# Towards Interpretable and Efficient Attention: Compressing All by Contracting a Few

arXiv: https://arxiv.org/abs/2509.16875 · HTML: https://mlsanity.com/paper/2509.16875/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 73 references that are in the map.
- First posted on arXiv 21 Sep 2025.

## Builds on (most cited first, 30 of 56)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [CBAM: Convolutional Block Attention Module](https://mlsanity.com/paper/1807.06521/) (2018)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [Semantic Understanding of Scenes through the ADE20K Dataset](https://mlsanity.com/paper/1608.05442/) (2016)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Vision Transformers Need Registers](https://mlsanity.com/paper/2309.16588/) (2023)
- [DynamicViT: Efficient Vision Transformers with Dynamic Token Sparsification](https://mlsanity.com/paper/2106.02034/) (2021)
- [Segmenter: Transformer for Semantic Segmentation](https://mlsanity.com/paper/2105.05633/) (2021)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [MetaFormer Is Actually What You Need for Vision](https://mlsanity.com/paper/2111.11418/) (2021)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Efficient Content-Based Sparse Attention with Routing Transformers](https://mlsanity.com/paper/2003.05997/) (2020)
- [Nystr"omformer: A Nystr"om-Based Algorithm for Approximating Self-Attention](https://mlsanity.com/paper/2102.03902/) (2021)
- [Symbolic Discovery of Optimization Algorithms](https://mlsanity.com/paper/2302.06675/) (2023)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)

## Built on by (most cited first, 2 of 2)

- [Mixture-of-Top-k Attention: Efficient Attention via Scalable Fast Weights](https://mlsanity.com/paper/2602.01219/) (2026)
- [Interpretable and Sparse Linear Attention with Decoupled Membership-Subspace Modeling via MCR2 Objective](https://mlsanity.com/paper/2601.17042/) (2026)

## Abstract (arXiv)

Attention mechanisms have achieved significant empirical success in multiple fields, but their underlying optimization objectives remain unclear yet. Moreover, the quadratic complexity of self-attention has become increasingly prohibitive. Although interpretability and efficiency are two mutually reinforcing pursuits, prior work typically investigates them separately. In this paper, we propose a unified optimization objective that derives inherently interpretable and efficient attention mechanisms through algorithm unrolling. Precisely, we construct a gradient step of the proposed objective with a set of forward-pass operations of our Contract-and-Broadcast Self-Attention (CBSA), which compresses input tokens towards low-dimensional structures by contracting a few representatives of them. This novel mechanism can not only scale linearly by fixing the number of representatives, but also covers the instantiations of varied attention mechanisms when using different sets of representatives. We conduct extensive experiments to demonstrate comparable performance and superior advantages over black-box attention mechanisms on visual tasks. Our work sheds light on the integration of interpretability and efficiency, as well as the unified formula of attention mechanisms.