Kohn-Sham Spectral Embedding on Sparse Graphs at the Nishimori Temperature for Image Classification
arXiv:2607.28428
The paper proposes Kohn‑Sham Spectral Embedding (KSSE), a physics‑inspired, sparse‑graph spectral method that replaces dense CNN classifiers with a regularized Laplacian evaluated at the Nishimori temperature, achieving high ImageNet accuracy with far fewer parameters.
Abstract
We propose Kohn-Sham Spectral Embedding (KSSE), an energy-based model replacing the top-layer classifier of convolutional networks with a sparse-graph spectral embedding at the Nishimori temperature of an associated Random-Bond Ising Model the spectral detectability threshold where class structure becomes marginally distinguishable from disorder. Mapping pre-trained features onto quasi-cyclic low-density parity-check graphs, we construct a regularized Laplacian (Bethe-Hessian) as an effective Kohn-Sham Hamiltonian, yielding D independent spectral problems-one per feature channel-solvable in time by FFT on circulant blocks (Pontryagin self-duality), with low-mode Rayleigh-Ritz refinement (). Physically, this is a k.p effective-mass reduction on a one-dimensional ring crystal: the circulant support is the perfect crystal, the data weights a slowly varying impurity potential, and the Nishimori crossing a Fermi level at the band edge. Star-domain surgery optimizes the graph: instead of eliminating all frustrated cycles impossible without destroying the codewords-edge shifts create certified convexity around codewords with bounded residual frustration, with multi-scale fractal certification (basins vs rough landscapes ). The theory includes a generalized Ihara-Bass identity with a sharp spectral threshold, a non-backtracking growth trichotomy with frustration as a gauge-invariant flux, a trapping-set spectral test, exact channel separability with a cup-product obstruction, plus loop-series, convexity, surgery, and quasi-stationarity bounds. On ImageNet-1000 with frozen EfficientNet-B4 features (D=1792) under a transductive protocol, KSSE achieves 88.93% Top-1 accuracy with ~21.24M parameters-beating Swin-L (197M, 86.4-87.3%) and matching the lower end of ViT-H/14 (632M, 88.0-89.5%) with 10x and 30x fewer parameters.
67 pages, 12 figures, 7 tables, was presented at the 10th International Conference 'Deep Learning on Computational Physics (DLCP2026)', under review for the Moscow University Physics Bulletin, Physics series