When do data mixtures improve scaling laws? Insights from high-dimensional regression
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
arXiv:2606. 08167v1 Announce Type: cross Abstract: Recent research has established empirical scaling laws to predict model performance on multi-domain data mixtures.
arXiv:2603. 05691v3 Announce Type: replace Abstract: It is increasingly common in machine learning to use learned models to label data and then employ such data to train more capable models.
arXiv:2608. 07281v1 Announce Type: cross Abstract: This paper investigates the asymptotic behavior of the out-of-sample prediction risk of the high-dimensional ridgeless least-squares estimator when the feature dimension $p$ and the sample size $n$ grow proportionally.
The paper analyzes training dynamics of multiclass logistic regression on high‑dimensional Gaussian mixture models with many classes. It finds that learning proceeds sequentially from the most to the least frequent classes and, when class priors follow a power‑law, the cross‑entropy risk evolves through an initial plateau, a power‑law decay phase, and a final convergence phase. The study also shows how model capacity and optimization trade‑off under a fixed compute budget, leading to a compute‑optimal scaling law that prescribes model size and training time as functions of compute.
The article proposes treating large language model (LLM) data mixing as a classical mixture experiment, where data domains are components, token shares are proportions, and proxy-training runs serve as design points. Using sparse second‑order Scheffé response‑surface models, the authors construct model‑robust Σ‑optimal designs that efficiently identify optimal data mixtures and reveal strong interaction effects, especially between weak domains and web‑derived text. Empirical results on RegMix show that these designs recover mixture rankings while reducing proxy runs by about 25%, demonstrating that data mixing can be optimized through experimental design rather than solely prediction.
arXiv:2608. 28564v1 Announce Type: cross Abstract: We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent $\alpha\geq 0$ for polynomial inner-product kernels.