Data Curation Through the Lens of Spectral Dynamics: Static Limits, Dynamic Acceleration, and Practical Oracles

TL;DR

This paper analyzes how different data curation strategies affect neural model training by examining their spectral properties, revealing limitations of static pruning and potential benefits of dynamic, oracle-guided approaches for accelerating learning.

Contribution

It formalizes data curation as spectral reweighting, proving static pruning cannot alter asymptotic scaling, and demonstrating that dynamic reweighting can theoretically accelerate training.

Findings

Static pruning cannot change spectral tail exponent.

Dynamic, oracle-based reweighting can accelerate learning.

Practical systems can only approximate ideal spectral tracking.

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.