The Dynamics of Memory: Replay, Diffusion, and Attractor Formation

Forgetting can be a structural mechanism that enables stable long-term intelligence, but most artificial memory stores rely on heuristic pruning rather than principled forgetting dynamics. We propose a continuous-time framework in which memory activation evolves on a semantic graph under coupled decay, graph-Laplacian diffusion, global inhibition, and associative replay. We analyze the resulting switched/averaged system and prove: (i) global boundedness under positive-definite decay and bounded replay forcing, (ii) spectral low-pass filtering by diffusion that exponentially attenuates high-frequency Laplacian modes, and (iii) conditions under which replay induces nontrivial equilibria and stable attractor states that resist continual forgetting. Synthetic simulations illustrate collapse under pure decay, semantic smoothing under diffusion, and stabilization when replay balances regulatory dynamics.