# Learning Spatial Decay for Vision Transformers

arXiv: https://arxiv.org/abs/2508.09525 · HTML: https://mlsanity.com/paper/2508.09525/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 60 references that are in the map.
- First posted on arXiv 13 Aug 2025.

## Builds on (most cited first, 30 of 45)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Random Erasing Data Augmentation](https://mlsanity.com/paper/1708.04896/) (2017)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [CoAtNet: Marrying Convolution and Attention for All Data Sizes](https://mlsanity.com/paper/2106.04803/) (2021)
- [CSWin Transformer: A General Vision Transformer Backbone with Cross-Shaped Windows](https://mlsanity.com/paper/2107.00652/) (2021)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [InternImage: Exploring Large-Scale Vision Foundation Models with Deformable Convolutions](https://mlsanity.com/paper/2211.05778/) (2022)
- [Conditional Positional Encodings for Vision Transformers](https://mlsanity.com/paper/2102.10882/) (2021)
- [Bottleneck Transformers for Visual Recognition](https://mlsanity.com/paper/2101.11605/) (2021)
- [CMT: Convolutional Neural Networks Meet Vision Transformers](https://mlsanity.com/paper/2107.06263/) (2021)
- [Focal Self-attention for Local-Global Interactions in Vision Transformers](https://mlsanity.com/paper/2107.00641/) (2021)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [MiniMax-01: Scaling Foundation Models with Lightning Attention](https://mlsanity.com/paper/2501.08313/) (2025)
- [BiFormer: Vision Transformer with Bi-Level Routing Attention](https://mlsanity.com/paper/2303.08810/) (2023)
- [RegionViT: Regional-to-Local Attention for Vision Transformers](https://mlsanity.com/paper/2106.02689/) (2021)
- [HGRN2: Gated Linear RNNs with State Expansion](https://mlsanity.com/paper/2404.07904/) (2024)
- [MPViT: Multi-Path Vision Transformer for Dense Prediction](https://mlsanity.com/paper/2112.11010/) (2021)

## Built on by (most cited first, 1 of 1)

- [AI-Driven Carbon Monitoring: Transformer-Based Reconstruction of Atmospheric CO2 in Canadian Poultry Regions](https://mlsanity.com/paper/2510.23663/) (2025)

## Abstract (arXiv)

Vision Transformers (ViTs) have revolutionized computer vision, yet their self-attention mechanism lacks explicit spatial inductive biases, leading to suboptimal performance on spatially-structured tasks. Existing approaches introduce data-independent spatial decay based on fixed distance metrics, applying uniform attention weighting regardless of image content and limiting adaptability to diverse visual scenarios. Inspired by recent advances in large language models where content-aware gating mechanisms (e.g., GLA, HGRN2, FOX) significantly outperform static alternatives, we present the first successful adaptation of data-dependent spatial decay to 2D vision transformers. We introduce Spatial Decay Transformer (SDT), featuring a novel Context-Aware Gating (CAG) mechanism that generates dynamic, data-dependent decay for patch interactions. Our approach learns to modulate spatial attention based on both content relevance and spatial proximity. We address the fundamental challenge of 1D-to-2D adaptation through a unified spatial-content fusion framework that integrates manhattan distance-based spatial priors with learned content representations. Extensive experiments on ImageNet-1K classification and generation tasks demonstrate consistent improvements over strong baselines. Our work establishes data-dependent spatial decay as a new paradigm for enhancing spatial attention in vision transformers.