Large language models (LLMs) have demonstrated impressive capabilities, yet their internal mechanisms for handling reasoning-intensive tasks remain underexplored. To advance the understanding of model-internal processing mechanisms, we present an investigation of how LLMs perform arithmetic operations by examining internal mechanisms during task execution. Using early decoding, we trace how next-token predictions are constructed across layers. Our experiments reveal that while the models recognize arithmetic tasks early, correct result generation occurs only in the final layers. Notably, models proficient in arithmetic exhibit a clear division of labor between attention and MLP modules, where attention propagates input information and MLP modules aggregate it. This division is absent in less proficient models. Furthermore, successful models appear to process more challenging arithmetic tasks functionally, suggesting reasoning capabilities beyond factual recall.
Recent studies have shown that Large Language Models (LLMs) can achieve strong reasoning performance by incorporating functional symbolic representations that abstractly describe graph traversal algorithms and step-by-step reasoning in few-shot learning settings. However, it remains unclear how LLMs genuinely understand the abstract meaning of each reasoning step and the overall algorithm from only a limited number of demonstrations. This work aims to localize the attention heads responsible for individual reasoning steps and characterize the types of information transferred among them. We first align constituent reasoning steps with their corresponding token logits under a symbolic-aided Chain-of-Thought (CoT) prompting framework. Our analysis shows that token positions that steer the reasoning process are associated with low confidence scores caused by constraints on satisfying reasoning behavior patterns in demonstrations. We then adopt causal mediation analysis techniques to identify the attention heads responsible for these patterns. In addition, our findings indicate that LLMs retrieve factual and rule-based information for individual sub-reasoning tasks through specialized attention heads (approximately 3% total heads), whereas higher layers predominantly facilitate information integration and the emergence of global reasoning strategies (e.g., graph traversal algorithms) that coordinate multiple intermediate reasoning steps to solve the overall task.
Understanding how LLMs reason is hindered by a practical asymmetry: while their generated outputs are observable, the underlying reasoning patterns remain opaque. Relying on single probes, such as Mutual Information Peak (MIP) or Deep-Thinking Ratio (DTR), risks underestimating the genuine inferential structure. To response this deficiency, we present an Integrated, cross-Architecture Reasoning (IAR) framework, designed to provide a unified approach to LLM reasoning interpretability. Specifically, we first propose to use bandwidth-calibrated MIP coupled with Tukey IQR peak-detection to isolate reasoning-crucial tokens at the output layer. Second, we performed an overlap analysis between MIP-picked tokens and DTR-deep tokens to trace the cross-layer trajectories of those tokens. This also discloses whether reasoning-crucial tokens are computation-intensive as well, further facilitating to understand how reasoning patterns evolve across model layers. Finally, we apply a Jaccard stability metric over multi-domain problems to verify if the MIP-identified tokens are reasoning quality-guaranteed. Extensive experiments on six models across four domains (mathematics, code, logic, and common sense) demonstrate IAR's generalizable interpretation capabilities across architectures. Our code is available at https://github.com/LeonardoMatthew/IAR.
Large language models often succeed on one formulation of a problem while failing on an equivalent formulation. Whether these failures arise from distinct internal circuits or different activation states of a shared circuit remains unknown. Recent mechanistic interpretability studies suggest that arithmetic in LLMs emerges from a "bag of heuristics," encoded by a sparse set of MLP neurons that represent distinct arithmetic strategies. We investigate whether arithmetic heuristic neurons are form-invariant across symbolic arithmetic, natural language word problems, and Python code in three Llama-3 models. In each format, we identify arithmetic heuristic neurons using a two-stage pipeline combining attribution patching and activation patching. A compact set of neurons is shared across all three formats, and targeted interventions show this shared circuit is both necessary and sufficient for late-layer arithmetic computation. Transferring the shared neurons' activations from a successful execution in one format to a failed execution in another recovers most incorrect predictions, exceeding 97% for addition and subtraction, indicating that cross-format failures arise from activation states rather than distinct circuits. Moreover, shared neurons consistently belong to the same heuristic families across formats, demonstrating that arithmetic computation in LLMs is largely form-invariant at the neuron level.
Sharath Naganna, Tanvir Ahmed Sijan, Uddipta Kalita