Causal Energy Minimization Recasts Transformer Layer Design
There's a new framework called Causal Energy Minimization, or CEM, which reimagines Transformer layers as processes focused on optimizing energy functions, particularly emphasizing how layers are parameterized. This builds on previous energy-focused perspectives of attention, showing that weight-tied multi-head attention can be viewed as a way to adjust gradients on interaction energy. Additionally, a gated MLP with shared projections can be understood through an element-wise energy framework. CEM opens up possibilities for designs involving within-layer weight sharing and lightweight preconditioners. These CEM-derived layers were tested on language modeling tasks with about one hundred million parameters. You can find the full paper on arXiv under the identifier 2605.07588.
Key facts
- Causal Energy Minimization (CEM) is introduced as a framework for Transformer layers.
- CEM recasts Transformer layers as optimization steps on conditional energy functions.
- Weight-tied MHA is derived as a gradient update on an interaction energy.
- Gated MLP with shared up/down projections is viewed through an element-wise energy.
- Design space includes within-layer weight sharing, diagonal-plus-low-rank interactions, lightweight preconditioners, and recursive updates.
- CEM-derived layers are evaluated in language-modeling experiments at moderate hundred-million parameter scale.
- The paper is published on arXiv with ID 2605.07588.
- The approach extends prior energy-based interpretations of attention.
Entities
Institutions
- arXiv