Data Scaling as Progressive Coverage of a Predictive Contribution Spectrum
Authors: Zihui Song, Shihao Ji, Hongxi Li et al.
Summary
arXiv:2605. 20196v1 Announce Type: new Abstract: We investigate the hypothesis that real-data scaling laws are governed by progressive coverage of a latent predictive contribution spectrum rather than by token-frequency tails alone.
Relevance
Read next because Data Scaling as Progressive Coverage of a Predictive Contribution Spectrum overlaps with clean result "LoRA persona trained on alone emits at 23.5% when a co-trained partner learns ..., vs 0% control on Qwen2.5-7B-Instruct (MODERATE confidence)", clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)", clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)". Matching terms: strong, text, token, line, alone, suffix. Source: arxiv cs.CL (NLP).
Abstract
arXiv:2605.20196v1 Announce Type: new Abstract: We investigate the hypothesis that real-data scaling laws are governed by progressive coverage of a latent predictive contribution spectrum rather than by token-frequency tails alone. We work with a suffix-automaton representation of text corpora and define a data-intrinsic global-KL predictive contribution spectrum, in which each state contributes according to its empirical mass times its KL deviation from a global next-token baseline. Across 12 real corpora, the tail slope of this spectrum is already strongly correlated with the empirical data-scaling exponent of a fixed small GPT learner. We then go beyond slope correlation and define, for each training size N, an effective truncation rank K(N) by matching the observed excess loss to the residual tail mass of the prepared 1000k global-KL spectrum. Empirically, log K is close to linear in log N, with pooled R^2 about 0.96 for the raw spectrum and R^2 about 0.90 for the smoothed spectrum. These findings provide strong empirical support for a simple mechanism picture: training scale advances an effective frontier through a predictive state spectrum, and the residual tail mass of that spectrum tracks the remaining excess loss.