Fractal basin geometry and the limits to predictability and reproducibility in deep learning

arXiv:2510.05606 · cs.LG · Submitted 2025-10-07 · Read on arXiv

cs.LG

Submitted: 2025-10-07

Updated: 2026-09-19

Comments: To be published in Nature Machine Intelligence; 12 pages, 5 figures

Code: https://github.com/anly2178/riddled_basins_neural_network

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 10× in this paper · explained in 1 episode
• Generalization — 8× in this paper · explained in 13 episodes
• Activation Function — 4× in this paper · explained in 1 episode
• Loss Function — 3× in this paper · explained in 2 episodes
• Data Augmentation — 2× in this paper · explained in 7 episodes
• Chaotic Dynamics — 1× in this paper · explained in 2 episodes
• Distillation — 1× in this paper · explained in 2 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• Meta-learning — 1× in this paper · explained in 2 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Quantifying Uncertainty — 1× in this paper · explained in 5 episodes
• Spectral Gap — 1× in this paper · explained in 5 episodes
• Stochastic Gradient Descent (SGD) — 1× in this paper · explained in 5 episodes

Sources

• Sources of Irreproducibility in Machine Learning: A Review
• On the Reproducibility of Neural Network Predictions
• Fine-Tuning Pretrained Language Models: Weight Initializations, Data Orders, and Early Stopping
• Understanding and Mitigating Numerical Sources of Nondeterminism in LLM Inference
• Parameter Symmetry Potentially Unifies Deep Learning Theory
• The boundary of neural network trainability is fractal

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