Natural Image Classification via Quasi-Cyclic Graph Ensembles and Random-Bond Ising Models at the Nishimori Temperature
This addresses the problem of computational efficiency in image classification for AI applications, though it appears incremental as it builds on existing physics and topology concepts.
The paper tackles efficient multi-class image classification by interpreting high-dimensional features as spins on a quasi-cyclic graph and operating a Random-Bond Ising Model at the Nishimori temperature to maximize class separability, achieving 98.7% accuracy on ImageNet-10 and 82.7% on ImageNet-100 with 40x fewer parameters.
We present a unified framework combining statistical physics, coding theory, and algebraic topology for efficient multi-class image classification. High-dimensional feature vectors from a frozen MobileNetV2 backbone are interpreted as spins on a sparse Multi-Edge Type quasi-cyclic LDPC (MET-QC-LDPC) graph, forming a Random-Bond Ising Model (RBIM). We operate this RBIM at its Nishimori temperature, $β_N$, where the smallest eigenvalue of the Bethe-Hessian matrix vanishes, maximizing class separability. Our theoretical contribution establishes a correspondence between local trapping sets in the code's graph and topological invariants (Betti numbers, bordism classes) of the feature manifold. A practical algorithm estimates $β_N$ efficiently with a quadratic interpolant and Newton correction, achieving a six-fold speed-up over bisection. Guided by topology, we design spherical and toroidal MET-QC-LDPC graph ensembles, using permanent bounds to suppress harmful trapping sets. This compresses 1280-dimensional features to 32 or 64 dimensions for ImageNet-10 and -100 subsets. Despite massive compression (40x fewer parameters), we achieve 98.7% accuracy on ImageNet-10 and 82.7% on ImageNet-100, demonstrating that topology-guided graph design yields highly efficient, physics-inspired embeddings with state-of-the-art performance.