# MViT: A vision transformer with fractal path reordering and dynamic positional encoding

## TL;DR

MViT is a new Vision Transformer that improves spatial coherence and structural adaptability using fractal path reordering and dynamic positional encoding.

## Contribution

The novel use of a recursive Moore curve and fractal-based components to enhance spatial continuity and structural modeling in Vision Transformers.

## Key findings

- MViT improves classification accuracy by 0.52% on CIFAR-100 and 0.31% on ImageNet-21k compared to ViT-B/16.
- The model achieves better PSNR and SSIM scores, indicating improved structural representation.
- MViT shows robustness to rotation and maintains performance across different Transformer backbones and tasks.

## Abstract

Vision Transformers have demonstrated remarkable performance in image classification and structural modeling; however, fixed patch partitioning and static positional encoding often disrupt spatial continuity, thereby limiting their ability to represent rotated structures and irregular boundary regions. To address these limitations, we propose the Moore-curve Vision Transformer (MViT), a Vision Transformer (ViT) framework based on a recursive Moore curve. The proposed framework comprises three key components. First, a multi-order fractal mapping is employed to optimize patch reordering and enhance the spatial coherence of the token sequence. Second, a 7×7 dynamic partitioning template together with a boundary compensation algorithm jointly optimizes dense structural representation and resolution adaptability. Third, a period-aware positional encoding module integrates fractal periodic parameters with convolutional features to align positional embeddings with the fractal traversal pattern. This design significantly enhances the structural adaptability of the model to complex image layouts. Experimental results show that MViT improves classification accuracy over ViT-B/16 by 0.52% and 0.31% on the CIFAR-100 and ImageNet-21k datasets, respectively, while also achieving noticeable improvements in PSNR and SSIM. Ablation and rotational perturbation experiments further confirm its robustness to rotation and localized focus variations. Moreover, MViT exhibits strong structural compatibility, maintaining stable performance across different Transformer backbones and diverse visual tasks.