Neural Manifolds as Crystallized Embeddings: A Synthesis of the Free Energy Principle, Generalized Synchronization, and Hebbian Plasticity

A new paper by Vikas N. O'Reilly-Shah (arXiv:2605.04200) proposes a unified framework for how neural manifolds—the low-dimensional geometric structures underlying cognitive functions like spatial navigation and visual perception—form in the brain. The author argues that the free energy principle's description of perception as variational inference doesn't require explicit Bayesian neural calculus. Instead, he shows that under generic conditions from reservoir-computing theory, a contractive recurrent circuit driven by structured sensory input can synchronize to the world's dynamics. This synchronization map automatically embeds the low-dimensional sensory manifold into neural state space, providing a bottom-up mechanism that replaces top-down Bayesian machinery.

The paper extends this to development: Hebbian plasticity acting on correlations generated by sensory-driven synchronization may crystallize the embedded manifold into recurrent connectivity, creating autonomous continuous attractor networks. O'Reilly-Shah suggests mature head-direction, grid-cell, and stimulus-driven visual manifolds are not genetically prespecified templates but developmental products of three interacting processes: dynamical contraction, generalized synchronization, and correlation-based plasticity. The synthesis yields testable predictions about dimensional thresholds for topological recovery, developmental sensitivity to plasticity, and how attractor geometry depends on input statistics. The main open problem is whether the Hebbian fixed point exists and preserves embedding quality.