Can Neural Networks Achieve Optimal Computational-statistical Tradeoff? An Analysis on Single-Index Model
In this work, we tackle the following question: Can neural networks trained with gradient-based methods achieve the optimal computational-statistical tradeoff in learning Gaussian single-index models? Prior research has shown that any polynomial-time algorithm under the statistical query (SQ) framework requires $Ω(d^{s^\star/2}\lor d)$ samples, where $s^\star$ is the generative exponent representing the intrinsic difficulty of learning the underlying model. However, it remains unknown whether neural networks can achieve this sample complexity. Inspired by prior techniques such as label transformation and landscape smoothing for learning single-index models, we propose a unified gradient-b...
| Authors | Siyu Chen, Beining Wu, Miao Lu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 13 June 2026 |
| Last updated at source | 13 June 2026 |
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