Joachim Koehler

Markus Frey, Behzad Shomali, Joachim Koehler et al.

Looped transformers apply a shared block multiple times and have emerged as a parameter-efficient route to scaling compute in language models. However, at fixed FLOPs a looped model has strictly less capacity than a baseline transformer. We propose a novel dual-path block that can flexibly scale compute, the number of sequential operations applied to a hidden state, and capacity, the parameters available at a single step. For this we expose both axes as parallel pathways within a single layer: a deep sublayer re-applied K times with shared parameters, and a wide sublayer with an enlarged feed-forward network applied once. Independent per-token gates combine both axes and allow detailed per-token routing analyses. We show that across two FLOP budgets, our dual-path model surpasses iso-FLOP matched models on language modeling and downstream evaluations, while using fewer parameters than the baseline at matched FLOPs. The learned gates are directly interpretable and show systematic per-token allocation with function words and lexical content trend wide, while punctuation, symbols, and arithmetic tokens trend deep.

Behzad Shomali, Luisa Victor, Tim Selbach et al.

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.