LLM Parameters for Math Across Languages: Shared or Separate?

2026-06-16

AI Summary

This study investigates the origins of performance disparities in multilingual mathematical reasoning among large language models—specifically, whether such differences stem from language-specific parameters or shared mechanisms. To address this, we introduce a cross-lingual mechanistic analysis framework that, for the first time, systematically identifies and compares the key parameters underpinning mathematical reasoning across languages in multilingual large models. Our experiments reveal that the mechanisms supporting mathematical reasoning are neither fully language-invariant nor entirely language-specific: while partial parameter overlap exists in intermediate layers across languages, English exhibits the richest set of math-relevant parameters, whereas low-resource languages possess significantly fewer. This finding uncovers a systematic linguistic dependency in the model’s reasoning capabilities.

Abstract

Large language models (LLMs) exhibit substantial cross-lingual variation in mathematical reasoning performance, but it remains unclear whether these differences reflect language-specific parameters or a shared mechanism that manifests differently by language. We present a cross-lingual mechanistic analysis of mathematical reasoning in LLMs, enabling us to localize and compare model parameters that support mathematical reasoning across languages. We find that the extracted math-associated parameters exhibit partial cross-lingual overlap, with the strongest overlap concentrated in intermediate model layers. We further observe that English consistently produces the largest set of math-relevant parameters, whereas lower-resource languages reveal smaller sets of relevant parameters. These results suggest that math-related behavior in multilingual LLMs is neither fully language-invariant nor fully language-specific, but instead exhibits partial cross-lingual parameter overlap with systematic language-dependent differences.

Problem

• cross-lingual
• mathematical reasoning
• large language models
• parameter overlap
• language-specific

Innovation

• cross-lingual analysis
• mathematical reasoning
• parameter localization
• multilingual LLMs
• language-specific parameters