Statistical Properties of Training & Generalization

2026-06-19 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Physical Sciences & Chemistry · Depth: Expert, extended

Summary

This article, part of the VERaiPHY Initiative, investigates the statistical properties governing deep learning training and generalization, particularly for physics applications. It explores how modern deep neural networks defy classical statistical intuitions due to their scale and non-convex loss landscapes. The review covers universal aspects like benign overfitting, the double descent phenomenon, and neural scaling laws, which describe predictable performance with model size, data, and compute. It also examines the impact of hyperparameter choices, including architecture, initialization, optimizers, and learning rates. Finally, the analysis addresses learning under specific constraints relevant to physics, such as data, parameter, compute, and time limitations, offering mitigation strategies for each.

Key takeaway

For AI Scientists and Machine Learning Engineers developing models for physics, you must move beyond classical statistical intuitions. Recognize that deep learning's unique behaviors, like benign overfitting and neural scaling laws, necessitate specific design choices. Prioritize incorporating physics-based inductive biases and employ scaling-aware hyperparameter strategies, such as Maximal Update Parametrization, to manage compute and parameter constraints effectively. This approach ensures robust performance and reliable uncertainty quantification in data-limited or resource-constrained environments.

Key insights

Deep learning's non-classical statistical behaviors, like benign overfitting and scaling laws, are crucial for its effective application in physics.

Principles

• Over-parameterization can improve generalization.
• Inductive biases shape model solutions.
• Neural scaling laws predict performance.

Method

Maximal Update Parametrization (P) ensures consistent performance scaling with model width. Compression via pruning, quantization, or distillation mitigates parameter limits. Active learning optimizes expensive label acquisition.

In practice

• Implement P scaling for large model hyperparameter transfer.
• Incorporate physics-based inductive biases into architectures.
• Pretrain on abundant unlabeled data, fine-tune on scarce labeled data.

Topics

• Deep Learning Statistics
• Neural Scaling Laws
• Benign Overfitting
• Physics-informed AI
• Hyperparameter Transfer
• Model Compression

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.