A Tale of Two Criticalities: How the Brain Learns through the Lens of Criticality

The question

The brain appears to operate near a critical point — the knife-edge between order and disorder where many physical systems show maximal sensitivity, dynamic range, and information capacity. But “criticality” in neuroscience is used loosely. This thesis asks a sharper question: which criticality, and what does each one actually buy a learning system?

Why spin glass theory

Learning reshapes a network’s connections, and the resulting landscape of possible states resembles the rugged energy landscape of a spin glass — a disordered magnetic system with many competing interactions and a vast number of metastable states. Spin glasses gave physics a vocabulary for systems that store many patterns and settle into them, which is exactly what associative memory does. Borrowing that vocabulary lets us ask precise questions about capacity, retrieval, and the transitions between learning regimes.

Approach

The work combines two lenses on criticality — hence the title. Renormalisation group methods track how the description of a learning system changes across scales, isolating the features that survive coarse-graining. Spin glass formalism characterises the structure of the state space the network learns to inhabit. Read together, the two perspectives clarify when a learning rule pushes a network toward a useful critical regime and when it tips into either rigidity or noise.

Why it matters

If learning is governed by proximity to criticality, then both the failures of learning (in ageing, in disease) and the design of artificial learners can be reasoned about in the same language. The thesis is a step toward a physics-grounded account of learning that does not stop at metaphor.

Supervised within the MRes Neurotechnology programme at Imperial College London. Graduated with Distinction, 2025.