arXiv AI By Igor Bogdanov, Changcheng Huang

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

Read the original on arXiv AI →

The study investigates whether multilingual language models solve mathematical problems using shared or language‑specific internal representations. By replaying reasoning traces across six languages and applying Centered Kernel Alignment, the authors identify layers with cross‑language alignment and train two sparse autoencoders— a baseline and a new Geometry‑Invariant SAE (GI‑SAE) that adds an InfoNCE loss to encourage language‑agnostic activations. Functional interchangeability tests reveal that higher geometric similarity does not always translate to interchangeable features, and cross‑language sharing varies by model and depth, with GI‑SAE amplifying existing structure in some models but not others.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

arXiv Computation and Language
2d ago

Double Trouble: Bilingual Pretraining Leaves Language-Conditioned Effects in Shared-Language Representations

The study compares an English-only and a bilingual decoder-only model, each 310 M parameters, trained on eight diverse languages while controlling for English exposure, compute, and document overlap. After aligning on shared English vocabulary, the authors find that token embeddings appear similar, but the deeper hidden states used for prediction diverge across models. This hidden‑state mismatch grows through middle transformer layers and persists despite controls, indicating that contextual processing differs between the models. "whyItMatters":"The findings show that embedding alignment can conceal significant internal representation differences, which is crucial for any downstream work that assumes aligned multilingual models are interchangeable."

By Anjishnu Mukherjee, Ziwei Zhu, Antonios Anastasopoulos
arXiv Computation and Language
2d ago

Cross-Lingual Alignment Without Joint Training: Do Monolingual Language Models Converge on Universal Representations?

The study investigates whether monolingual language models, trained without joint multilingual objectives, develop cross-lingual alignment. By evaluating models such as Goldfish and independently built monolingual systems, the authors find that alignable representational geometry emerges across layers, strengthening with larger data, larger models, or closer linguistic proximity. A single Procrustes rotation on parallel sentences can map hidden states between models, and applying this rotation to a German model’s residuals swaps factual predictions to those of the donor English model, demonstrating functional transfer.

By Ej Zhou, Suchir Salhan, Catherine Arnett, Anna Korhonen
arXiv AI
2d ago

Beyond the Rosetta Stone: Unification Forces in Generalization Dynamics

The paper investigates why large language models sometimes hallucinate when asked about facts in a language different from the one in which the facts were learned. By training small Transformer models on synthetic multilingual datasets, the authors show that the degree of correlation between facts and their learning language (informativeness) and the ease of language identification (extractability) determine whether models develop unified or separate representations across languages. Unified representations enable cross‑lingual fact transfer, while separate representations do not. The study proposes a unifying perspective on cross‑lingual transfer and suggests training methods to promote representational unification.

By Carter Blum, Katja Filippova, Ann Yuan, Asma Ghandeharioun, Julian Zimmert, Fred Zhang, Jessica Hoffmann, Tal Linzen, Martin Wattenberg, Lucas Dixon, Mor Geva