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Discovering Cross-Language Reasoning Invariance in LLMs with Geometry-Invariant Sparse Autoencoders

arXiv · AI, language, vision and robotics · article · Aug 24, 2026 · UTC

Multilingual language models can solve the same mathematical problem in different languages, but it remains unclear whether they rely on shared features or on language-specific computations that only produce similar outputs. We study this question in five models from four families using the Multilingual Grade School Math (MGSM) dataset, with problems solved in English, German, French, Spanish, Russian, and Chinese, retaining problems with valid reasoning traces in all six languages and replaying those traces through the model to record representations at multiple layers. For each model, we fir

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