Physics of Learning: Neural Networks Self-Organize into Critical States

What is it about?

This study reveals that artificial neural networks aren’t just collections of code. Instead, they behave like physical systems operating near a critical state. Much like the release of energy in an earthquake or the coordinated firing of neurons in a human brain, neural networks display signs of "self-organized criticality" during training. When neural networks learn, their parameters (connection strengths between nodes) change. The magnitude of these changes follows a heavy-tailed power-law-like pattern: while most changes are small, large changes occasionally occur. This power-law-like behavior consistently emerged regardless of batch size, learning rate, or network depth, suggesting a fundamental principle rather than an artifact of the specific implementation. The authors developed a theoretical framework based on nonequilibrium statistical physics showing that this pattern arises from balancing two forces: maximum entropy (promoting random exploration) and mutual information constraint (ensuring task relevance). This trade-off naturally pushes the network into a critical regime with power-law signatures where it is flexible enough to learn but disciplined enough to succeed.

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Photo by Conny Schneider on Unsplash

Photo by Conny Schneider on Unsplash

Why is it important?

By framing neural network learning as a nonequilibrium process governed by the fundamental trade-off between randomness and relevance, this bridges AI with physics, enabling tools from statistical mechanics to optimize machine learning systems.

Perspectives