[Submitted on 11 Feb 2026 (v1), last revised 3 Nov 2026 (this version, v2)]
Abstract:Why depth yields a computational advantage over shallow methods remains a central open question in learning theory. We study this question in a controlled high-dimensional Gaussian setting, focusing on compositional target functions. We analyze their learnability using an explicit three-layer fitting model trained via layer-wise spectral estimators. The target combines polynomial latent features with a scalar readout, and its compositional structure allows learning to proceed in stages. Recovering an intermediate representation reduces the problem to lower-degree spectral estimation tasks, as in multi-index models. Our analysis establishes Gaussian comparison bounds for projected moments when $0
Submission history
From: Hugo Tabanelli [view email]
[v1] Wed, 11 Feb 2026 13:54:20 UTC (227 KB)
[v2] Tue, 3 Nov 2026 14:15:01 UTC (703 KB)
