Machine learning has long ceased to be just a tool — it is becoming an investigator, independently fishing out the laws of nature from data. But how does a silicon mind come to understand? To spy on this process, physicists turned to a toy-like yet profound model — the Ising lattice, where spins dance to the dictates of temperature. A classic problem of statistical mechanics, formulated by Ludwig Boltzmann, turned out to be an ideal testing ground. An autoencoder (a neural network that compresses and reconstructs data) was trained on millions of spin patterns, and scientists watched its metamorphoses with the meticulousness of naturalists.

Training an autoencoder is like an archaeological dig. First, massive walls emerge from the sand — this is magnetization, a global order parameter that the network captures almost instantly. Then, layer by layer, floor mosaics and inscriptions on amphorae are uncovered — this is energy, subtle correlations between neighboring spins. The shift in focus happens by itself, without any hints: the neural network seems to know that it must first grasp the overall shape, and only then the details.

Researchers, manipulating network depth and learning rate, discovered two distinct dynamic modes. Small networks and low learning rates smoothly switch from magnetization to energy. But deep architectures at high rates get stuck — like a shovel hitting bedrock. They produce only an averaged pattern, never reaching the fine correlations.

This scenario echoes glass transition effects studied in quantum thermodynamics: the system freezes in a suboptimal state, never reaching the global minimum. Inside the network, topological stability emerges: the shape of the path in latent space does not change, even when the error is still large — as if the city plan is already sketched, and the houses are yet to be built. By measuring error at different scales, scientists traced how the network builds up order, lowering the entropy of its predictions. Topological robustness resembles the global magnetic field of a magnetar — the structure is set before accuracy is achieved.

This story is not only about spin lattices. It emerges as a general principle: neural network learning can be understood as a cascade of symmetry breaking, where global concepts arise first, and then local ones. This hierarchy brings machine learning closer to critical phenomena studied by Lev Landau. Perhaps renormalization group methods, honed on phase transitions in superconductors and Bose-Einstein condensates, will help peer into the black box of deep networks. If we learn to guide the self-organization of concepts, neural networks could independently discover physical laws in unfamiliar data — from turbulence to quantum materials. In perspective, this is a step toward an artificial scientist that not only recognizes patterns but derives equations. Ponder this: perhaps the laws we consider fundamental are merely coarse-grained artifacts of an even deeper structure, and a neural network will one day show us this vividly.