Customizing the Inductive Biases of Softmax Attention using Structured Matrices

• URL: http://arxiv.org/abs/2509.07963v1
• Date: Tue, 09 Sep 2025 17:50:58 GMT
• Title: Customizing the Inductive Biases of Softmax Attention using Structured Matrices
• Authors: Yilun Kuang, Noah Amsel, Sanae Lotfi, Shikai Qiu, Andres Potapczynski, Andrew Gordon Wilson,
• Abstract summary: Core component of attention is the scoring function, which transforms the inputs into low-dimensional queries and keys.<n>We propose new scoring functions based on computationally efficient structured matrices with high ranks, including Block-Train (BTT) and Multi-Level Low Rank (MLR)<n>Our MLR-based attention method achieves improved scaling laws compared to both standard attention and variants of sliding window attention.
• Score: 46.30740502186753
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The core component of attention is the scoring function, which transforms the inputs into low-dimensional queries and keys and takes the dot product of each pair. While the low-dimensional projection improves efficiency, it causes information loss for certain tasks that have intrinsically high-dimensional inputs. Additionally, attention uses the same scoring function for all input pairs, without imposing a distance-dependent compute bias for neighboring tokens in the sequence. In this work, we address these shortcomings by proposing new scoring functions based on computationally efficient structured matrices with high ranks, including Block Tensor-Train (BTT) and Multi-Level Low Rank (MLR) matrices. On in-context regression tasks with high-dimensional inputs, our proposed scoring functions outperform standard attention for any fixed compute budget. On language modeling, a task that exhibits locality patterns, our MLR-based attention method achieves improved scaling laws compared to both standard attention and variants of sliding window attention. Additionally, we show that both BTT and MLR fall under a broader family of efficient structured matrices capable of encoding either full-rank or distance-dependent compute biases, thereby addressing significant shortcomings of standard attention. Finally, we show that MLR attention has promising results for long-range time-series forecasting.

Related papers

• STILL: Selecting Tokens for Intra-Layer Hybrid Attention to Linearize LLMs [23.745366354566315]
  Linearizing pretrained large language models (LLMs) primarily relies on intra-layer hybrid attention mechanisms.<n>We propose STILL, an intra-layer hybrid linearization framework for efficiently linearizing LLMs.
  arXiv  Detail & Related papers  (2026-02-02T14:49:18Z)
• LUNA: Linear Universal Neural Attention with Generalization Guarantees [27.74721677870656]
  textscLuna achieves state-of-the-art average accuracy among efficient Transformers under compute parity.<n>textscLuna also excels at post-hoc conversion: replacing softmax in fine-tuned BERT and ViT-B/16 checkpoints.
  arXiv  Detail & Related papers  (2025-12-08T21:49:55Z)
• Modality Agnostic Efficient Long Range Encoder [14.705955027331674]
  We address the challenge of long-context processing on a single device using generic implementations.<n>To overcome these limitations, we propose MAELRE, a unified and efficient transformer architecture.<n>We demonstrate that MAELRE achieves superior accuracy while reducing computational cost compared to existing long-context models.
  arXiv  Detail & Related papers  (2025-07-25T16:19:47Z)
• Attention Condensation via Sparsity Induced Regularized Training [0.0]
  Self-attention dominates the transformer's inference time as the context window expands.<n>We extend a theoretical framework of attention sparsity in Large Language Models.<n>A customized loss function is designed to enforce the sparsity by restricting the number of top elements in the attention matrix.
  arXiv  Detail & Related papers  (2025-03-03T14:09:13Z)
• Short-Long Convolutions Help Hardware-Efficient Linear Attention to Focus on Long Sequences [60.489682735061415]
  We propose CHELA, which replaces state space models with short-long convolutions and implements linear attention in a divide-and-conquer manner. Our experiments on the Long Range Arena benchmark and language modeling tasks demonstrate the effectiveness of the proposed method.
  arXiv  Detail & Related papers  (2024-06-12T12:12:38Z)
• Spectral Entry-wise Matrix Estimation for Low-Rank Reinforcement Learning [53.445068584013896]
  We study matrix estimation problems arising in reinforcement learning (RL) with low-rank structure. In low-rank bandits, the matrix to be recovered specifies the expected arm rewards, and for low-rank Markov Decision Processes (MDPs), it may for example characterize the transition kernel of the MDP. We show that simple spectral-based matrix estimation approaches efficiently recover the singular subspaces of the matrix and exhibit nearly-minimal entry-wise error.
  arXiv  Detail & Related papers  (2023-10-10T17:06:41Z)
• SEA: Sparse Linear Attention with Estimated Attention Mask [51.22399593954608]
  Long seqeuences pose a problem due to the quadratic complexity of the attention operation. Previous research has aimed to lower the complexity by sparsifying or linearly approximating the attention matrix. We propose SEA: Sparse linear attention with an Estimated Attention mask.
  arXiv  Detail & Related papers  (2023-10-03T03:56:26Z)
• 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)
• Towards Model-Size Agnostic, Compute-Free, Memorization-based Inference of Deep Learning [5.41530201129053]
  This paper proposes a novel memorization-based inference (MBI) that is compute free and only requires lookups. Specifically, our work capitalizes on the inference mechanism of the recurrent attention model (RAM) By leveraging the low-dimensionality of glimpse, our inference procedure stores key value pairs comprising of glimpse location, patch vector, etc. in a table. The computations are obviated during inference by utilizing the table to read out key-value pairs and performing compute-free inference by memorization.
  arXiv  Detail & Related papers  (2023-07-14T21:01:59Z)
• Learning distributed representations with efficient SoftMax normalization [3.8673630752805437]
  We propose a linear-time approximation to compute the normalization constants of $rm SoftMax(XYT)$ for embedding vectors with bounded norms.<n>We show on some pre-trained embedding datasets that the proposed estimation method achieves higher or comparable accuracy with competing methods.<n>The proposed algorithm is interpretable and easily adapted to arbitrary embedding problems.
  arXiv  Detail & Related papers  (2023-03-30T15:48:26Z)
• DBA: Efficient Transformer with Dynamic Bilinear Low-Rank Attention [53.02648818164273]
  We present an efficient yet effective attention mechanism, namely the Dynamic Bilinear Low-Rank Attention (DBA) DBA compresses the sequence length by input-sensitive dynamic projection matrices and achieves linear time and space complexity. Experiments over tasks with diverse sequence length conditions show that DBA achieves state-of-the-art performance.
  arXiv  Detail & Related papers  (2022-11-24T03:06:36Z)

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.