Hermite-Schatten spectral layer

Integrate this as a structured linear layer in a small CNN, MLP, or image-operator network. The input feature map should first be projected into a fixed Hermite basis; for an image, use separable discrete Hermite functions or a numerically orthogonalized two-dimensional Hermite basis. Store only K scalar coefficients c_k instead of a dense n by n matrix. Precompute the basis matrix H and projection blocks P_k = H_k H_k^T, or apply each projection as H_k(H_k^T x) without materializing P_k. The forward pass is: initialize y = 0; for each k, compute z_k = H_k^T x, add c_k H_k z_k to y, and accumulate r_k (c_k^2 + delta)^(p/2) for the regularizer. Use p = 1 to encourage truncation, p = 2 for smooth energy control, or approximate p = infinity by penalizing the largest coefficient. The paper supplies the Hermite projection/Weyl structure and Schatten interpretation; basis discretization, K, and lambda are engineering choices. First test on CIFAR-10 with one convolution in ResNet-18 replaced by this layer, or on MNIST with a dense layer. Compare against a dense or standard convolutional layer at equal parameter budgets. Measure parameter count, wall-clock inference, validation accuracy, and largest singular value. Success means at least two times fewer learned parameters with no accuracy loss, or lower operator gain with equal accuracy.