Temporal Memory for Resource-Constrained Agents: Continual Learning via Stochastic Compress-Add-Smooth
Summary: arXiv:2604.00067v1 Announce Type: cross
Abstract: An agent that operates sequentially must incorporate new experience without forgetting old experience, under a fixed memory budget. We propose a framework in which memory is not a parameter vector but a stochastic process: a Bridge Diffusion on a replay interval [0,1], whose terminal marginal encodes the present and whose intermediate marginals encode the past. New experience is incorporated via a three-step Compress–Add–Smooth (CAS) recursion. We test the framework on the class of models with marginal probability densities modeled via Gaussian mixtures of fixed number of components K in d dimensions; temporal complexity is controlled by a fixed number L of piecewise-linear protocol segments whose nodes store Gaussian-mixture states. The entire recursion costs O(LKd2) flops per day — no backpropagation, no stored data, no neural networks — making it viable for controller-light hardware.
Forgetting in this framework arises not from parameter interference but from lossy temporal compression: the re-approximation of a finer protocol by a coarser one under a fixed segment budget. We find that the retention half-life scales linearly as a1/2 ≈ cL with a constant c>1 that depends on the dynamics but not on the mixture complexity K, the dimension d, or the geometry of the target family. The constant c admits an information-theoretic interpretation analogous to the Shannon channel capacity. The stochastic process underlying the bridge provides temporally coherent “movie” replay — compressed narratives of the agent’s history, demonstrated visually on an MNIST latent-space illustration. The framework provides a fully analytical “Ising model” of continual learning in which the mechanism, rate, and form of forgetting can be studied with mathematical precision.
Key Features of the Framework
- Stochastic Memory Process: Utilizes a Bridge Diffusion to manage memory efficiently.
- Compress–Add–Smooth (CAS) Recursion: Integrates new experiences while maintaining older memories.
- Gaussian Mixture Modeling: Employs fixed number of components for effective probability density modeling.
- Low Computational Cost: Achieves operational efficiency with O(LKd2) flops per day.
- No Backpropagation Required: Operates independently of neural networks and stored data.
Implications for Future Research
The proposed framework opens up numerous avenues for further research in the field of continual learning. By refining the CAS recursion and exploring its applications across various domains, researchers can better understand how agents can learn in resource-constrained environments. The insights gained from this model can enhance the design of more efficient algorithms that maintain performance while adapting to new information.
In summary, the development of a framework based on stochastic processes for continual learning is a significant advancement in the field of artificial intelligence. By addressing the challenges of memory management in agents, this approach offers a promising path for future exploration and innovation.