← 研踪 PaperTrailarXiv:2602.10867 · v2
Deep Learning of Compositional Targets with Hierarchical Spectral Methods
首次提交 2026-02-11 21:54
版本更新 2026-11-03 22:15
雷达观测 2026-11-04 23:39
摘要
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 $0<\varepsilon<1/3$, and motivates separations in sample complexity between two- and three-layer learning strategies, conditional on a conjectured spectral recovery step.
作者备注：Accepted at ICML 2026. Revised version
期刊信息：Proceedings of Machine Learning Research, vol. 306, pp. 117916-117938, 2026
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v2 · 2026-11-03 22:15 · 最新观测版本
Deep Learning of Compositional Targets with Hierarchical Spectral Methods
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 $0<\varepsilon<1/3$, and motivates separations in sample complexity between two- and three-layer learning strategies, conditional on a conjectured spectral recovery step.
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