Geometry of Irreversible Neural Computation in Non-Reciprocal Attractor Networks

Neural computation is often described through attractor landscapes, where stable activity states correspond to minima of an effective potential and rare transitions are controlled by barrier heights. This landscape picture is powerful, but it becomes incomplete when neural dynamics is non-reciprocal and violates detailed balance. In such systems, two networks may share the same stationary density and the same leading quasipotential barrier while exhibiting different transition routes, irreversible probability currents, and thermodynamic precision costs.

This talk presents a geometric and stochastic-thermodynamic framework for analyzing irreversible attractor computation. Using Freidlin–Wentzell large-deviation theory, I describe rare neural transitions as minimum-action paths rather than as local fluctuations around stable states. In a solvable bistable model, the non-reciprocal component of the drift leaves the quasipotential unchanged but bends escape and relaxation trajectories into directed loops. This produces a path-asymmetry index that grows linearly with non-reciprocity, while the entropy production rate grows quadratically. The result is a quantitative path–current–dissipation relation: geometric irreversibility becomes an observable signature of hidden nonequilibrium currents beneath an apparently equilibrium-like landscape.

The framework is then extended to high-dimensional non-reciprocal attractor networks, where full-space geometric minimum-action optimization confirms the persistence of the same structure. Monte Carlo simulations validate the Freidlin–Wentzell barrier, and time-integrated current observables satisfy thermodynamic uncertainty bounds. These results suggest a falsifiable principle for neural and neuromorphic systems: reliable directed computation through attractor space requires not only stable states and transition barriers, but also a measurable thermodynamic cost associated with irreversible probability flow.