Large Language Model (LLM) unlearning is essential for removing sensitive or copyrighted knowledge while preserving general utility. Existing methods often leave residual knowledge in intermediate representations, which can still be recovered. To address this, we propose Cascade, a hierarchical recoverability control framework that minimizes the internal identifiability of target knowledge. Cascade combines three complementary controls: path-level routing to suppress privacy-associated activation routes, representation-level compression to reduce geometric separability, and decoding-level intervention to limit residual recovery. Experiments on TOFU, MUSE-News, and WMDP, including robustness tests with query reformulation and extraction-style prompts, show that Cascade effectively reduces recoverability while maintaining stable model utility.

Hidden states of large language models (LLMs) are typically analyzed as flat Euclidean vectors through probing, anisotropy, and intrinsic-dimension lenses. Yet much of what these models process (taxonomies, program structure, multi-step derivations) is hierarchical, and whether hidden-state distances reflect such hierarchy remains untested. We present the first systematic study of Gromov hyperbolicity (GH), a distance-based measure of tree-likeness, in prompt-token hidden states of open-weight LLMs. Across model families, scales, layer depths, and domains spanning math, code, commonsense, and truthfulness benchmarks, we construct a hyperbolicity atlas charting the normalized statistic 𝛿_rel along each axis. Four findings emerge: (i) depth dominates, with middle layers forming a high-𝛿_rel plateau and final layers dropping toward tree-like structure; (ii) scale is weak and non-monotonic; (iii) matched-scale families occupy distinct regimes, with specialization gaps exceeding scale effects; and (iv) domains interact with specialization, e.g., HumanEval shifts from the highest- to the lowest-𝛿_rel domain between base and coder checkpoints. GH thus serves as a lightweight diagnostic that localizes where hierarchical distance structure emerges and which comparisons warrant deeper analysis.