Interpretable Memory Models for Spaced Repetition

Continual pre-training of large language models must acquire new information without erasing old knowledge. Existing replay methods often choose a global old/new mixture and sample uniformly, ignoring that examples differ in how quickly they are forgotten. We formulate continual pre-training as adaptive review scheduling: the training loop should decide not only how much history to replay, but which examples should return at each step. We introduce Spaced Repetition Training (SRT), a continual learning framework inspired by cognitive science, which schedules sample-rehearsal using the SuperMemo-2 (SM-2) algorithm. SRT maintains per-example review state, maps per-example perplexity to a recall-quality signal, and schedules historical examples for retention and new examples for consolidation while leaving the model, objective, and optimizer unchanged. On temporally separated Wikipedia and code corpora, SRT improves the stability-plasticity trade-off, recovering 5 to 37 percentage points of old-knowledge accuracy lost by naive continual pre-training across model scales while preserving or improving new-knowledge acquisition. At larger scale, SRT preserves broad benchmark performance that naive continual pre-training and uniform replay substantially degrade. Experiments with vision and tabular data further suggest that the scheduling principle extends beyond language when paired with an appropriate recall signal.

While scaling laws govern aggregate large language model performance, no scaling law has linked factual recall to both model size and training-data composition. We evaluated 38 models on over 8,900 scholarly references evaluated by an automated reference verification system. Recall quality follows a sigmoid in the log-linear combination of model parameter count and topic representation in training data. These two variables alone explain 60% of the variance across 16 dense models from four families, rising to 74-94% within individual families. The form matches a superposition-inspired account in which recall is gated by a signal-to-noise ratio: signal strength scales with concept frequency and the noise floor with model capacity.

A language model with a bounded working memory must repeatedly decide which stored items to keep. Every deployed method decides the moment an item arrives, from the past (StreamingLLM, H2O) or from a guess about the future (SnapKV). We recast the choice as an estimation problem on a hidden signal, whether an item will be reused, placing existing methods on one axis, the commit lag $H$: online filters and learned predictors commit at $H=0$, while Belady's offline optimum sits where the whole future is known. The missing regime in between, fixed-lag smoothing, waits a bounded number of steps, observes which items a correct near-future prediction attended to, and only then commits. This measurement, demonstrated utility, turns Belady's unobservable future request into something we read off the model itself. We instantiate it as a training-free policy, RMM, a strict generalization of H2O that reduces to it exactly when the measurement is uniform. In controlled settings where reuse is endogenous and separated in time, demonstrated utility identifies used memory far better than accumulated attention, and a small bounded memory behaves like a much larger one. But on independent third-party benchmarks, run inside NVIDIA's KVPress harness against its own SnapKV, H2O, and StreamingLLM implementations, the advantage mostly disappears: RMM is on par with H2O for single-turn question answering and loses to both H2O and SnapKV in a streaming multi-turn setting. The cause is simple: on natural text the model is correct about most tokens, so weighting attention by correctness barely changes it, and demonstrated utility collapses onto accumulated attention unless reuse is sharp and endogenous, which standard benchmarks do not exercise. Our contribution is the framework and an honest map of when measuring beats accumulating, not a new state of the art.