Fine-tuning LLMs to inject new knowledge faces a critical challenge: LLMs can quickly memorize new facts, yet fail to use them for downstream reasoning tasks. We formalize this failure as the Knowing-Using Gap, characterized by an accuracy gap and a temporal lag between memorization and generalization. To understand this phenomenon, we fine-tune LLMs with unseen knowledge and monitor the spatial permeation dynamics of the knowledge internally with self-patching, an adaptation of activation patching that scans all layer pairs at every fine-tuning check-point. Self-patching identifies activation locations where relocating representations substantially improves failed generalization cases. These results are consistent with a knowledge-circuit misalignment hypothesis: memorized representations can exist internally but may not be routed to computation-effective layers. Experiments are done cross-domain for the robustness of this finding. Building on this diagnosis, we propose layer-wise representation self-distillation (LRSD) that aligns knowledge representation from late storage layer to middle layer. LRSD keeps improving generalization after fine-tuning saturates and nearly doubles multi-hop chaining accuracy on Qwen, while leaving memorization intact.

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