arXiv Machine Learning By Yizhou Liu, Jeff Gore

Neural Scaling Universality: If Exponents Are Fixed, Time to Understand Coefficients

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arXiv:2606. 25008v1 Announce Type: new Abstract: Neural scaling laws describe how pre-training loss decays as power laws with training time, model size, and compute.

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arXiv AI
Jul 7

Deriving Neural Scaling Laws from the statistics of natural language

arXiv:2602. 07488v3 Announce Type: replace-cross Abstract: Despite the fact that experimental neural scaling laws have substantially guided empirical progress in large-scale machine learning, no existing theory can quantitatively predict the exponents of these important laws for any modern LLM trained on any natural language dataset.

By Francesco Cagnetta, Allan Ravent\'os, Surya Ganguli, Matthieu Wyart
arXiv Machine Learning
Aug 31

Negligible in Size, Significant in Effect: On Scale Vectors in Large Language Models

The paper investigates the often-overlooked scale vectors in large language models, showing that despite their tiny size they are crucial for pre‑training performance. The authors provide theoretical insights that scale vectors mainly aid optimization rather than expressivity, and they analyze how weight decay affects different normalization layers. Building on these findings, they propose lightweight improvements—branch‑specific heterogeneity, better placement, and magnitude‑direction reparameterization—that consistently reduce loss across a range of model sizes and training settings.

By Mingze Wang, Shuchen Zhu, Yuxin Fang, Binghui Li, Kai Shen, Shu Zhong
arXiv Machine Learning
Sep 2

Performance-Efficiency Tradeoffs in Transformers: An Approximation Theory Perspective

The paper examines how to allocate attention heads and head dimensions across Transformer layers to balance expressivity and efficiency. It provides a mathematical analysis of early layers’ role in information extraction and characterizes the trade‑off between head count and dimension under a fixed parameter budget. The authors prove a saturation effect of softmax activations, showing that increasing head dimensions yields diminishing returns, especially for long sequences, and propose strategies for efficient parameter allocation across layers.

By Ruoxi Yu, Haotian Jiang, Jingpu Cheng, Penghao Yu, Qianxiao Li, Zhong Li