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S-GAI is a spectral geometry-aware initialization framework for one-hidden-layer sigmoidal MLPs that uses class-wise spectral geometry from image data to initialize weights, outperforming random initialization in terms of starting hidden state quality and achieving comparable final accuracy on benchmarks like MNIST and CIFAR-10.
Introduces NEO, a neural framework that predicts low-frequency Laplace-Beltrami eigenspace from point clouds, achieving near-linear scaling and strong zero-shot generalization using a mass-aware neural operator and Rayleigh-Ritz refinement.
This paper performs full Jacobian eigendecomposition across production-scale LLMs, revealing a learned spectral gradient from rotation-dominated early layers to symmetric late layers, along with a low-rank bottleneck that compresses perturbations. The results link perturbation propagation and compression to network functional topology.