0e-05
* 768 Heads: 5.0e-05
* 1024 Heads: 4.0e-05
**5. Math Calculation:**
* Trend: Sharp decline, then leveling.
* Data Points (approximate):
* 1 Head: 1.6e-03
* 256 Heads: 1.0e-04
* 512 Heads: 8.0e-05
* 768 Heads: 7.0e-05
* 1024 Heads: 6.0e-05
**6. Retrieval:**
* Trend: Very steep initial drop, then a plateau.
* Data Points (approximate):
* 1 Head: 5.0e-03
* 256 Heads: 2.0e-04
* 512 Heads: 1.5e-04
* 768 Heads: 1.3e-04
* 1024 Heads: 1.2e-04
**7. Semantic Understanding:**
* Trend: Similar to Knowledge Recall.
* Data Points (approximate):
* 1 Head: 4.5e-03
* 256 Heads: 1.5e-04
* 512 Heads: 1.0e-04
* 768 Heads: 9.0e-05
* 1024 Heads: 8.0e-05
**8. Syntactic Understanding:**
* Trend: Similar to Logical Reasoning.
* Data Points (approximate):
* 1 Head: 3.0e-03
* 256 Heads: 8.0e-05
* 512 Heads: 6.0e-05
* 768 Heads: 5.0e-05
* 1024 Heads: 4.0e-05
### Key Observations
* All tasks exhibit a significant decrease in importance as the number of heads increases.
* The most substantial drop in importance occurs between 1 and 256 heads.
* Beyond 256 heads, the importance levels off for all tasks, indicating diminishing returns.
* Inference and Retrieval show the highest initial importance values.
* Logical Reasoning and Syntactic Understanding show the lowest initial importance values.
### Interpretation
The data suggests that increasing the number of "heads" (likely referring to model parameters or attention heads in a neural network) initially provides substantial benefits in terms of importance for all cognitive tasks. However, there is a point of diminishing returns, around 256 heads, where adding more heads yields progressively smaller improvements. This implies an optimal range for model size or complexity for these tasks. The differences in initial importance values between tasks suggest that some tasks inherently benefit more from increased model capacity than others. The rapid decline in importance with increasing heads could be related to overfitting or the introduction of redundant parameters. The consistent pattern across all tasks suggests a fundamental principle governing the relationship between model capacity and performance in these cognitive domains.
</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 $64× numberofheads$ . 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 $×$ 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.