# Shared circuits predict whether LLMs generalize across formats in arithmetic reasoning

arXiv: https://arxiv.org/abs/2609.04463 · HTML: https://mlsanity.com/paper/2609.04463/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- Mechanistic interpretability / [Steering and interpreting LLM reasoning](https://mlsanity.com/mechinterp/steering-and-interpreting-llm-reasoning/)

## Builds on (most cited first, 10 of 10)

- [Right for the Wrong Reasons: Diagnosing Syntactic Heuristics in Natural Language Inference](https://mlsanity.com/paper/1902.01007/) (2019)
- [Do Llamas Work in English? On the Latent Language of Multilingual Transformers](https://mlsanity.com/paper/2402.10588/) (2024)
- [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (2023)
- [Revisiting Out-of-distribution Robustness in NLP: Benchmark, Analysis, and LLMs Evaluations](https://mlsanity.com/paper/2306.04618/) (2023)
- [The Semantic Hub Hypothesis: Language Models Share Semantic Representations Across Languages and Modalities](https://mlsanity.com/paper/2411.04986/) (2024)
- [On the Similarity of Circuits across Languages: a Case Study on the Subject-verb Agreement Task](https://mlsanity.com/paper/2410.06496/) (2024)
- [The Validation Gap: A Mechanistic Analysis of How Language Models Compute Arithmetic but Fail to Validate It](https://mlsanity.com/paper/2502.11771/) (2025)
- [Circuit Stability Characterizes Language Model Generalization](https://mlsanity.com/paper/2505.24731/) (2025)
- [Differentiable Faithfulness Alignment for Cross-Model Circuit Transfer](https://mlsanity.com/paper/2604.24302/) (2026)
- [CircuitProbe: Predicting Reasoning Circuits in Transformers via Stability Zone Detection](https://mlsanity.com/paper/2604.00716/) (2026)

## Abstract (arXiv)

In many forms of reasoning, including arithmetic reasoning, generalizing across superficial changes in input format is effortless for humans: anyone who can solve 2+5 can also solve 'two plus five'. In contrast, LLMs are more brittle to surface variations of the prompts: for example, they solve numeric arithmetic problems almost perfectly but are substantially less accurate on verbal renditions of the same problems. Here, we ask whether generalization across formats can be predicted from the models' internals. Using attribution patching, we first independently localize the circuit that each model recruits to solve numeric arithmetic problems (2+5) vs. verbal ones, in three languages: English ('two plus five'), Spanish ('dos m'as cinco'), and Italian ('due pi`u cinque'); then, we test whether overlap with the model's own numeric circuit predicts its generalization to the verbal formats. Indeed, we find support for this idea at three levels: circuit overlap accounts for the relative difficulty of the three verbal formats, for which models generalize best, and for which items are solved correctly, rivaling supervised probes while requiring no labeled data.