Temporal Memory for Resource-Constrained Agents: Continual Learning via Stochastic Compress-Add-Smooth

Michael Chertkov's groundbreaking paper introduces a novel framework for continual learning in resource-constrained agents, replacing traditional parameter-based memory with a stochastic process called Bridge Diffusion. The core innovation is the Compress-Add-Smooth (CAS) recursion—a three-step method where memory isn't stored as static vectors but as temporal narratives on a replay interval [0,1]. This approach operates with O(LKd²) floating-point operations per day, requiring no backpropagation, no stored datasets, and no neural network architectures, making it viable for controller-light hardware like embedded systems and IoT devices.

The framework models probability densities using Gaussian mixtures with K components in d dimensions, controlled by L piecewise-linear protocol segments. Forgetting occurs not from catastrophic interference but from lossy temporal compression—re-approximating detailed protocols with coarser versions under fixed segment budgets. The research demonstrates that retention half-life scales linearly as a₁/₂ ≈ cL, where constant c>1 depends on dynamics but not on mixture complexity K, dimension d, or target geometry. This constant admits an information-theoretic interpretation analogous to Shannon channel capacity.

Visual demonstrations on MNIST latent-space illustrations show the system generates temporally coherent 'movie' replays—compressed narratives of agent history. The stochastic process underlying the bridge provides fully analytical control, creating what Chertkov describes as an 'Ising model' of continual learning where forgetting mechanisms, rates, and forms can be studied with mathematical precision. This represents a paradigm shift from empirical neural network approaches to theoretically grounded memory systems.