The least-control principle for local learning at equilibrium
This work addresses the challenge of local learning in neural computations, offering potential insights for neuroscience and machine learning, though it appears incremental as it builds on existing equilibrium models.
The authors tackled the problem of learning in equilibrium systems by proposing a least-control principle that uses an optimal controller to guide learning, achieving performance comparable to leading gradient-based methods on recurrent neural networks and meta-learning tasks.
Equilibrium systems are a powerful way to express neural computations. As special cases, they include models of great current interest in both neuroscience and machine learning, such as deep neural networks, equilibrium recurrent neural networks, deep equilibrium models, or meta-learning. Here, we present a new principle for learning such systems with a temporally- and spatially-local rule. Our principle casts learning as a least-control problem, where we first introduce an optimal controller to lead the system towards a solution state, and then define learning as reducing the amount of control needed to reach such a state. We show that incorporating learning signals within a dynamics as an optimal control enables transmitting activity-dependent credit assignment information, avoids storing intermediate states in memory, and does not rely on infinitesimal learning signals. In practice, our principle leads to strong performance matching that of leading gradient-based learning methods when applied to an array of problems involving recurrent neural networks and meta-learning. Our results shed light on how the brain might learn and offer new ways of approaching a broad class of machine learning problems.