@inproceedings{naganna-etal-2026-arithmetic,
title = "Are Arithmetic Heuristic Neurons Form-Invariant? A Mechanistic Analysis of Symbols, Text, and Code in {LLM}s",
author = "Naganna, Sharath and
Sijan, Tanvir Ahmed and
Kalita, Uddipta",
editor = "Arad, Dana and
Belinkov, Yonatan and
Chen, Hanjie and
Feldhus, Nils and
Mueller, Aaron and
Mohebbi, Hosein and
Sarti, Gabriele and
Tutek, Martin",
booktitle = "Proceedings of the 9th {B}lackbox{NLP} Workshop: Analyzing and Interpreting Neural Networks for {NLP}",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.blackboxnlp-1.34/",
pages = "573--589",
ISBN = "979-8-89176-476-7",
abstract = "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 largely belong to the same heuristic families across formats, indicating that arithmetic computation in LLMs is substantially form-invariant at the neuron level."
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<abstract>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 largely belong to the same heuristic families across formats, indicating that arithmetic computation in LLMs is substantially form-invariant at the neuron level.</abstract>
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%0 Conference Proceedings
%T Are Arithmetic Heuristic Neurons Form-Invariant? A Mechanistic Analysis of Symbols, Text, and Code in LLMs
%A Naganna, Sharath
%A Sijan, Tanvir Ahmed
%A Kalita, Uddipta
%Y Arad, Dana
%Y Belinkov, Yonatan
%Y Chen, Hanjie
%Y Feldhus, Nils
%Y Mueller, Aaron
%Y Mohebbi, Hosein
%Y Sarti, Gabriele
%Y Tutek, Martin
%S Proceedings of the 9th BlackboxNLP Workshop: Analyzing and Interpreting Neural Networks for NLP
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-476-7
%F naganna-etal-2026-arithmetic
%X 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 largely belong to the same heuristic families across formats, indicating that arithmetic computation in LLMs is substantially form-invariant at the neuron level.
%U https://aclanthology.org/2026.blackboxnlp-1.34/
%P 573-589
Markdown (Informal)
[Are Arithmetic Heuristic Neurons Form-Invariant? A Mechanistic Analysis of Symbols, Text, and Code in LLMs](https://aclanthology.org/2026.blackboxnlp-1.34/) (Naganna et al., BlackboxNLP 2026)
ACL