# Energy-Mamba: A Physics-Constrained State-Space Model for Medical Image Classification

arXiv: https://arxiv.org/abs/2608.19813 · HTML: https://mlsanity.com/paper/2608.19813/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mamba for medical image analysis, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 14 of its 18 references that are in the map.
- First posted on arXiv 20 Aug 2026.

## Placed in

- State-space sequence models (S4, Mamba) / [Mamba for medical image analysis](https://mlsanity.com/ssm/mamba-for-medical-image-analysis/)

## Builds on (most cited first, 14 of 14)

- [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)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [MedMNIST Classification Decathlon: A Lightweight AutoML Benchmark for Medical Image Analysis](https://mlsanity.com/paper/2010.14925/) (2020)
- [MedViT: A Robust Vision Transformer for Generalized Medical Image Classification](https://mlsanity.com/paper/2302.09462/) (2023)
- [MedMamba: Vision Mamba for Medical Image Classification](https://mlsanity.com/paper/2403.03849/) (2024)
- [Transformers-based architectures for stroke segmentation: A review](https://mlsanity.com/paper/2403.18637/) (2024)
- [Flatten Wisely: How Patch Order Shapes Mamba-Powered Vision for MRI Segmentation](https://mlsanity.com/paper/2507.13384/) (2025)
- [A Hybrid CNN-VSSM model for Multi-View, Multi-Task Mammography Analysis: Robust Diagnosis with Attention-Based Fusion](https://mlsanity.com/paper/2507.16955/) (2025)

## Abstract (arXiv)

State-Space Models (SSMs), particularly Mamba, offer linear-time complexity for long-range dependencies, making them attractive for medical imaging with limited annotated data. However, adapting these sequential models to 2D images through unconstrained state evolution causes representational drift, the dynamic hidden state progressively loses fidelity to local image features. We introduce Energy-Mamba, integrating SSM dynamics with physics-informed constraints via a learnable potential energy function that quantifies compatibility between evolving states and static local features. Our Energy-Mamba Block introduces a gradient-based forcing term, computed dynamically via automatic differentiation, that pulls states toward low-energy configurations maintaining local visual fidelity. This formulation mirrors Hamiltonian dynamics: kinetic energy (SSM scan) plus potential energy (our constraint function) govern state trajectories. This architectural prior enables learning implicit constraints for robust, faithful representations, crucial in medical imaging where fine-grained local detail drives accurate diagnosis. Evaluated on four datasets (retinal OCT, chest X-ray, microscopy, abdominal CT), Energy-Mamba achieves state-of-the-art classification performance with significantly fewer parameters, demonstrating that physics-informed grounding can enhance both efficiency and representational quality in medical vision tasks.