Understanding Empirical Unlearning with Combinatorial Interpretability

While an unlearned language model may no longer recall a fact directly, the fact often remains recoverable through multi-hop reasoning over related knowledge. Most existing unlearning techniques overlook this vulnerability, targeting facts in isolation while leaving their supporting knowledge intact. To achieve true forgetting, we propose a general deep unlearning framework compatible with existing unlearning algorithms. Our approach adaptively explores both explicit responses and latent internal representations to discover valid reasoning paths, compiles them into a confidence-aware supporting subgraph, and we apply a graph minimum cut to sever all recovery paths while preserving unrelated knowledge. To rigorously evaluate deep unlearning, we introduce a model-specific pipeline that extracts and completes knowledge graphs from raw text, filtering them by calibrated model confidence to reflect what the model genuinely retains. Comprehensive experiments demonstrate that selectively unlearning supporting knowledge yields substantially deeper forgetting than superficial methods while preserving model utility, highlighting that genuine unlearning requires breaking the relational structures that enable factual reconstruction.

Prior white-box studies show that large language models can retain latent traces of target knowledge after unlearning, even when the knowledge is no longer expressed in their outputs. However, existing audits remain limited to one-off diagnostics: it is unclear whether these residual signals can predict future recovery under continued training or serve as reliable optimization targets. Resolving this gap is essential to determine whether internal auditing can move beyond post-hoc evaluation toward proactive risk monitoring and safer unlearning. We propose J-Access, an inference-time audit that uses the Jacobian lens to map intermediate representations into vocabulary space and measures how often target concepts remain accessible along the model's output pathway. We hypothesize that residual accessibility reflects recovery susceptibility: knowledge that remains closer to the output pathway requires less fine-tuning to restore, leading to faster recovery. We audit 398 public unlearned models spanning eight unlearning methods. We find that: (1) most unlearned models retain access above the retain-only gold level; (2) pre-attack accessibility predicts recovery speed and extent at the model level, but cannot identify which specific facts will be recovered; and (3) directly minimizing J-Access does not promote genuine deletion. Instead, the model learns to hide knowledge from the audit, producing lower audit scores but greater post-attack recovery. These findings position J-Access as a model-level diagnostic for assessing residual susceptibility in unlearned models. We argue internal audits should serve as an independent diagnostic dimension in unlearning evaluation, and should not be converted into optimization targets without validation.

Machine unlearning aims to remove specific knowledge from a trained large language model (LLM) without retraining from scratch. Existing methods modify model weights via gradient ascent and its advances. While effective on certain benchmarks, these weight-based approaches exhibit a sharp forget-utility trade-off, where stronger forgetting of target knowledge can degrade model utility, and unlearned knowledge may reappear under post-unlearning fine-tuning or prompt attacks. We propose ARIA (autoencoder-gated inference-time unlearning), a test-time unlearning method that leaves model weights intact and gates access to unwanted knowledge only when generation enters a forget-related state. ARIA uses sparse autoencoder (SAE) latents to train a lightweight linear detector, then applies an interpretable intervention on triggered states with negligible test-time overhead. Empirical evaluations on TOFU, R-TOFU, and WMDP show that ARIA improves the forget-retain trade-off over weight-based baselines across both a thinking model (DeepSeek-R1-Distilled-Qwen-1.5B) and an instruction model (Gemma-3-1B-it), e.g., reducing WMDP-cyber forget-set accuracy significantly while keeping MMLU within 1% of the pre-unlearning model. We further introduce three post-unlearning adversarial attacks targeting weight-space and decoding-space recovery, and find that ARIA remains robust under all three, with forgetting changing by less than 1% under attack. A feature-level case study leveraging the interpretability of ARIA suggests that some retain degradation may reflect response styles underlying the unlearning data rather than leakage of the targeted knowledge itself, highlighting a potential source of bias in unlearning task construction.