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

arXiv: https://arxiv.org/abs/2604.00067 · HTML: https://mlsanity.com/paper/2604.00067/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [SDDGR: Stable Diffusion-based Deep Generative Replay for Class Incremental Object Detection](https://mlsanity.com/paper/2402.17323/) (2024)
- [Class-Incremental Learning using Diffusion Model for Distillation and Replay](https://mlsanity.com/paper/2306.17560/) (2023)
- [DiffClass: Diffusion-Based Class Incremental Learning](https://mlsanity.com/paper/2403.05016/) (2024)
- [Diffusion-Driven Data Replay: A Novel Approach to Combat Forgetting in Federated Class Continual Learning](https://mlsanity.com/paper/2409.01128/) (2024)
- [Harmonic Path Integral Diffusion](https://mlsanity.com/paper/2409.15166/) (2024)
- [ReplayCAD: Generative Diffusion Replay for Continual Anomaly Detection](https://mlsanity.com/paper/2505.06603/) (2025)
- [Continual Learning with Diffusion-based Generative Replay for Industrial Streaming Data](https://mlsanity.com/paper/2406.15766/) (2024)
- [Generative Stochastic Optimal Transport: Guided Harmonic Path-Integral Diffusion](https://mlsanity.com/paper/2512.11859/) (2025)
- [Mean-Field Path-Integral Diffusion: From Samples to Interacting Agents](https://mlsanity.com/paper/2605.00007/) (2026)

## Abstract (arXiv)

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≈ c,L 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.