arXiv:2508.18717v2 Announce Type: replace
Abstract: Modern multi-class image classification relies on high-dimensional CNN feature vectors, which are computationally expensive and obscure the underlying data geometry. Conventional graph-based classifiers degrade on natural multi-class images because typical graphs fail to preserve separability on feature manifolds with complex topology. We address this with a physics-inspired pipeline frozen MobileNetV2 embeddings are treated as Ising spins on a sparse Multi-Edge Type QC-LDPC graph forming a Random Bond Ising Model. The system is tuned to its Nishimori temperature identified where the smallest Bethe-Hessian eigenvalue vanishes. Our method rests on two innovations: we prove a spectral-topological correspondence linking graph trapping sets to invariants via the Ihara-Bass zeta function removing these structures boosts top-1 accuracy over four-fold in multi-class settings; we develop a quadratic-Newton estimator for the Nishimori temperature converging in around 9 Arnoldi iterations for a 6-times speedup enabling spectral embedding on scales like ImageNet-100. The resulting graphs compress 1280-dimensional MobileNetV2 features to 32 dimensions for ImageNet10 and 64 for ImageNet-100 We achieve 98.7% top-1 accuracy on ImageNet-10 and 84.92% on ImageNet-100 with a three-graph soft ensemble Versus MobileNetV2 our hard ensemble increases top-1 by 0.1% while cutting FLOPs by 2.67-times compared to ResNet50 the soft ensemble drops top1 by only 1.09% yet reduces FLOPs by 29-times. Novelty lies in (a) rigorously linking trapping sets to topological defects, (b) an efficient Nishimori temperature estimator and (c) demonstrating that topology-guided LDPC embedding produces highly compressed accurate classifiers for resource-constrained deployment