Use a bounded function of the response to form a supervised, label-weighted covariance of the input and initialize the first neural layer from its leading outlier eigenspace. For vector-valued responses, use a matrix-valued response preprocessing map so several label statistics are combined in one lifted spectral estimator.
Initialize VQ-VAE, product-quantization, or prototype embeddings from a matrix-scrambled digital net after mapping points into the data latent region. This aims to prevent early codebook collisions and dead entries by giving codewords broad coverage and controlled minimum separation, rather than relying on Gaussian initialization or random samples that contain increasingly large local gaps.
Use Marchenko–Pastur spectral edges to calibrate tensorized random features even when the base vector has exchangeable, sign-symmetric dependent coordinates. Rescale the tensor features and select their retained dimension so the predicted covariance bulk remains well-conditioned instead of assuming independent Gaussian coordinates.
Initialize a univariate polynomial-activation hidden layer to realize a prescribed polynomial exactly, rather than relying on gradient descent to learn the required cancellation between shifted monomials. This provides an analytically controlled starting point for polynomial MLPs, polynomial feature extractors, and teacher-to-student initialization when the desired local map is known or fitted from data.
Paper: Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functionsarXiv:2607.15173
Initialize directional prototypes, cosine-classifier weights, or angular attention directions with a spherical t-design rather than iid random vectors. Exact matching of spherical moments through degree t should provide uniform angular coverage and reduce initialization anisotropy, especially when the number of prototypes is small.
Split a recurrent state into two blocks and initialize their variances and cross-correlation according to the stationary projective energy distribution induced by the transition. This places the initial hidden state near the typical invariant direction of the dynamics instead of forcing a long transient from zero or isotropic noise.
Calibrate the scales of several additive self-adjoint residual or attention operators so their aggregate spectrum has a controlled higher-moment Berry–Esseen certificate. Penalize unusually large normalized (2+δ)-moments, which should reduce spectral outliers and make the summed operator closer to a predictable semicircle-shaped spectrum.