Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

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

TL;DR

This work rethinks image classification by replacing the dense classifier head with a physics‑inspired RBIM embedded on MET QC‑LDPC graphs, achieving extreme feature compression while preserving accuracy. A fast Quadratic–Newton Nishimori temperature estimator leverages the Bethe–Hessian spectral condition $\lambda_{\min}(H_{\beta,J})=0$ to identify the critical $\beta_N$, aligning the decision boundary with the spin glass transition. The authors establish a spectral–topological link between trapping sets and topological invariants via the Ihara–Bass zeta function, enabling removal of harmful subgraphs to improve separability; this is implemented on two graph families (spherical and toroidal) and demonstrated on ImageNet‑10/10k subsets with up to 29× FLOP reductions. The results show competitive top‑1 accuracy (e.g., 98.7% on ImageNet‑10 and 84.9% on ImageNet‑100 with soft ensembling) using embeddings of dimension 32–64, highlighting a practical, edge‑friendly classification paradigm grounded in statistical physics and algebraic topology.

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

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

TL;DR

This work rethinks image classification by replacing the dense classifier head with a physics‑inspired RBIM embedded on MET QC‑LDPC graphs, achieving extreme feature compression while preserving accuracy. A fast Quadratic–Newton Nishimori temperature estimator leverages the Bethe–Hessian spectral condition to identify the critical , aligning the decision boundary with the spin glass transition. The authors establish a spectral–topological link between trapping sets and topological invariants via the Ihara–Bass zeta function, enabling removal of harmful subgraphs to improve separability; this is implemented on two graph families (spherical and toroidal) and demonstrated on ImageNet‑10/10k subsets with up to 29× FLOP reductions. The results show competitive top‑1 accuracy (e.g., 98.7% on ImageNet‑10 and 84.9% on ImageNet‑100 with soft ensembling) using embeddings of dimension 32–64, highlighting a practical, edge‑friendly classification paradigm grounded in statistical physics and algebraic topology.

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

Paper Structure

This paper contains 21 sections, 4 theorems, 25 equations, 8 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Random Bond Ising Models
  3. Nishimori condition and phase transition
  4. Bethe free energy and the Bethe--Hessian
  5. Multi-Edge Type Quasi‑Cyclic LDPC Graphs
  6. Quadratic--Newton estimation of the Nishimori temperature $\beta_N$
  7. Graph construction from CNN features
  8. Experimental evaluation
  9. Graph Ensembles for ImageNet‑100
  10. Training protocol
  11. Results and Discussion
  12. Future Directions
  13. Conclusions
  14. Topological Signatures of Trapping Sets
  15. Spectral manifestation of trapping sets
  16. ...and 6 more sections

Key Result

Lemma 2.1

Let $\mathcal{T}$ be any trapping set. Then $H_{\beta,J}^{\mathcal{T}}= D^{\mathcal{T}}(\beta)-B^{\mathcal{T}}(\beta),$ where Thus $H_{\beta,J}^{\mathcal{T}}$ is the (weighted) signed Laplacian of the subgraph $\mathcal{T}$.

Figures (8)

  • Figure 1: In (a) and (b) we see cluster structures (community) from phase transaction described by adjacency matrices and network related graph, Fig. 20 from 5
  • Figure 2: (Left) Tanner graph corresponding to the parity-check matrix $H_1$, composed by 2 and 3 ring of size 7, Fig.2 11. (Right) Multi-graph protograph $M(H_2)$ representation of the QC-LDPC code $H_2$.
  • Figure 3: Dependence of the smallest eigenvalue $\lambda_{\min}$ on the temperature parameter $\beta$. The red curve shows the polynomial part, the blue curve the tail, and the black dashed line is a quadratic approximation to the polynomial part. The coefficient of determination for the fit is $R^{2}=0.9998$.
  • Figure 4: Pipeline: MobileNetV2 feature extraction followed by graph spectral embedding.
  • Figure 5: Spectral embedding histogram with adjacency matrix of clusters (visualized by colors) under estimated Nishimori temperature $\beta_N$. (left) MET QC-LDPC Torical graph. (right) QC Spherical graph.
  • ...and 3 more figures

Theorems & Definitions (10)

  • Lemma 2.1
  • proof
  • Definition 1: Nishimori temperature, 123
  • Proposition 1
  • proof
  • Theorem 2.2
  • proof
  • Definition 2: Ihara–Bass zeta function
  • Corollary 2.2.1
  • proof