Logit Leakage through Floating-Point Bias Addition

Shaomin Chen, Xiaorui Gong

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…