Degrees of Freedom for Linear Attention: Distilling Softmax Attention with Optimal Feature Efficiency

• URL: http://arxiv.org/abs/2507.03340v1
• Date: Fri, 04 Jul 2025 06:59:17 GMT
• Title: Degrees of Freedom for Linear Attention: Distilling Softmax Attention with Optimal Feature Efficiency
• Authors: Naoki Nishikawa, Rei Higuchi, Taiji Suzuki,
• Abstract summary: We propose a principled method to determine the feature dimension in linear attention using the concept of statistical degrees of freedom.<n>We show that our method achieves smaller error under a fixed computational budget.<n>Our findings also provide insight into how the complexity of the attention mechanism evolves across layers.
• Score: 37.02934235737917
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Linear attention has attracted interest as a computationally efficient approximation to softmax attention, especially for long sequences. Recent studies have explored distilling softmax attention in pre-trained Transformers into linear attention. However, a critical challenge remains: how to choose the feature dimension that governs the approximation quality. Existing methods fix this dimension uniformly across all attention layers, overlooking the diverse roles and complexities of them. In this paper, we propose a principled method to automatically determine the feature dimension in linear attention using the concept of statistical degrees of freedom, which represent the effective dimensionality of the inputs. We provide a theoretical bound on the approximation error and show that the dimension chosen by our method achieves smaller error under a fixed computational budget. Furthermore, we introduce an efficient layerwise training strategy to learn nonlinear features tailored to each layer. Experiments on multiple pre-trained transformers demonstrate that our method improves the performance of distilled models compared to baselines without increasing the inference cost. Our findings also provide insight into how the complexity of the attention mechanism evolves across layers.

Related papers

• In-Context Linear Regression Demystified: Training Dynamics and Mechanistic Interpretability of Multi-Head Softmax Attention [52.159541540613915]
  We study how multi-head softmax attention models are trained to perform in-context learning on linear data.<n>Our results reveal that in-context learning ability emerges from the trained transformer as an aggregated effect of its architecture and the underlying data distribution.
  arXiv  Detail & Related papers  (2025-03-17T02:00:49Z)
• ESPFormer: Doubly-Stochastic Attention with Expected Sliced Transport Plans [13.695885742446027]
  Self-attention can lead to over-concentration on a few tokens during training, resulting in suboptimal information flow.<n>We introduce a novel, fully parallelizable doubly-stochastic attention mechanism based on sliced optimal transport.<n>Our method enforces doubleity without iterative Sinkhorn normalization, significantly enhancing efficiency.
  arXiv  Detail & Related papers  (2025-02-11T21:20:48Z)
• Bridging the Divide: Reconsidering Softmax and Linear Attention [116.34723260730405]
  We present two key perspectives to understand and alleviate the limitations of linear attention.<n>We prove that linear attention is not injective, which is prone to assign identical attention weights to different query vectors.<n> Secondly, we confirm that effective local modeling is essential for the success of Softmax attention, in which linear attention falls short.
  arXiv  Detail & Related papers  (2024-12-09T15:44:22Z)
• Beyond Linear Approximations: A Novel Pruning Approach for Attention Matrix [17.086679273053853]
  Large Language Models (LLMs) have shown immense potential in enhancing various aspects of our daily lives.<n>Their growing capabilities come at the cost of extremely large model sizes, making deployment on edge devices challenging.<n>This paper introduces a novel approach to LLM weight pruning that directly optimize for approximating the attention matrix.
  arXiv  Detail & Related papers  (2024-10-15T04:35:56Z)
• Training Dynamics of Multi-Head Softmax Attention for In-Context Learning: Emergence, Convergence, and Optimality [54.20763128054692]
  We study the dynamics of gradient flow for training a multi-head softmax attention model for in-context learning of multi-task linear regression. We prove that an interesting "task allocation" phenomenon emerges during the gradient flow dynamics.
  arXiv  Detail & Related papers  (2024-02-29T18:43:52Z)
• FLatten Transformer: Vision Transformer using Focused Linear Attention [80.61335173752146]
  Linear attention offers a much more efficient alternative with its linear complexity. Current linear attention approaches either suffer from significant performance degradation or introduce additional computation overhead. We propose a novel Focused Linear Attention module to achieve both high efficiency and expressiveness.
  arXiv  Detail & Related papers  (2023-08-01T10:37:12Z)
• Indirect-Instant Attention Optimization for Crowd Counting in Dense Scenes [3.8950254639440094]
  Indirect-Instant Attention Optimization (IIAO) module based on SoftMax-Attention. Special transformation yields relatively coarse features and, originally, the predictive fallibility of regions varies by crowd density distribution. We tailor the Regional Correlation Loss (RCLoss) to retrieve continuous error-prone regions and smooth spatial information.
  arXiv  Detail & Related papers  (2022-06-12T03:29:50Z)
• Stabilizing Q-learning with Linear Architectures for Provably Efficient Learning [53.17258888552998]
  This work proposes an exploration variant of the basic $Q$-learning protocol with linear function approximation. We show that the performance of the algorithm degrades very gracefully under a novel and more permissive notion of approximation error.
  arXiv  Detail & Related papers  (2022-06-01T23:26:51Z)
• Doubly Adaptive Scaled Algorithm for Machine Learning Using Second-Order Information [37.70729542263343]
  We present a novel adaptive optimization algorithm for large-scale machine learning problems. Our method dynamically adapts the direction and step-size. Our methodology does not require a tedious tuning rate tuning.
  arXiv  Detail & Related papers  (2021-09-11T06:39:50Z)

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.