Provable Data Scaling Law for Meta Learning via Complexity Minimization

• URL: http://arxiv.org/abs/2606.02008v1
• Date: Mon, 01 Jun 2026 10:02:29 GMT
• Title: Provable Data Scaling Law for Meta Learning via Complexity Minimization
• Abstract summary: We introduce complexity minimization, which learns representations by evaluating the downstream model complexity best suited to each domain.<n>Our end-to-end theoretical analysis, spanning pre-training through downstream regression, shows that this framework provably captures this scaling behavior.<n>We demonstrate that incorporating complexity regularization into existing meta-learning methods consistently improves downstream sample efficiency.
• Score: 6.964881957695288
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Pre-training has become a fundamental paradigm in modern machine learning, with one of its key empirical benefits being reduced downstream sample complexity as the scale of pre-training data increases. However, existing theoretical frameworks for pre-training do not fully explain this phenomenon. In this paper, we introduce complexity minimization, a novel meta-representation learning framework designed to enable theoretical analysis of this scaling behavior, which learns representations by evaluating the downstream model complexity best suited to each domain and minimizing the worst-case such complexity across source domains. Our end-to-end theoretical analysis, spanning pre-training through downstream regression, shows that this framework provably captures this scaling behavior; in particular, we show that the error rate of few-shot adaptation improves as the amount of meta-training data grows. Empirically, we demonstrate that incorporating complexity regularization into existing meta-learning methods consistently improves downstream sample efficiency.

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