Abstract <p>Modern multiclass image classification relies on high-dimensional convolutional-neural-network (CNN) feature vectors, which incur large memory and computational costs and provide little insight into the geometry and properties of the underlying vision data manifold. Existing graph-based spectral classifiers have shown promise on synthetic or binary classification problems, but they degrade on natural images with multiclasses because the feature manifolds possess nontrivial topology that destroys class separability when conventional graphs are used. We introduce a physics-inspired pipeline in which frozen MobileNetV2 features are interpreted as Ising spins placed on the vertices of a sparse multiedge type quasi-cyclic LDPC (MET-QC-LDPC) graph, thereby defining a random-bond Ising model (RBIM). The model is operated at its Nishimori temperature—identified as the unique point where the smallest eigenvalue of the Bethe–Hessian matrix vanishes. Two methodological pillars underpin the design. An exact spectral–topological correspondence that links local trapping sets in the Tanner graph to topological invariants (via poles of the Ihara–Bass zeta function), enabling systematic suppression of harmful substructures through permanent and Bethe-permanent bounds. Such a harmful subgraph reduces top-1 performance by more than a factor of four in multiclass classification. A fast quadratic–Newton estimator for the Nishimori temperature that converges in roughly nine Arnoldi iterations, providing a sixfold speed-up over standard bisection. This method enables spectral graph embedding training on large-scale datasets such as ImageNet-100. The resulting graph ensembles compress the original <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(1280\)</EquationSource>  </InlineEquation>-dimensional MobileNetV2 representation to 32 dimensions for a ten-class ImageNet subset (ImageNet-10) and to 64 dimensions for a hundred-class subset (ImageNet-100). Despite this compression we achieve <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(98.7\%\)</EquationSource>  </InlineEquation> top-1 accuracy on ImageNet-10, and up to 84.92<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\%\)</EquationSource>  </InlineEquation> top-1 accuracy on ImageNet-100 using three-graph soft ensemble. Compared with MobileNetV2, our hard-ensemble approach yields a 0.10<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\%\)</EquationSource>  </InlineEquation> increase in top-1 accuracy while reducing the number of FLOPs by a factor of 2.67. In contrast, when benchmark against ResNet-50, the soft-ensemble variant suffers only a 1.09<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\%\)</EquationSource>  </InlineEquation> drop in top-1 accuracy yet cuts FLOPs by 29 times, thereby achieving a favorable accuracy–efficiency trade-off. The novelty of this work lies in (a) establishing a rigorous link between graph trapping sets and algebraic-topological defects, (b) providing an efficient Nishimori-temperature estimator, and (c) demonstrating that topology-guided LDPC graph embedding yields highly compressed classifiers.</p>

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

期刊论文
发表日期：

2025年12月1日

查看全文

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

摘要

Abstract

Modern multiclass image classification relies on high-dimensional convolutional-neural-network (CNN) feature vectors, which incur large memory and computational costs and provide little insight into the geometry and properties of the underlying vision data manifold. Existing graph-based spectral classifiers have shown promise on synthetic or binary classification problems, but they degrade on natural images with multiclasses because the feature manifolds possess nontrivial topology that destroys class separability when conventional graphs are used. We introduce a physics-inspired pipeline in which frozen MobileNetV2 features are interpreted as Ising spins placed on the vertices of a sparse multiedge type quasi-cyclic LDPC (MET-QC-LDPC) graph, thereby defining a random-bond Ising model (RBIM). The model is operated at its Nishimori temperature—identified as the unique point where the smallest eigenvalue of the Bethe–Hessian matrix vanishes. Two methodological pillars underpin the design. An exact spectral–topological correspondence that links local trapping sets in the Tanner graph to topological invariants (via poles of the Ihara–Bass zeta function), enabling systematic suppression of harmful substructures through permanent and Bethe-permanent bounds. Such a harmful subgraph reduces top-1 performance by more than a factor of four in multiclass classification. A fast quadratic–Newton estimator for the Nishimori temperature that converges in roughly nine Arnoldi iterations, providing a sixfold speed-up over standard bisection. This method enables spectral graph embedding training on large-scale datasets such as ImageNet-100. The resulting graph ensembles compress the original \(1280\) -dimensional MobileNetV2 representation to 32 dimensions for a ten-class ImageNet subset (ImageNet-10) and to 64 dimensions for a hundred-class subset (ImageNet-100). Despite this compression we achieve \(98.7\%\) top-1 accuracy on ImageNet-10, and up to 84.92 \(\%\) top-1 accuracy on ImageNet-100 using three-graph soft ensemble. Compared with MobileNetV2, our hard-ensemble approach yields a 0.10 \(\%\) increase in top-1 accuracy while reducing the number of FLOPs by a factor of 2.67. In contrast, when benchmark against ResNet-50, the soft-ensemble variant suffers only a 1.09 \(\%\) drop in top-1 accuracy yet cuts FLOPs by 29 times, thereby achieving a favorable accuracy–efficiency trade-off. The novelty of this work lies in (a) establishing a rigorous link between graph trapping sets and algebraic-topological defects, (b) providing an efficient Nishimori-temperature estimator, and (c) demonstrating that topology-guided LDPC graph embedding yields highly compressed classifiers.