Revisiting Transformer Layer Parameterization Through Causal Energy Minimization

• URL: http://arxiv.org/abs/2605.07588v1
• Date: Fri, 08 May 2026 11:02:11 GMT
• Title: Revisiting Transformer Layer Parameterization Through Causal Energy Minimization
• Abstract summary: We introduce Causal Energy Minimization (CEM), a framework that recasts Transformer layers as optimization steps on conditional energy functions.<n>We show that CEM connects Transformer architectures to energy-based models and motivate further exploration of energy-guided layer designs.
• Score: 19.719105230471282
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• YuriiFormer: A Suite of Nesterov-Accelerated Transformers [62.40952219538543]
  We propose a variational framework that interprets transformer layers as iterations of an optimization algorithm acting on token embeddings.<n>In this view, self-attention implements gradient step of an interaction energy, while layers correspond to gradient updates of a potential energy.<n>Standard GPT-style transformers emerge as vanilla gradient descent on the resulting composite objective, implemented via Lie-Trotter splitting between these two energys.
  arXiv  Detail & Related papers  (2026-01-30T18:06:21Z)
• Wavy Transformer [5.4806374384787695]
  We propose Wavy Transformer, which consists of a novel attention layer based on second-order wavy dynamics.<n>We also introduce a feed-forward network and a normalization layer designed to preserve the physical state-velocity relationship under the chain rule.
  arXiv  Detail & Related papers  (2025-08-18T10:03:38Z)
• Hyper-SET: Designing Transformers via Hyperspherical Energy Minimization [32.04194224236952]
  We formalize token dynamics as a joint maximum likelihood estimation on the hypersphere.<n>We present textitHyper-Spherical Energy Transformer (Hyper-SET), a recurrent-depth alternative to vanilla Transformers.
  arXiv  Detail & Related papers  (2025-02-17T10:39:11Z)
• Skip-Layer Attention: Bridging Abstract and Detailed Dependencies in Transformers [56.264673865476986]
  This paper introduces Skip-Layer Attention (SLA) to enhance Transformer models. SLA improves the model's ability to capture dependencies between high-level abstract features and low-level details. Our implementation extends the Transformer's functionality by enabling queries in a given layer to interact with keys and values from both the current layer and one preceding layer.
  arXiv  Detail & Related papers  (2024-06-17T07:24:38Z)
• MoEUT: Mixture-of-Experts Universal Transformers [75.96744719516813]
  Universal Transformers (UTs) have advantages over standard Transformers in learning compositional generalizations. Layer-sharing drastically reduces the parameter count compared to the non-shared model with the same dimensionality. No previous work has succeeded in proposing a shared-layer Transformer design that is competitive in parameter count-dominated tasks such as language modeling.
  arXiv  Detail & Related papers  (2024-05-25T03:24:32Z)
• Isomer: Isomerous Transformer for Zero-shot Video Object Segmentation [59.91357714415056]
  We propose two Transformer variants: Context-Sharing Transformer (CST) and Semantic Gathering-Scattering Transformer (S GST) CST learns the global-shared contextual information within image frames with a lightweight computation; S GST models the semantic correlation separately for the foreground and background. Compared with the baseline that uses vanilla Transformers for multi-stage fusion, ours significantly increase the speed by 13 times and achieves new state-of-the-art ZVOS performance.
  arXiv  Detail & Related papers  (2023-08-13T06:12:00Z)
• Transformers from an Optimization Perspective [24.78739299952529]
  We study the problem of finding an energy function underlying the Transformer model. By finding such a function, we can reinterpret Transformers as the unfolding of an interpretable optimization process. This work contributes to our intuition and understanding of Transformers, while potentially laying the ground-work for new model designs.
  arXiv  Detail & Related papers  (2022-05-27T10:45:15Z)
• Towards Lightweight Transformer via Group-wise Transformation for Vision-and-Language Tasks [126.33843752332139]
  We introduce Group-wise Transformation towards a universal yet lightweight Transformer for vision-and-language tasks, termed as LW-Transformer. We apply LW-Transformer to a set of Transformer-based networks, and quantitatively measure them on three vision-and-language tasks and six benchmark datasets. Experimental results show that while saving a large number of parameters and computations, LW-Transformer achieves very competitive performance against the original Transformer networks for vision-and-language tasks.
  arXiv  Detail & Related papers  (2022-04-16T11:30:26Z)
• Rewiring the Transformer with Depth-Wise LSTMs [55.50278212605607]
  We present a Transformer with depth-wise LSTMs connecting cascading Transformer layers and sub-layers. Experiments with the 6-layer Transformer show significant BLEU improvements in both WMT 14 English-German / French tasks and the OPUS-100 many-to-many multilingual NMT task.
  arXiv  Detail & Related papers  (2020-07-13T09:19:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.