Spectral Indistinguishability and Learning-Curve Identifiability in Quadratic Networks
We study what spectral summaries and scalar learning curves reveal about centered quadratic networks. We construct analytic positive input densities with exactly Gaussian one- and two-coordinate marginals. Their complete fourth-moment operators are intertwined by an orthogonal map fixing the entire diagonal teacher algebra, so the corresponding anchored spectral measures agree. For selected common teachers with a nonzero cycle invariant, their factorized loss curves differ because the map does not preserve matrix multiplication. Cycle length $r$, which can be arbitrarily large, gives $O(\varepsilon^r)$ contrast uniformly in training time for each fixed construction. For a supplied pair, n...
| Authors | Dekun Yang |
|---|---|
| Primary category | cs.LG |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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