Learning Neural Networks with Distribution Shift: Efficiently Certifiable Guarantees

Fuente: arXiv
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Main Authors: Chandrasekaran, Gautam, Klivans, Adam R., Lee, Lin Lin, Stavropoulos, Konstantinos
Format: Preprint
Published: 2025
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author Chandrasekaran, Gautam
Klivans, Adam R.
Lee, Lin Lin
Stavropoulos, Konstantinos
author_facet Chandrasekaran, Gautam
Klivans, Adam R.
Lee, Lin Lin
Stavropoulos, Konstantinos
contents We give the first provably efficient algorithms for learning neural networks with distribution shift. We work in the Testable Learning with Distribution Shift framework (TDS learning) of Klivans et al. (2024), where the learner receives labeled examples from a training distribution and unlabeled examples from a test distribution and must either output a hypothesis with low test error or reject if distribution shift is detected. No assumptions are made on the test distribution. All prior work in TDS learning focuses on classification, while here we must handle the setting of nonconvex regression. Our results apply to real-valued networks with arbitrary Lipschitz activations and work whenever the training distribution has strictly sub-exponential tails. For training distributions that are bounded and hypercontractive, we give a fully polynomial-time algorithm for TDS learning one hidden-layer networks with sigmoid activations. We achieve this by importing classical kernel methods into the TDS framework using data-dependent feature maps and a type of kernel matrix that couples samples from both train and test distributions.
format Preprint
id arxiv_https___arxiv_org_abs_2502_16021
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Learning Neural Networks with Distribution Shift: Efficiently Certifiable Guarantees
Chandrasekaran, Gautam
Klivans, Adam R.
Lee, Lin Lin
Stavropoulos, Konstantinos
Data Structures and Algorithms
Machine Learning
We give the first provably efficient algorithms for learning neural networks with distribution shift. We work in the Testable Learning with Distribution Shift framework (TDS learning) of Klivans et al. (2024), where the learner receives labeled examples from a training distribution and unlabeled examples from a test distribution and must either output a hypothesis with low test error or reject if distribution shift is detected. No assumptions are made on the test distribution. All prior work in TDS learning focuses on classification, while here we must handle the setting of nonconvex regression. Our results apply to real-valued networks with arbitrary Lipschitz activations and work whenever the training distribution has strictly sub-exponential tails. For training distributions that are bounded and hypercontractive, we give a fully polynomial-time algorithm for TDS learning one hidden-layer networks with sigmoid activations. We achieve this by importing classical kernel methods into the TDS framework using data-dependent feature maps and a type of kernel matrix that couples samples from both train and test distributions.
title Learning Neural Networks with Distribution Shift: Efficiently Certifiable Guarantees
topic Data Structures and Algorithms
Machine Learning
url https://arxiv.org/abs/2502.16021