What Does Loss Optimization Actually Teach, If Anything? Knowledge Dynamics in Continual Pre-training of LLMs

Continual Pre-Training (CPT) is widely used for acquiring and updating factual knowledge in LLMs. This practice treats loss as a proxy for knowledge learning, while offering no grounding into how it changes during training. We study CPT as a knowledge learning process rather than a solely optimization problem. We construct a controlled, distribution-matched benchmark of factual documents and interleave diagnostic probes directly into the CPT loop, enabling epoch-level measurement of knowledge acquisition dynamics and changes in Out-Of-Domain (OOD) general skills (e.g., math). We further analyze how CPT reshapes knowledge circuits during training. Across three instruction-tuned LLMs and multiple CPT strategies, optimization and learning systematically diverge as loss decreases monotonically while factual learning is unstable and non-monotonic. Acquired facts are rarely consolidated, learning is strongly conditioned on prior exposure, and OOD performance degrades from early epochs. Circuit analysis reveals rapid reconfiguration of knowledge pathways across epochs, providing an explanation for narrow acquisition windows and systematic forgetting. These results show that loss optimization is misaligned with learning progress in CPT and motivate evaluation of stopping criteria based on task-level learning dynamics.