Kohn-Sham Spectral Embedding on Sparse Graphs at the Nishimori Temperature for Image Classification

תקציר מקורי באנגליתarXiv:2607.28428v1 Announce Type: new Abstract: We introduce Kohn--Sham Spectral Embedding (KSSE), a physics-inspired energy-based model replacing dense CNN classifiers with a sparse-graph spectral embedding evaluated at the Nishimori temperature of an associated Random-Bond Ising Model. By mapping pre-trained features onto quasi-cyclic low-density parity-check graphs and constructing a regularized Laplacian acting as a Kohn--Sham Hamiltonian, we solve $D$ independent channel spectral problems in $\mathcal{O}(N\log N + k^2_{\text{mode}} N)$ time via FFT on circulant blocks (leveraging Pontryagin self-duality of $\mathbb{Z}/p\mathbb{Z}$) and low-order Rayleigh refinement. Graph topology is optimized using \emph{star-domain surgery}: rather than destroying information-carrying codewords by r