Data Curation Through the Lens of Spectral Dynamics: Static Limits, Dynamic Acceleration, and Practical Oracles
Yizhou Zhang, Lun Du
TL;DR
The paper introduces an operator-theoretic, spectral framework to explain when data-centric interventions like pruning, synthetic data, and distillation improve large-model training. It proves that static sampling cannot change the spectral tail and thus cannot affect asymptotic learning, while dynamic, frontier-aware sampling could provably accelerate learning by reweighting the spectral tail. The authors connect four practical paradigms—online probes, heterogeneous-model distillation, self-scoring, and synthetic data—to components of an ideal frontier-tracking oracle, clarifying why some interventions help and others stall. They also discuss fundamental limits of self-generated data and RLHF, offering guidance for designing data-curation pipelines that target frontier localization and tail expansion. Overall, the work bridges spectral theory and practical data strategies, elucidating both opportunities and intrinsic limits of data-centric training.
Abstract
Large-scale neural models are increasingly trained with data pruning, synthetic data generation, cross-model distillation, reinforcement learning from human feedback (RLHF), and difficulty-based sampling. While several of these data-centric strategies reliably improve training efficiency and downstream performance, others fail to provide meaningful gains -- most notably self-generated synthetic data, which often increases dataset volume without enhancing model capability. We formalize data curation as reweighting the sampling distribution and map its effect onto the eigenstructure of the data-induced operator. Our first main result shows that \textbf{static pruning induces a bounded operator and therefore cannot change the spectral tail exponent}; it provides at most finite-region improvements and cannot alter asymptotic neural scaling. Our second result analyzes \textbf{time-dependent data curation}, showing that an ideal oracle capable of tracking spectral residuals and continuously re-normalizing the tail can provably accelerate learning -- although practical systems can only approximate this behavior.