What do your logits know?

Language model APIs can expose token-specific biases while withholding logits and token probabilities. Existing bias-based extraction recovers relative logits, leaving a common additive component undetermined in ideal arithmetic. We identify a numerical side channel in floating-point bias addition that exposes information about this component through token identities alone. The channel distinguishes score vectors with identical complete unperturbed log probabilities. Our method exploits changes in representable spacing at binary exponent boundaries. Under the stated binary32 arithmetic assumptions and a known reachable score interval, it recovers a logit pair and its unknown tie-breaking priority exactly in at most 52 token queries. Given complete relative logits, one recovered anchor determines the original logit vector. We evaluate recovery across 11 public checkpoints from seven model families and extend the local method with adaptive interval search and anchor selection. In end-to-end experiments with vLLM, SGLang, and llama.cpp, adaptive recovery succeeds on all 128 Qwen3-0.6B inputs per system, including 64 held-out inputs. A separate token-only experiment extracts a pretrained small model's complete output-head representation up to an invertible hidden-basis transformation. We also establish a sufficient condition for suppressing common-shift disclosure by subtracting the maximum before bias addition. In controlled experiments, this mitigation eliminates all observed distinctions between common-shift variants and preserves token decisions under the tested random biases.

Unlearning in large language models (LLMs) is typically evaluated at the output level, where a model appears to suppress sensitive or undesirable content. In this work, we show that such evaluations can create an illusion of forgetting: even when output-level leakage is eliminated, sensitive information can remain encoded in the model's hidden representations. We first provide a theoretical analysis establishing a fundamental separation between output suppression and representational erasure. Specifically, we show that the decoder can be made arbitrarily insensitive to sensitive directions, driving output-level leakage to zero, while the hidden representations retain the underlying information. To empirically validate this phenomenon, we train generative probe decoders on hidden states across transformer layers, enabling layer-wise measurement of information leakage. Across three widely used benchmarks, TOFU, MUSE, and WMDP, and state-of-the-art unlearning methods, we find that substantial sensitive information remains recoverable from hidden representations, even when standard output-level metrics indicate successful unlearning. To address this gap, we propose Probe-Adversarial Representation Suppression (PARS), an unlearning objective that adversarially minimizes the extractable information from hidden representations. PARS directly targets representational leakage and provides significantly stronger guarantees of erasure under adversarial probing and relearning attacks, outperforming all evaluated baselines. Our results highlight a fundamental limitation of existing unlearning paradigms and suggest that true forgetting in LLMs requires controlling not only model outputs, but also the information encoded in hidden representations. Codes are available at https://github.com/OptimAI-Lab/HiddenStateUnlearning.

For AI agents to be useful beyond simple chat, they must hold sensitive user context such as calendars, credentials, health records, and financial data. We study whether the mere presence of such secrets in a model's context window introduces hidden correlations into the model's benign outputs, allowing reconstruction even when the model correctly refuses direct extraction. We further study whether an adversary can actively engineer prompts that amplify this effect, using the model as a covert carrier to transmit secrets through seemingly innocuous text. In both cases, this limited leakage is exploited using a novel adaptive attack that assumes black-box access to the underlying model. In controlled experiments across eight proprietary models, we find that 2-digit in-context secrets are reconstructed with near-perfect accuracy and 4-digit secrets at 82% exact match, all from outputs the model produces in response to ordinary, non-adversarial requests. We observe that more capable models leak more: stronger instruction-following amplifies sensitivity to in-context secrets, suggesting leakage is a byproduct of capability as opposed to a patchable bug. We show this leakage enables two practical attacks: (1) a trained classifier that infers semantic predicates about user memories (e.g., health conditions, financial events) from routine natural-language outputs, and (2) an RL-trained adversary that extracts full Social Security Numbers from a production-style agent.