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.

Children efficiently acquire language not just by listening, but by interacting with others in their social environment. Conversely, large language models are typically trained with next-word prediction on massive amounts of text. Motivated by this contrast, we investigate whether language models can be trained with less data by learning not only from next-word prediction but also from high-level, cognitively inspired feedback. We train a student model to generate stories, which a teacher model rates on readability, narrative coherence, and creativity. By varying the amount of pretraining before the feedback loop, we assess the impact of this interactive learning on formal and functional linguistic competence. We find that the high-level feedback is highly data efficient: With just 1 M words of input in interactive learning, storytelling skills can improve as much as with 410 M words of next-word prediction.