Memorization-Compression Cycles Improve Generalization
Authors: name: Fangyuan Yu

We prove theoretically that generalization improves not only through data
scaling but also by compressing internal representations. To operationalize
this insight, we introduce the Information Bottleneck Language Modeling (IBLM)
objective, which reframes language modeling as a constrained optimization
problem: minimizing representation entropy subject to optimal prediction
performance. Empirically, we observe an emergent memorization-compression cycle
during LLM pretraining, evidenced by oscillation positive/negative gradient
alignment between cross-entropy and Matrix-Based Entropy (MBE), a measure of
representation entropy. This pattern closely mirrors the predictive-compressive
trade-off prescribed by IBLM and also parallels the biological alternation
between awake learning and sleep consolidation. Motivated by this observation,
we propose Gated Phase Transition (GAPT), a training algorithm that adaptively
switches between memorization and compression phases. When applied to GPT-2
pretraining on FineWeb dataset, GAPT reduces MBE by 50% and improves
cross-entropy by 4.8%. GAPT improves OOD generalizatino by 35% in a pretraining
task on arithmetic multiplication. In a setting designed to simulate
catastrophic forgetting, GAPT reduces interference by compressing and
separating representations, achieving a 97% improvement in separation -
paralleling the functional role of sleep consolidation.