{"ID":2877931,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.18717","arxiv_id":"2508.18717","title":"Natural Image Classification via Quasi-Cyclic Graph Ensembles and Random-Bond Ising Models at the Nishimori Temperature","abstract":"Modern multi-class image classification uses high-dimensional CNN features that incur large memory and computational costs and obscure the data manifold's geometry. Existing graph-based spectral classifiers work on synthetic or binary tasks but degrade on natural images with many classes because feature manifolds have non-trivial topology. We introduce a physics-inspired pipeline where frozen MobileNetV2 features are interpreted as Ising spins on a sparse multi-edge type quasi-cyclic LDPC graph, defining a Random-Bond Ising Model (RBIM). The model is operated at its Nishimori temperature -- where the smallest eigenvalue of the Bethe-Hessian matrix vanishes. A spectral-topological correspondence links trapping sets in the Tanner graph to topological invariants via poles of the Ihara-Bass zeta function, enabling systematic suppression of harmful substructures that otherwise reduce top-1 accuracy by more than a factor of four. A fast quadratic-Newton estimator finds the Nishimori temperature in $\\sim 9$ Arnoldi iterations, a sixfold speed-up over bisection. The resulting ensembles compress the original $1280$-dimensional MobileNetV2 representation to $32$ dimensions (ImageNet-10) or $64$ dimensions (ImageNet-100). We achieve $98.7\\%$ top-1 accuracy on ImageNet-10 and $84.92\\%$ on ImageNet-100 using a three-graph soft ensemble. Relative to MobileNetV2, our hard ensemble increases accuracy by $0.10\\%$ while reducing FLOPs by a factor of $2.67$. Against ResNet-50, the soft ensemble drops only 1.09% accuracy yet cuts FLOPs by $29\\times$. The novelty lies in (a) establishing a rigorous link between graph trapping sets and algebraic-topological defects, (b) an efficient Nishimori-temperature estimator, and (c) demonstrating topology-guided LDPC graph embedding for highly compressed classifiers.","short_abstract":"Modern multi-class image classification uses high-dimensional CNN features that incur large memory and computational costs and obscure the data manifold's geometry. Existing graph-based spectral classifiers work on synthetic or binary tasks but degrade on natural images with many classes because feature manifolds have...","url_abs":"https://arxiv.org/abs/2508.18717","url_pdf":"https://arxiv.org/pdf/2508.18717v3","authors":"[\"V. S. Usatyuk\",\"D. A. Sapozhnikov\",\"S. I. Egorov\"]","published":"2025-08-26T06:27:50Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CV\",\"cs.IT\",\"math.AT\"]","methods":"[\"Convolutional Neural Network\"]","has_code":false}