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The Spectral Neuron

arXiv:2608.08003MLLG8 aug 20261 min readHN ×4PDF

A neuron that outputs an eigenvalue of a learned matrix, staying readable as it grows.

How it works

  1. Transparency or power

    Linear models show what each feature does but stay simple. Neural nets scale in power but hide how features act.

  2. Eigenvalue as nonlinearity

    Each feature scales a learned symmetric matrix. The sum is one matrix, and its k-th smallest eigenvalue is the prediction.

  3. Scales, stays readable

    Bigger matrices fit harder functions. Results land near MLPs on HIGGS and factorization machines on Criteo, with explicit influence bounds.

scaleread λkInputfeaturesCoefficientmatricesWeightedmatrix sumEigensolverk-theigenvaluescaleread λkInputfeaturesCoefficientmatricesWeightedmatrix sumEigensolverk-theigenvalue
From the paper