arXiv Machine Learning
Sep 10

SGD in Multiclass Logistic Regression: Sequential Learning and Scaling Laws

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.

By Konstantinos Christopher Tsiolis, Denny Wu, Christos Thrampoulidis, Murat A. Erdogdu
arXiv AI
Aug 26

Data Mixing as Mixture Experiment: Response Surface Methodology and Optimal Design for Large Language Model Pretraining

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.

By Yicheng Mao, Hongru Du