David Berghaus, Arber Zela, Behzad Shomali, Markus Frey, Mehdi Ali, Rafet Sifa, Volkan Cevher
Typed decision models choose among a fixed set of answer options in a single forward pass, so unlike generative language models they cannot spend more test-time compute on hard inputs by generating more tokens. Looping a block of layers offers this compute in latent space without adding parameters, but prior work found no gain from loops retrofitted into conventionally pretrained models. We show that such loops help when trained together with the decision model. Our method, RELOAD (retrofitted loops for adaptive decisions), fine-tunes a pretrained encoder or decoder with a damped loop over its middle block and a lightweight controller picks the number of passes adaptively for each input. Across six models from 0.4B to 4B parameters, looping improves both accuracy and calibration, mostly on problems that need longer chains of reasoning than any seen in training, where encoders gain up to 23 points. Neither matched training compute nor more data closes this gap, and separate layers for each pass come close only with nearly twice the parameters. The controller keeps most of the gain at about three quarters of the compute.
Markus Frey, Behzad Shomali, Joachim Koehler, Mehdi Ali
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 argue that compute, the number of sequential operations applied to a hidden state, and capacity, the parameters available at a single step, are distinct scaling axes that standard transformer layers conflate. We propose a dual-path block that exposes 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, combined by independent per-token gates. At two FLOP budgets, the best dual-path configuration surpasses both iso-FLOP single-axis controls on aggregate language modelling, commonsense, and math metrics, while using 17-33% fewer parameters than the width-scaled baseline. The learned gates are directly interpretable and show systematic per-token allocation: function words and lexical content trend wide, while punctuation, symbols, and arithmetic tokens trend deep. Our results suggest that compute and capacity can be scaled separately, with the model balancing the two token by token.
Behzad Shomali Rheinische Friedrich-Wilhelms Universität Bonn, Luisa Victor Rheinische Friedrich-Wilhelms Universität Bonn, Tim Selbach Rheinische Friedrich-Wilhelms Universität Bonn and Fraunhofer Institute IAIS, Fraunhofer IAIS, Ali Hamza Bashir Georg-August Universität Göttingen and Fraunhofer Institute IAIS, Fraunhofer IAIS, David Berghaus Fraunhofer Institute IAIS, Fraunhofer IAIS, Joachim Koehler, Mehdi Ali Fraunhofer Institute IAIS, Fraunhofer IAIS, Markus Frey Fraunhofer Institute IAIS, Fraunhofer IAIS
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.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 4: Student Research Workshop) · 2026 · 正式发表