# Natural Image Classification via Quasi-Cyclic Graph Ensembles and Random-Bond Ising Models at the Nishimori Temperature

Source: [Natural Image Classification via Quasi-Cyclic Graph Ensembles and Random-Bond Ising Models at the Nishimori Temperature](<https://www.sota2.com/research/paper/68fa5e1d1e209131ce9df866>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-04-30T05:00:04.703Z

Authors: V.S. Usatyuk, D.A. Sapozhnikov, S.I. Egorov

Published: 2025-08-26T06:27:50.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Image Classification on ImageNet-100](<https://www.sota2.com/research/sota/image-classification-on-imagenet-100.md>): Image Classification; ImageNet-100; Accuracy: not recorded.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2508.18717>)

[PDF](<https://arxiv.org/pdf/2508.18717.pdf>)