Lluís Arola-Fernández

Lluís Arola-Fernández, Lucas Lacasa

Unraveling the emergence of collective learning in systems of coupled artificial neural networks points to broader implications for machine learning, neuroscience, and society. Here we introduce a minimal model that condenses several recent decentralized algorithms by considering a competition between two terms: the local learning dynamics in the parameters of each neural network unit, and a diffusive coupling among units that tends to homogenize the parameters of the ensemble. We derive an effective theory for linear networks to show that the coarse-grained behavior of our system is equivalent to a deformed Ginzburg-Landau model with quenched disorder. This framework predicts depth-dependent disorder-order-disorder phase transitions in the parameters' solutions that reveal a depth-delayed onset of a collective learning phase and a low-rank microscopic learning path. We validate the theory in coupled ensembles of realistic neural networks trained on the MNIST dataset under privacy constraints. Interestingly, experiments confirm that individual networks -- trained on private data -- can fully generalize to unseen data classes when the collective learning phase emerges. Our work establishes the physics of collective learning and contributes to the mechanistic interpretability of deep learning in decentralized settings.

Lluís Arola-Fernández

Whether large predictive models merely parrot their training data or produce genuine insight lacks a physical explanation. This work reports a primitive form of intuition that emerges as a metastable phase of learning that critically balances next-token prediction against future path-entropy. The intuition mechanism is discovered via mind-tuning, the minimal principle that imposes Maximum Caliber in predictive models with a control temperature-like parameter $λ$. Training on random walks in deterministic mazes reveals a rich phase diagram: imitation (low $λ$), rule-breaking hallucination (high $λ$), and a fragile in-between window exhibiting strong protocol-dependence (hysteresis) and multistability, where models spontaneously discover novel goal-directed strategies. These results are captured by an effective low-dimensional theory and frame intuition as an emergent property at the critical balance between memorizing what is and wondering what could be.