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.
Replace a dense token-mixing, MLP, or low-rank-adapter projection with a Bernoulli-signed sparse matrix normalized by the paper's predicted operator scale. Estimate the active representation dimension and use the effective scale to detect regimes in which extreme sparsity is likely to cause unstable amplification or dead rows.
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