LLMs use shared arithmetic neurons across symbols, text, and code

A new paper on arXiv (2607.16693) by Naganna, Sijan, and Kalita investigates whether large language models use the same internal 'arithmetic heuristic neurons' when solving math problems expressed as symbols (e.g., '3+5'), natural language word problems (e.g., 'John has 3 apples and buys 5 more'), or Python code (e.g., 'print(3+5)'). The researchers leveraged mechanistic interpretability techniques on three Llama-3 models, employing a two-stage pipeline of attribution patching and activation patching to identify sparse sets of MLP neurons that encode distinct arithmetic strategies.

The results reveal that a compact set of these heuristic neurons is shared across all three formats. Importantly, when a model fails on one format but succeeds on another, transferring the activation values of those shared neurons from the successful execution to the failed execution corrected over 97% of incorrect predictions for addition and subtraction. This indicates that the failures are due to different activation states of a single, shared circuit rather than entirely separate internal circuits. The finding strongly supports the 'form-invariant' nature of arithmetic computation in LLMs at the neuron level, with shared neurons consistently belonging to the same heuristic families across formats.