# Self-Attention And Beyond the Infinite: Towards Linear Transformers with Infinite Self-Attention

arXiv: https://arxiv.org/abs/2603.00175 · HTML: https://mlsanity.com/paper/2603.00175/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 49 of its 76 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Builds on (most cited first, 30 of 49)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Quantifying Attention Flow in Transformers](https://mlsanity.com/paper/2005.00928/) (2020)
- [Transformer Interpretability Beyond Attention Visualization](https://mlsanity.com/paper/2012.09838/) (2020)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [InternImage: Exploring Large-Scale Vision Foundation Models with Deformable Convolutions](https://mlsanity.com/paper/2211.05778/) (2022)
- [Nystr"omformer: A Nystr"om-Based Algorithm for Approximating Self-Attention](https://mlsanity.com/paper/2102.03902/) (2021)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [MambaVision: A Hybrid Mamba-Transformer Vision Backbone](https://mlsanity.com/paper/2407.08083/) (2024)
- [FLatten Transformer: Vision Transformer using Focused Linear Attention](https://mlsanity.com/paper/2308.00442/) (2023)
- [SOFT: Softmax-free Transformer with Linear Complexity](https://mlsanity.com/paper/2110.11945/) (2021)
- [Demystify Mamba in Vision: A Linear Attention Perspective](https://mlsanity.com/paper/2405.16605/) (2024)
- [Global Context Vision Transformers](https://mlsanity.com/paper/2206.09959/) (2022)
- [Agent Attention: On the Integration of Softmax and Linear Attention](https://mlsanity.com/paper/2312.08874/) (2023)
- [RMT: Retentive Networks Meet Vision Transformers](https://mlsanity.com/paper/2309.11523/) (2023)

## Abstract (arXiv)

The quadratic cost of softmax attention limits Transformer scalability in high-resolution vision. We introduce Infinite Self-Attention (InfSA), a spectral reformulation that treats each attention layer as a diffusion step on a content-adaptive token graph, accumulating multi-hop interactions through a discounted Neumann series over attention matrices. This links self-attention to classical graph centrality (Katz, PageRank, eigenvector centrality) for interpretable token weighting. We also show the Neumann kernel equals the fundamental matrix of an absorbing Markov chain, so a token's centrality is its expected number of random-walk visits before absorption. We then propose Linear-InfSA, a linear-time variant that approximates the principal eigenvector of the implicit attention operator without forming the full attention matrix. It keeps an auxiliary state of fixed size proportional to per-head dimension dh (independent of sequence length N), is drop-in compatible with Vision Transformers, and supports stable training at 4096 by 4096 and inference at 9216 by 9216 (about 332k tokens). In a 4-layer ViT (53.5M parameters, 59 GFLOPs at 224 by 224), Linear-InfSA reaches 84.7% top-1 on ImageNet-1K, a +3.2 point architectural gain over an equal-depth softmax ViT trained with the same recipe. On ImageNet-V2, InfViT variants outperform all compared baselines (up to 79.8% vs 76.8%), indicating robustness under distribution shift. On an A100 40GB GPU, Linear-InfViT runs at 231 images/s and 0.87 J/image (13x better throughput and energy than equal-depth ViT) and is the only tested model to complete 9216 by 9216 inference without out-of-memory. The linear approximation closely matches the dominant eigenvector of the quadratic operator (cosine 0.985).