用于图像分类的西村温度下稀疏图上的Kohn-Sham谱嵌入
Kohn-Sham Spectral Embedding on Sparse Graphs at the Nishimori Temperature for Image Classification
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中文总结 AI 辅助
该研究提出受物理学启发的KSSE模型，将预训练特征映射到稀疏图并优化拓扑，在ImageNet-1000直推式任务中以更少参数实现高准确率，优于Swin-L、匹配ViT-H/14并减少模型占用。
中文摘要 AI 辅助
我们提出Kohn-Sham谱嵌入（KSSE），这是一种受物理学启发的基于能量的模型，用与关联的随机键伊辛模型西村温度下评估的稀疏图谱嵌入替代密集卷积神经网络分类器。通过将预训练特征映射到准循环低密度奇偶校验图上，并构建作为Kohn-Sham哈密顿量的正则化拉普拉斯算子，我们利用循环块上的快速傅里叶变换（利用ℤ/pℤ的庞特里亚金自对偶性）和低阶瑞利细化，在𝒪(N log N + k²_mode N)时间内求解D个独立通道谱问题。图拓扑使用“星域手术”优化：不是通过去除受挫循环破坏携带信息的码字，而是构造边移位在码字周围创建局部凸性，同时将残余受挫限制为ρ(B_γ)≤1+δ。多尺度分形分析（D₂谱）和分形学习率景观证实了从粗糙区域（D₂>3）到星域盆地（D₂<1）的景观转变，使得k_mode=5个模式的瑞利细化成为可能。我们证明了六个理论结果：将信念传播与拉普拉斯算子关联的广义Ihara-Bass恒等式；陷阱集特征值对应；具有显式交换关联界的加性通道可分性；将受挫与吸引子宽度Ω(1/√d_min)绑定的手术定理；准平稳扰动界；以及不动点收敛定理。在使用冻结EfficientNet-B4特征（D=1792）的ImageNet-1000直推式协议中，KSSE使用约2124万个参数达到88.93%的Top-1准确率，优于Swin-L（1.97亿参数，86.4%–87.3%），并在标准归纳设置下匹配ViT-H/14（6.32亿参数，88.0%–89.5%），同时分别将模型占用减少10倍和30倍。
英文摘要
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 $O(N log N + k_{mode}^{2} N)$ time by FFT on circulant blocks (Pontryagin self-duality), with low-mode Rayleigh-Ritz refinement ($k_{mode}=5$). 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 $D_{2}<1$ vs rough landscapes $D_{2}>3$). The theory includes a generalized Ihara-Bass identity with a sharp spectral threshold, a non-backtracking growth trichotomy with frustration as a gauge-invariant $Z_{2}$ 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.
发表机构
- South-West State University (SWSU)（西南州立大学（SWSU））
- T8 LLC（T8有限责任公司）
机构由 AI 辅助整理，请以论文原文为准。
