[2603.21377] HamVision: Hamiltonian Dynamics as Inductive Bias for Medical Image Analysis

Computer Science > Computer Vision and Pattern Recognition arXiv:2603.21377 (cs) [Submitted on 22 Mar 2026] Title:HamVision: Hamiltonian Dynamics as Inductive Bias for Medical Image Analysis Authors:Mohamed A Mabrok View a PDF of the paper titled HamVision: Hamiltonian Dynamics as Inductive Bias for Medical Image Analysis, by Mohamed A Mabrok View PDF HTML (experimental) Abstract: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 $H = \tfrac{1}{2}|z|^2$ (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...