The Geometry of Low-Resource Language Representations

We investigate how large language models perform on low-resource languages by benchmarking eight LLMs across five experimental conditions in English, Kazakh, and Mongolian. Using 50 hand-crafted questions spanning factual, reasoning, technical, and culturally grounded categories, we evaluate 2,000 responses on accuracy, fluency, and completeness. We find a consistent performance gap of 13.8-16.7 percentage points between English and low-resource language conditions, with models maintaining surface-level fluency while producing significantly less accurate content. Cross-lingual transfer-prompting models to reason in English before translating back-yields selective gains for bilingual architectures (+2.2pp to +4.3pp) but provides no benefit to English-dominant models. Our results demonstrate that current LLMs systematically underserve low-resource language communities, and that effective mitigation strategies are architecture-dependent rather than universal.

On-Policy Self-distillation is a self-improvement paradigm that enables large language models (LLMs) to improve their capabilities by leveraging the same model as both teacher and student under different conditioning contexts. However, we find that OPSD methods can progressively degrade previously acquired capabilities: queries that are correctly responded at earlier training stages may become incorrectly responded as optimization proceeds, even the overall performance continues to improve. Further analysis reveals that this degradation coincides with a deterioration of the geometry of hidden representations, characterized by reduced intra-cluster compactness and diminished inter-cluster separation. Motivated by this observation, we propose Representation Geometry Regularization (RGR), which preserves representation geometry during post-training by encouraging compactness within cluster and separation across cluster. RGR can be seamlessly integrated into existing OPSD methods without altering their core optimization procedures. Extensive experiments on multiple OPSD methods and benchmarks show that RGR generally alleviates capability degradation while retaining capability improvements. Our code is available in https://github.com/supermachinelearner/RGR.

Large language models exhibit substantial performance variation across languages, even when solving semantically equivalent tasks. Existing analyses often treat this phenomenon as an observational disparity caused by differences in pretraining data, tokenization, or benchmark coverage. We study a complementary hypothesis: high-resource languages (HRLs) may more reliably elicit latent computations useful for task-specific (i.e. mathematical) reasoning, while lower-resource languages (LRLs) may under-activate those computations despite expressing the same task. To test this hypothesis, we introduce a mechanistic intervention framework for identifying and transferring task-relevant sparse latent features across languages. Using sparse autoencoders over residual-stream activations, we isolate features enriched in successful HRL task-specific reasoning while filtering out source-language and generic-generation features. We then construct steering directions from these features and inject them during LRL inference. The resulting interventions test whether the selected features are functionally involved in the observed reasoning gap: suppressing them should impair source-language reasoning, while activating them should partially recover target-language reasoning beyond random and non-task controls. Our framework reframes some cross-lingual reasoning gaps as failures of mechanism elicitation rather than capability absence, and offers a causally testable route to feature-mediated transfer without translation, fine-tuning, or changing the user-facing language.