Gradient Span Algorithms Make Predictable Progress in High Dimension

2025-12-31 · Source: JMLR · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new proof published in 27(121):1−62, 2026, demonstrates that "gradient span algorithms" exhibit asymptotically deterministic behavior on scaled Gaussian random functions as dimension increases. This finding extends previous results concerning random quadratic functions and spin glasses. It explains the counterintuitive observation that diverse training runs of many large machine learning models yield approximately equal cost curves, despite random initialization within complex non-convex landscapes. This "predictable progress" phenomenon is actively leveraged by the AutoML community, allowing them to avoid multiple redundant retries with identical hyperparameters because a single optimization run is sufficiently representative.

Key takeaway

For AI Scientists and Research Scientists optimizing large machine learning models, understanding the "predictable progress" phenomenon is crucial. You can confidently reduce the number of redundant training runs for hyperparameter tuning, as a single run's optimization curve is highly representative. This insight streamlines your AutoML processes, significantly saving computational resources and accelerating model development cycles.

Key insights

Gradient span algorithms achieve predictable, deterministic optimization progress in high-dimensional machine learning environments.

Principles

• Gradient span algorithms show asymptotically deterministic behavior.
• Optimization progress is predictable despite random initialization.
• A single training run can be representative.

In practice

• Reduce redundant training runs for hyperparameter tuning.
• Enhance efficiency in AutoML workflows.
• Apply findings to large model optimization.

Topics

• Gradient Span Algorithms
• Predictable Progress
• High-Dimensional Optimization
• Machine Learning Models
• AutoML
• Gaussian Random Functions

Code references

• FelixBenning/pyGRF

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by JMLR.