Revisiting Transformer Layer Parameterization Through Causal Energy Minimization

Fuente: arXiv
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Autori principali: Xu, Jin, Couturier, Camille, Rühle, Victor, Rajmohan, Saravan, Hensman, James
Natura: Preprint
Pubblicazione: 2026
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author Xu, Jin
Couturier, Camille
Rühle, Victor
Rajmohan, Saravan
Hensman, James
author_facet Xu, Jin
Couturier, Camille
Rühle, Victor
Rajmohan, Saravan
Hensman, James
contents Transformer blocks typically combine multi-head attention (MHA) for token mixing with gated MLPs for token-wise feature transformation, yet many choices in their parameterization remain largely empirical. We introduce Causal Energy Minimization (CEM), a framework that recasts Transformer layers as optimization steps on conditional energy functions while explicitly accounting for layer parameterization. Extending prior energy-based interpretations of attention, CEM shows that weight-tied MHA can be derived as a gradient update on an interaction energy, and that a gated MLP with shared up/down projections can be viewed through an element-wise energy. This perspective identifies a design space for Transformer layers that includes within-layer weight sharing, diagonal-plus-low-rank interactions, lightweight preconditioners, and recursive updates. We evaluate CEM-derived layers in language-modeling experiments at the moderate hundred-million-parameter scale. Despite their constrained parameterizations, these layers train stably and can match corresponding Transformer baselines. Overall, our results suggest that CEM provides a useful lens for understanding Transformer layer parameterization, connecting Transformer architectures to energy-based models and motivating further exploration of energy-guided layer designs.
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id arxiv_https___arxiv_org_abs_2605_07588
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Revisiting Transformer Layer Parameterization Through Causal Energy Minimization
Xu, Jin
Couturier, Camille
Rühle, Victor
Rajmohan, Saravan
Hensman, James
Machine Learning
Artificial Intelligence
Transformer blocks typically combine multi-head attention (MHA) for token mixing with gated MLPs for token-wise feature transformation, yet many choices in their parameterization remain largely empirical. We introduce Causal Energy Minimization (CEM), a framework that recasts Transformer layers as optimization steps on conditional energy functions while explicitly accounting for layer parameterization. Extending prior energy-based interpretations of attention, CEM shows that weight-tied MHA can be derived as a gradient update on an interaction energy, and that a gated MLP with shared up/down projections can be viewed through an element-wise energy. This perspective identifies a design space for Transformer layers that includes within-layer weight sharing, diagonal-plus-low-rank interactions, lightweight preconditioners, and recursive updates. We evaluate CEM-derived layers in language-modeling experiments at the moderate hundred-million-parameter scale. Despite their constrained parameterizations, these layers train stably and can match corresponding Transformer baselines. Overall, our results suggest that CEM provides a useful lens for understanding Transformer layer parameterization, connecting Transformer architectures to energy-based models and motivating further exploration of energy-guided layer designs.
title Revisiting Transformer Layer Parameterization Through Causal Energy Minimization
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2605.07588