Beyond the empirical results, our sleep paradigm is grounded in a theory that clarifies why its two stages (memory consolidation and dreaming) can support continual learning without simply trading new knowledge for old capabilities.

For memory consolidation, the analysis shows that knowledge seeding can be understood as a structured, low-rank compression problem. The model is not asked to copy every detail of its short-term traces into its parameters. Instead, it identifies a compact set of directions that best preserve both the model’s own on-policy behavior and the semantic qualities rewarded by the learning objective.

This perspective explains the complementary roles of the two signals: on-policy distillation aligns consolidation with the trajectories the model will actually produce at inference time, reducing the mismatch that can arise when training only on teacher-generated distributions; meanwhile, the semantic reward changes what is worth retaining, prioritizing directions that preserve meaning and task-relevant behavior rather than merely matching token probabilities. Parameter expansion then provides the capacity needed to write these selected memories without overwriting previously consolidated knowledge.

For dreaming, the theory characterizes random expert activation and reward-based sample selection as mechanisms for improving the geometry of learning. Injecting different MoEs broadens the set of gradient directions explored during synthetic generation, exposing the model to a richer collection of updates than those induced by its ordinary wake-time data alone. Gradient-based filtering then emphasizes the synthetic experiences that carry the most useful learning signal, strengthening informative directions while preserving the structure of the underlying gradient space.

Together, these steps yield a more balanced optimization landscape: learning is less dominated by a small number of directions, gradients are better conditioned, and the model can make more stable progress when refining its capabilities. In this view, dreaming is not simply self-generated data augmentation; it is a deliberate process for diversifying, selecting, and consolidating the updates through which the model improves itself.