# Proximal Vision Transformer: Enhancing Feature Representation through Two-Stage Manifold Geometry

arXiv: https://arxiv.org/abs/2508.17081 · HTML: https://mlsanity.com/paper/2508.17081/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 22 references that are in the map.
- First posted on arXiv 23 Aug 2025.

## Builds on (most cited first, 13 of 13)

- [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)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Tokens-to-Token ViT: Training Vision Transformers from Scratch on ImageNet](https://mlsanity.com/paper/2101.11986/) (2021)
- [CrossViT: Cross-Attention Multi-Scale Vision Transformer for Image Classification](https://mlsanity.com/paper/2103.14899/) (2021)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [ImageNet-21K Pretraining for the Masses](https://mlsanity.com/paper/2104.10972/) (2021)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Deep Unfolding of a Proximal Interior Point Method for Image Restoration](https://mlsanity.com/paper/1812.04276/) (2018)
- [Quasi-Newton Methods for Machine Learning: Forget the Past, Just Sample](https://mlsanity.com/paper/1901.09997/) (2019)
- [Deep Transform and Metric Learning Network: Wedding Deep Dictionary Learning and Neural Networks](https://mlsanity.com/paper/2002.07898/) (2020)
- [Deep Transform and Metric Learning Networks](https://mlsanity.com/paper/2104.10329/) (2021)

## Abstract (arXiv)

The Vision Transformer (ViT) architecture has become widely recognized in computer vision, leveraging its self-attention mechanism to achieve remarkable success across various tasks. Despite its strengths, ViT's optimization remains confined to modeling local relationships within individual images, limiting its ability to capture the global geometric relationships between data points. To address this limitation, this paper proposes a novel framework that integrates ViT with the proximal tools, enabling a unified geometric optimization approach to enhance feature representation and classification performance. In this framework, ViT constructs the tangent bundle of the manifold through its self-attention mechanism, where each attention head corresponds to a tangent space, offering geometric representations from diverse local perspectives. Proximal iterations are then introduced to define sections within the tangent bundle and project data from tangent spaces onto the base space, achieving global feature alignment and optimization. Experimental results confirm that the proposed method outperforms traditional ViT in terms of classification accuracy and data distribution.