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

翻译：现代多类图像分类依赖于高维CNN特征向量，这种方法计算成本高昂且模糊了底层数据几何结构。传统的基于图的分类器在自然多类图像上性能下降，因为典型图结构难以在具有复杂拓扑的特征流形上保持可分性。我们通过一种受物理学启发的流程解决此问题：冻结的MobileNetV2嵌入被视为稀疏多边类型QC-LDPC图上的伊辛自旋，构成随机键伊辛模型。该系统被调节至其西岛温度，该温度通过最小贝特-黑塞特征值消失点确定。我们的方法基于两项创新：我们证明了谱-拓扑对应关系，通过伊原-巴斯ζ函数将图陷阱集与不变量联系起来，移除这些结构使多类场景下的top-1准确率提升超过四倍；我们开发了西岛温度的二次-牛顿估计器，约9次阿诺尔迪迭代即可收敛，实现6倍加速，从而支持ImageNet-100等规模的谱嵌入。所得图将1280维MobileNetV2特征压缩至32维（ImageNet-10）和64维（ImageNet-100）。通过三图软集成，我们在ImageNet-10上达到98.7%的top-1准确率，在ImageNet-100上达到84.92%。相较于MobileNetV2，我们的硬集成将top-1准确率提升0.1%，同时将FLOPs降低2.67倍；与ResNet50相比，软集成仅使top-1准确率下降1.09%，却将FLOPs减少29倍。创新性体现在：（a）严格建立陷阱集与拓扑缺陷的关联，（b）高效的西岛温度估计器，（c）证明拓扑引导的LDPC嵌入能为资源受限部署生成高度压缩的精确分类器。