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

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 $\mathbf{\text{static}}\mathbf{\text{pruning}}\mathbf{\text{induces}}\mathbf{\text{a}}\mathbf{\text{bounded}}\mathbf{\text{operator}}\mathbf{\text{and}}\mathbf{\text{therefore}}\mathbf{\text{cannot}}\mathbf{\text{change}}\mathbf{\text{the}}\mathbf{\text{spectral}}\mathbf{\text{tail}}\mathbf{\text{exponent}}$; it provides at most finite-region improvements and cannot alter asymptotic neural scaling. Our second result analyzes $\mathbf{\text{time-dependent}}\mathbf{\text{data}}\mathbf{\text{curation}}$, 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.