Joint sparse coding and temporal dynamics support context reconfiguration

One of the critical limitations of artificial neural networks is their lack of ability to continually learn: training on new tasks often leads to interference and forgetting of the previous ones. While several algorithms have been proposed to protect old memories from interference, they are typically applied during or immediately after each new episode of training. In contrast, humans and animals can learn continuously, acquiring multiple new memories during active learning before consolidating all of them into long-term storage. Here we show that multiple new tasks can be trained sequentially before an unsupervised sleep-like replay phase is applied to partially restore performance across all previously learned tasks. Our study further suggests that task-specific information remains resilient to new training but decays gradually as network is trained on new tasks. These findings point to novel principles for developing a broad range of continual learning AI solutions.

Continual learning (CL) systems often forget previously acquired knowledge, yet the mechanisms driving forgetting remain hard to isolate in practice because real datasets entangle many factors. We present a controlled, toy-world framework that makes these mechanisms observable and testable. Using a synthetic generator-separator pipeline, we define ground-truth latent features, build tasks with tunable sparsity and overlap, and introduce measurable quantities for representation strength and superposition (directional overlap among features). We then study retention dynamics-the temporal change of representation strength by fitting sparse dynamical relations (via SINDy) between retention, superposition, and exposure history. A complementary task-level analysis based on effective rank characterizes how representational capacity is allocated across tasks. Our controlled experiments yield three takeaways. (1) Superposition tends to increase over time with transient dips at task boundaries, suggesting boundary-specific interference rather than steady drift. (2) Higher feature sparsity induces more superposition yet does not inevitably cause forgetting; when representations remain strong, forgetting can be reduced despite overlap. (3) Task-level effective rank grows with sparsity, indicating broader capacity usage under sparse regimes. Together, these results nuance the common intuition that more superposition leads to more forgetting by showing that overlap interacts with representation strength and capacity allocation. Our toy analysis provides falsifiable hypotheses and diagnostic tools for CL.

Dissipative cognitive architectures maintain computation through continuous energy expenditure, where units that exhaust their energy are stochastically replaced with fresh random state. This creates a fundamental challenge: how can persistent, context-specific memory survive when all learnable state is periodically destroyed? Existing memory mechanisms -- including elastic weight consolidation, synaptic intelligence, and surprise-driven gating -- rely on gradient computation and are inapplicable to systems that do not perform it. We introduce Deep Memory (DM), a backpropagation-free persistent memory mechanism operating through a triple-loop consolidation cycle: (1) recording of expert-specific content centroids, (2) seeding of replaced units with stored representations, and (3) stabilization through continuous re-entry. Discrete expert routing via Mixture-of-Experts (MoE) gating is required, in the regimes tested, to prevent the centroid convergence that would render stored memories identical. We derive a Foster-Lyapunov drift bound for the full triple loop, showing that seeding rescales the turnover noise floor. Across $1{,}007$ simulation runs over thirteen blocks: (i) removing stable context-expert binding removes specialization ($\mathrm{MI}=1.10$ vs. $0.001$; $n=91$); (ii) DM achieves $R=0.984$ vs. $0.385$ without memory ($n=16$); (iii) continuous seeding reconstructs representations after interference ($R_\mathrm{recon}=0.978$; one-shot fails; $n=30$); (iv) the mechanism operates within a characterized $(K,p)$ envelope ($n=350$); (v) recording $\times$ seeding is the minimal critical dyad ($n=40$); (vi) associative and reservoir baselines (Hopfield, ESN) are compared under matched turnover ($n=370$). DM is thus a falsifiable, bounded mechanism for persistent memory in backpropagation-free cognitive systems, with functional parallels to hippocampal consolidation.