Data Curation Through the Lens of Spectral Dynamics: Static Limits, Dynamic Acceleration, and Practical Oracles
This work addresses the problem of optimizing data curation for large-scale neural models, offering theoretical insights into static and dynamic methods, though it is incremental in nature.
The paper formalizes data curation as reweighting sampling distributions and analyzes its effects on spectral dynamics, showing that static pruning cannot change asymptotic neural scaling, while an ideal dynamic oracle can provably accelerate learning.
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.