# TailProp: content-adaptive light- and heavy-tailed propagation for vision

arXiv: https://arxiv.org/abs/2609.11081 · HTML: https://mlsanity.com/paper/2609.11081/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 46 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Unified Perceptual Parsing for Scene Understanding](https://mlsanity.com/paper/1807.10221/) (2018)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [CSWin Transformer: A General Vision Transformer Backbone with Cross-Shaped Windows](https://mlsanity.com/paper/2107.00652/) (2021)
- [InternImage: Exploring Large-Scale Vision Foundation Models with Deformable Convolutions](https://mlsanity.com/paper/2211.05778/) (2022)
- [XCiT: Cross-Covariance Image Transformers](https://mlsanity.com/paper/2106.09681/) (2021)
- [Deep Learning in Spiking Neural Networks](https://mlsanity.com/paper/1804.08150/) (2018)
- [MambaVision: A Hybrid Mamba-Transformer Vision Backbone](https://mlsanity.com/paper/2407.08083/) (2024)
- [DaViT: Dual Attention Vision Transformers](https://mlsanity.com/paper/2204.03645/) (2022)
- [EfficientVMamba: Atrous Selective Scan for Light Weight Visual Mamba](https://mlsanity.com/paper/2403.09977/) (2024)
- [MambaOut: Do We Really Need Mamba for Vision?](https://mlsanity.com/paper/2405.07992/) (2024)
- [Encoding physics to learn reaction-diffusion processes](https://mlsanity.com/paper/2106.04781/) (2021)
- [Guided Depth Super-Resolution by Deep Anisotropic Diffusion](https://mlsanity.com/paper/2211.11592/) (2022)
- [Building Vision Models upon Heat Conduction](https://mlsanity.com/paper/2405.16555/) (2024)
- [WaveFormer: Frequency-Time Decoupled Vision Modeling with Wave Equation](https://mlsanity.com/paper/2601.08602/) (2026)

## Abstract (arXiv)

Science-inspired vision models show that explicit propagation dynamics can provide structured and interpretable alternatives to conventional token mixing. Existing formulations, however, typically construct and adapt visual propagation within a particular dynamical family, while visual representations can require substantially different spatial interactions across samples, channels, and network stages. We explore cross-regime adaptive propagation and introduce TailProp, a hierarchical vision backbone built upon the Tail Propagation Operator (TPO). TPO uses Gaussian and Cauchy stable-process propagators as complementary bases with rapidly decaying and heavy-tailed spatial influence, and predicts a content-conditioned channel-wise coefficient to adaptively combine them. Because this coefficient is spatially shared, the two responses are fused directly in the DCT domain with a single DCT/IDCT pair, yielding O(N1.5) spatial mixing for square feature maps with N=HW and fixed channel width. Across image classification, object detection, semantic segmentation, robustness, and cross-backbone restoration, TailProp consistently outperforms matched propagation baselines; TailProp-B reaches 84.4% Top-1 accuracy on ImageNet-1K, 50.3/44.8 box/mask AP under the 3x Mask R-CNN schedule, and 50.8% mIoU on ADE20K. Controlled ablations further show that these gains are not explained by single-basis propagation, an additional same-family branch, or within-family adaptive order alone, supporting complementary two-basis propagation as an effective design principle for visual representation learning.