Attractor Networks via Constraint-Induced Concentration in High-Dimensional Function Spaces

We present AttractorNet, a neural architecture that enforces global geometric constraintsthrough exact projection onto structured manifolds in function space. Unlike soft regularization,constraints are satisfied at every forward pass, inducing concentration of representations aroundlow-complexity attractor sets. We analyze the geometric mechanism underlying this concen-tration, establish equivariance under orthogonal transformations, and show that constrainedattention leads to interpretable mode selection. Minimal experiments demonstrate improvedstability and sample efficiency relative to unconstrained baselines.