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Learning by Steering the Neural Dynamics: A Statistical Mechanics Perspective

Despite the striking successes of deep neural networks trained with gradient-based optimization, these methods differ fundamentally from their biological counterparts. This gap raises key questions about how nature achieves robust, sample-efficient learning at minimal energy costs and solves the credit-assignment problem without backpropagation. We take a step toward bridging contemporary AI and computational neuroscience by studying how neural dynamics can support fully local, distributed learning that scales to simple machine-learning benchmarks. Using tools from statistical mechanics, we identify conditions for the emergence of robust dynamical attractors in random asymmetric recurrent networks. We derive a closed-form expression for the number of fixed points as a function of self-coupling strength, and we reveal a phase transition in their structure: below a critical self-coupling, isolated fixed points coexist with exponentially many narrow clusters showing the overlap-gap property; above it, subdominant yet dense and extensive clusters appear. These fixed points become accessible, including to a simple asynchronous dynamical rule, after an algorithm-dependent self-coupling threshold. Building on this analysis, we propose a biologically plausible algorithm for supervised learning with any binary recurrent network. Inputs are mapped to fixed points of the dynamics, by relaxing under transient external stimuli and stabilizing the resulting configurations via local plasticity. We show that our algorithm can learn an entangled version of MNIST, leverages depth to develop hierarchical representations and increase hetero-association capacity, and is applicable to several architectures. Finally, we highlight the strong connection between algorithm performance and the unveiled phase transition, and we suggest a cortex-inspired alternative to self-couplings for its emergence.

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