# Spatial Entropy as an Inductive Bias for Vision Transformers

arXiv: https://arxiv.org/abs/2206.04636 · HTML: https://mlsanity.com/paper/2206.04636/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 86 of its 113 references that are in the map.
- First posted on arXiv 9 Jun 2022.

## Builds on (most cited first, 30 of 86)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [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)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [BEiT: BERT Pre-Training of Image Transformers](https://mlsanity.com/paper/2106.08254/) (2021)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)

## Built on by (most cited first, 5 of 5)

- [Your Large Vision-Language Model Only Needs A Few Attention Heads For Visual Grounding](https://mlsanity.com/paper/2503.06287/) (2025)
- [Sparsity Forcing: Reinforcing Token Sparsity of MLLMs](https://mlsanity.com/paper/2504.18579/) (2025)
- [Guiding the Experts: Semantic Priors for Efficient and Focused MoE Routing](https://mlsanity.com/paper/2505.18586/) (2025)
- [OSS: Open Suturing Skills Vision-Based Assessment Challenge 2024-2025](https://mlsanity.com/paper/2605.22200/) (2026)
- [Controlling Motion Transfer in Diffusion Transformers via Attention Heads](https://mlsanity.com/paper/2607.11081/) (2026)

## Abstract (arXiv)

Recent work on Vision Transformers (VTs) showed that introducing a local inductive bias in the VT architecture helps reducing the number of samples necessary for training. However, the architecture modifications lead to a loss of generality of the Transformer backbone, partially contradicting the push towards the development of uniform architectures, shared, e.g., by both the Computer Vision and the Natural Language Processing areas. In this work, we propose a different and complementary direction, in which a local bias is introduced using an auxiliary self-supervised task, performed jointly with standard supervised training. Specifically, we exploit the observation that the attention maps of VTs, when trained with self-supervision, can contain a semantic segmentation structure which does not spontaneously emerge when training is supervised. Thus, we explicitly encourage the emergence of this spatial clustering as a form of training regularization. In more detail, we exploit the assumption that, in a given image, objects usually correspond to few connected regions, and we propose a spatial formulation of the information entropy to quantify this object-based inductive bias. By minimizing the proposed spatial entropy, we include an additional self-supervised signal during training. Using extensive experiments, we show that the proposed regularization leads to equivalent or better results than other VT proposals which include a local bias by changing the basic Transformer architecture, and it can drastically boost the VT final accuracy when using small-medium training sets. The code is available at https://github.com/helia95/SAR.