Understanding how large language models (LLMs) store, retain, and remove knowledge is critical for interpretability, reliability, and privacy compliance. We reveal a key phenomenon: machine unlearning imprints distinct geometric signatures in the model’s input loss landscape (ILL), with unlearned examples forming flat, low-curvature plateaus that contrast sharply with the high-curvature basins of retained or unseen examples. Remarkably, these patterns emerge even when pointwise losses overlap, exposing residual memorization through input-output behavior alone. Building on this insight, we introduce **REMIND (Residual Memorization in Neighborhood Dynamics)**, a framework that diagnoses memorization states (retained, forgotten, holdout) by probing local ILL curvature over semantically coherent neighborhoods. REMIND operates using only loss queries and a novel embedding-proximity perturbation method to generate controlled, interpretable variants. In evaluations, REMIND achieves 82% multi-class ROC-AUC, outperforming baselines like ROUGE-L and MIN-K%++, with roughly 2× higher AUC at 1% FPR, and remains robust on paraphrased inputs. This neighborhood-level geometric analysis provides a practical, interpretable lens on LLM knowledge retention and unlearning, detecting subtle residual signals missed by pointwise or aggregated metrics.