2025/08/26 by Usatyuk, V. S., Sapoznikov, D. A., Egorov, S. I. · 1 citation
#Algebraic Topology (math.AT) #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Machine Learning (cs.LG)
paper · doi:10.48550/arxiv.2508.18717
We present a unified framework combining statistical physics, coding theory, and algebraic topology for efficient multi-class image classification. High-dimensional feature vectors from a frozen MobileNetV2 backbone are interpreted as spins on a sparse Multi-Edge Type quasi-cyclic LDPC (MET-QC-LDPC) graph, forming a Random-Bond Ising Model (RBIM). We operate this RBIM at its Nishimori temperature, βN, where the smallest eigenvalue of the Bethe-Hessian matrix vanishes, maximizing class separability. Our theoretical contribution establishes a correspondence between local trapping sets in the code's graph and topological invariants (Betti numbers, bordism classes) of the feature manifold. A practical algorithm estimates βN efficiently with a quadratic interpolant and Newton correction, achieving a six-fold speed-up over bisection. Guided by topology, we design spherical and toroidal MET-QC-LDPC graph ensembles, using permanent bounds to suppress harmful trapping sets. This compresses 1280-dimensional features to 32 or 64 dimensions for ImageNet-10 and -100 subsets. Despite massive compression (40x fewer parameters), we achieve 98.7% accuracy on ImageNet-10 and 82.7% on ImageNet-100, demonstrating that topology-guided graph design yields highly efficient, physics-inspired embeddings with state-of-the-art performance.