One Token Is Enough: Fingerprinting and Verifying Large Language Models from Single-Token Output Distributions

We report a striking statistical regularity in frontier LLM outputs that enables a CPU-only scoring primitive running at 2.6 microseconds per token, with estimated latency up to 100,000$\times$ (five orders of magnitude) below existing sampling-based detectors. Across six contemporary models from five independent vendors, two generation sizes, and five held-out domains, token rank-frequency distributions converge to the same two-parameter Mandelbrot ranking distribution, with 34 of 36 model-by-domain fits exceeding $R^{2} = 0.94$ and 35 of 36 favoring Mandelbrot over Zipf by AIC. The shared family does not collapse the models into statistical duplicates. Fitted Mandelbrot parameters remain cleanly separable between models: the cross-model spread in $q$ (1.63 to 3.69) exceeds its per-model bootstrap standard deviation (0.03 to 0.10) by more than an order of magnitude, yielding tens of standard deviations of separation per few thousand output tokens. Two capabilities follow. First, statistical model fingerprinting: text from a vendor-delivered LLM can be tested against its claimed model family without cryptographic watermarks or access to model internals, supporting provenance verification and silent-substitution audits. Second, a model-agnostic reference distribution for black-box output assessment, from which we derive a single-pass scoring primitive that composes with model log probabilities when available and degrades to a rank-only mode usable on closed APIs. Pilot results on FRANK, TruthfulQA, and HaluEval map where the primitive helps (lexical anomalies, unsupported entities) and where it structurally cannot (reasoning errors in domain-appropriate vocabulary). We position the primitive as a first-pass triage layer in compound evaluation stacks, not as a replacement for sampling-based or source-conditioned verifiers.

Establishing the provenance of a language model---including its base checkpoint and possible overlap in training distributions---is a governance challenge that metadata alone cannot resolve. We introduce a training-free fingerprint based on the top-$k$ vocabulary projections of late hidden states elicited by 250 fixed knowledge probes, compared using Jaccard overlap over decoded token strings. We evaluate the method on 32 open-weight models from nine families (0.6B--32B) with documented relationships. (1)~A \emph{similarity ladder} broadly follows model relatedness: independently trained models on identical data score 0.48 raw (0.35 vocabulary-corrected), followed by shared-base fine-tunes (0.39/0.33), same-developer relatives (0.38/0.28), and models with no documented relationship (0.22/0.17). This identical-data signal persists across three organizations, two tokenizer families, and two architecture classes, and emerges within the first 1% of training before measurable task competence, suggesting a contribution from shared training data beyond capability convergence. (2)~As a nearest-neighbor \emph{lineage-retrieval} method, the fingerprint ranks the exact documented base among the top two candidates for all five R1 distillations (mean rank 1.8, MRR 0.60), including a math-specialized base not identifiable from coarse metadata. (3)~A \emph{depth ablation} shows that lineage group discrimination strengthens toward the output distribution, with AUC increasing from 0.72 at quarter depth to 0.90 at the output; using only the top 5 output tokens retains AUC 0.87. (4)~The fingerprint remains stable under quantization, with Jaccard similarity of 0.92 under int8 and 0.82--0.85 under int4, compared with a maximum cross-model similarity of 0.81 in the calibration pool. We release the probes, code, and fingerprints.

Growing concerns over the theft and misuse of Large Language Models (LLMs) underscore the need for effective fingerprinting to link a model to its original version and detect misuse. We define five essential properties for a successful fingerprint: Transparency, Efficiency, Persistence, Robustness, and Unforgeability. We present a novel fingerprinting framework that provides verifiable proof of ownership while preserving fingerprint integrity. Our approach makes two main contributions. First, a chain and hash technique that cryptographically binds fingerprint prompts to their responses, preventing collisions and enabling irrefutable ownership claims. Second, we address a realistic threat model in which instruction-tuned models' output distribution can be significantly altered through meta-prompts. By incorporating random padding and varied meta-prompt configurations during training, our method maintains robustness even under significant output style changes. Experiments show that our framework securely proves ownership, resists both benign transformations (e.g., fine-tuning) and adversarial fingerprint removal, and extends to fingerprinting LoRA adapters\footnote{We release our code at: https://github.com/microsoft/Chain-Hash.