# HamVision: Hamiltonian Dynamics as Inductive Bias for Medical Image Analysis

arXiv: https://arxiv.org/abs/2603.21377 · HTML: https://mlsanity.com/paper/2603.21377/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 37 references that are in the map.
- First posted on arXiv 22 Mar 2026.

## Builds on (most cited first, 23 of 23)

- [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)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Swin-Unet: Unet-like Pure Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2105.05537/) (2021)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [U-Mamba: Enhancing Long-range Dependency for Biomedical Image Segmentation](https://mlsanity.com/paper/2401.04722/) (2024)
- [UNet 3+: A Full-Scale Connected UNet for Medical Image Segmentation](https://mlsanity.com/paper/2004.08790/) (2020)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [VM-UNet: Vision Mamba UNet for Medical Image Segmentation](https://mlsanity.com/paper/2402.02491/) (2024)
- [MedViT: A Robust Vision Transformer for Generalized Medical Image Classification](https://mlsanity.com/paper/2302.09462/) (2023)
- [Mamba-3: Improved Sequence Modeling using State Space Principles](https://mlsanity.com/paper/2603.15569/) (2026)
- [MedMamba: Vision Mamba for Medical Image Classification](https://mlsanity.com/paper/2403.03849/) (2024)
- [Gabor Convolutional Networks](https://mlsanity.com/paper/1705.01450/) (2017)

## Abstract (arXiv)

We present HamVision, a framework for medical image analysis that uses the damped harmonic oscillator, a fundamental building block of signal processing, as a structured inductive bias for both segmentation and classification tasks. The oscillator's phase-space decomposition yields three functionally distinct representations: position~q (feature content), momentum~p (spatial gradients that encode boundary and texture information), and energy H = tfrac12|z|2 (a parameter-free saliency map). These representations emerge from the dynamics, not from supervision, and can be exploited by different task-specific heads without any modification to the oscillator itself. For segmentation, energy gates the skip connections while momentum injects boundary information at every decoder level (HamSeg). For classification, the three representations are globally pooled and concatenated into a phase-space feature vector (HamCls). We evaluate HamVision across ten medical imaging benchmarks spanning five imaging modalities. On segmentation, HamSeg achieves state-of-the-art Dice scores on ISIC,2018 (89.38%), ISIC,2017 (88.40%), TN3K (87.05%), and ACDC (92.40%), outperforming most baselines with only 8.57M parameters. On classification, HamCls achieves state-of-the-art accuracy on BloodMNIST (98.85%) and PathMNIST (96.65%), and competitive results on the remaining MedMNIST datasets against MedMamba and MedViT. Diagnostic analysis confirms that the oscillator's momentum consistently encodes an interior,>,boundary,>,exterior gradient for segmentation and that the energy map correlates with discriminative regions for classification, properties that emerge entirely from the Hamiltonian dynamics. Code is available at https://github.com/Minds-R-Lab/hamvision.