TME-FUSE: A Norm-Clamped Geometric Fusion Framework for Correcting Rotationally Biased Volumetric Cell Graphs

Abstract

TME-FUSE: A Norm-Clamped Geometric Fusion Framework for Correcting Rotationally Biased Volumetric Cell Graphs This document establishes the mathematical foundations of the TME-FUSE architecture, a two-stage hybrid framework designed to resolve the inherent spatial incompatibilities between discrete convolutional feature extraction and continuous geometric reasoning. While 3D Convolutional Neural Networks (CNNs) excel at extracting local cellular textures from multiplexed imaging, their reliance on anisotropic voxel grids fundamentally shatters rotational symmetry. We present TME-FUSE as a geometric fusion and correction engine that projects these rotationally biased features into an exactly -equivariant Graph Neural Network (EGNN). To prevent catastrophic spatial drift during this fusion process, we introduce a continuous, 1-Lipschitz norm-clamping operator, , which acts as a bounded geometric regularizer. We mathematically prove that this regularized dynamical system fuses biased inputs into a stable equivariant space, bounding maximum per-node latent displacement to . Furthermore, empirical programmatic verification confirms topological preservation compliance on clustered biological phantoms, validating the framework's mathematical stability bounds.