Revisiting Transformer Layer Parameterization Through Causal Energy Minimization

2026-05-08

AI Summary

This work addresses the empirical and theoretically unprincipled parameterization of multi-head attention and gated MLP modules in standard Transformer layers. The authors propose the Causal Energy Minimization (CEM) framework, which reformulates a Transformer layer as an optimization step governed by a conditional energy function, thereby establishing—for the first time—an explicit connection between Transformers and energy-based models. This unified perspective not only provides a principled foundation for architectural design but also reveals novel structural possibilities, such as weight sharing and diagonal-plus-low-rank interactions. Furthermore, the framework incorporates lightweight preconditioners and recursive update mechanisms. Experiments on billion-parameter language models demonstrate that CEM-derived layers achieve performance comparable to standard Transformers while maintaining training stability and parameter efficiency.

Abstract

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.

Problem

• Transformer parameterization
• energy-based models
• layer design
• weight sharing
• causal energy minimization

Innovation

• Causal Energy Minimization
• Energy-based Models
• Weight-tied Attention
• Gated MLP
• Transformer Parameterization