Beyond Turing: Memory-Amortized Inference as a Foundation for Cognitive Computation

Intelligence is fundamentally non-ergodic: it emerges not from uniform sampling or optimization from scratch, but from the structured reuse of prior inference trajectories. We introduce Memory-Amortized Inference (MAI) as a formal framework in which cognition is modeled as inference over latent cycles in memory, rather than recomputation through gradient descent. MAI systems encode inductive biases via structural reuse, minimizing entropy and enabling context-aware, structure-preserving inference. This approach reframes cognitive systems not as ergodic samplers, but as navigators over constrained latent manifolds, guided by persistent topological memory. Through the lens of delta-homology, we show that MAI provides a principled foundation for Mountcastle's Universal Cortical Algorithm, modeling each cortical column as a local inference operator over cycle-consistent memory states. Furthermore, we establish a time-reversal duality between MAI and reinforcement learning: whereas RL propagates value forward from reward, MAI reconstructs latent causes backward from memory. This inversion paves a path toward energy-efficient inference and addresses the computational bottlenecks facing modern AI. MAI thus offers a unified, biologically grounded theory of intelligence based on structure, reuse, and memory. We also briefly discuss the profound implications of MAI for achieving artificial general intelligence (AGI).