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REVIEW 5 major objections 6 minor 27 references

Zero-Shot Attribution for Large Language Models: A Distribution Testing Approach

T0 review · 5 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

Pith's one-line read The paper claims that LLM code attribution can be solved by distribution testing, and that its tool Anubis outperforms detectGPT in zero-shot code attribution.

desk verdict Practical heuristic for zero-shot LLM attribution with strong AUROC numbers, but the EVAL+ oracle breaks the theoretical link, so the distribution-testing guarantees do not carry over. read the letter →

arxiv 2506.20197 v1 pith:E32HWFM5 submitted 2025-06-25 cs.LG cs.AIcs.SE

classification cs.LGcs.AIcs.SE MSC 62F0362G1068T50
keywords zero-shotattributiondistributiontestingLLMcodedetectionEVALoracletokenizercollisionAUROCAnubishypothesis
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Anubis is a zero-shot method for attributing a set of code samples to a suspect language model: it decides, with high confidence, whether at least a large fraction of the samples came from that model, using no training and no watermarking. The paper's central claim is that this task can be recast as a hypothesis-testing problem over the probability mass function of the model, provided the model allows both sampling and per-sequence probability queries. On code generated by DeepSeek-Coder, CodeGemma, and Stable-Code, Anubis is reported to separate target-model samples from others with AUROC consistently above 0.9 when the acceptance/rejection gap is at least 70 percentage points, and to remain useful with as few as about 1000 samples. The authors argue this matters because attribution of machine-written code is becoming a practical need, and existing zero-shot statistical detectors such as detectGPT degrade on code.

What carries the argument

The central object is the pair of testing algorithms Global and Local applied over a bucketing of the token-sequence domain. Buckets are probability shells $\{x : 2^{-j} < L^*(x) \le 2^{-j+1}\}$ under the suspect model; Global compares the empirical CDFs of sample counts per bucket using the Dvoretzky–Kiefer–Wolfowitz inequality, and Local applies a chi-square-type statistic within each bucket. The load-bearing practical piece is EVAL+, which estimates $L(s)$ by calling the model's next-token EVAL oracle over tokenizer collision sequences; getCollision enumerates all depth-$d$ token sequences decoding to the same text, and for long texts the computation splits recursively.

What would settle it

A decisive experiment would be to compare EVAL+ with true model probabilities on a white-box model: if the relative error on typical code samples is large, or if Anubis's acceptance decision flips when EVAL+ is replaced by exact $L(s)$, then the statistical test is not operating on the distributions the paper claims.

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Extended reading notes

Core claim

The authors claim that attribution reduces to a test between two hypotheses about the $\ell_1$ distance between the empirical distribution of the sample set and the target model's distribution, and that the test can be run with oracle access combining samples and density evaluations. The algorithm partitions the domain into buckets by target-model probability, checks the empirical bucket CDFs against a DKW-based threshold, then runs a chi-square-type local test inside each bucket. The practical contribution is an implementation whose EVAL+ procedure estimates $L(s)$ by summing over tokenizer collision sequences, and experiments showing this pipeline reaches AUROC $\ge 0.9$ distinguishing DeepSeek-Coder and CodeGemma from Stable-Code with roughly 2000 samples while outperforming detectGPT.

Load-bearing premise

The whole pipeline depends on EVAL+ returning an accurate estimate of the probability that the target model assigned to each sample, but the paper describes EVAL+ as a lower bound that searches only depth-2 tokenizer collisions and gives no error guarantee matching the approximate EVAL oracle needed by the theory.

Editorial extensions

If this is right

  • If the reported AUROC transfers, organizations can audit code provenance without training a detector or modifying generation.
  • The approach is agnostic to post-processing such as formatting or dead-code removal, because it queries the suspect model's probabilities rather than matching surface text.
  • The method's sample complexity becomes a practical design parameter: the paper finds roughly 1000 samples already give AUROC around 0.8–0.9 depending on the model and gap.
  • Because the test is zero-shot, a new suspect model only requires access to its log-probabilities; no labeled dataset of that model's outputs is needed.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: the experiments do not separate the value of the bucketing-and-testing idea from the error introduced by EVAL+ with depth $d=2$; replacing EVAL+ with exact probabilities on a white-box model would isolate that.
  • Editorial inference: the same bucket-and-test scheme could apply to natural-language text, but the collision enumeration in EVAL+ would become far more expensive as vocabulary and subword ambiguity grow.
  • Editorial inference: a minimally fair baseline would be a detector using the same probability oracle but a simpler statistic, such as mean log-probability; if that baseline matches Anubis, the bucketing machinery is not the source of the gain.
  • Editorial inference: for pairs of models whose output distributions are close in $\ell_1$, the theoretical sample bound scales with vocabulary size, so applying Anubis to larger models or near-twin checkpoints may require many more samples than the experiments used.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 6 minor

Summary. The paper introduces Anubis, a zero-shot attribution method for code samples generated by LLMs, framing attribution as a distribution testing problem. The authors present a theoretical tester (Algorithm 1) adapted from prior work, then propose a practical implementation (EVAL+ in Algorithm 5) that estimates the probability of a text under a target LLM using token-level conditional probabilities. Experiments on code datasets from HumanEval compare Anubis against detectGPT, reporting AUROC above 0.9 in several settings and above 0.8 with as few as 1000 samples. The paper includes proofs in the appendix and claims a strong theoretical foundation for the method.

Significance. If the reported empirical results are reliable, Anubis is a useful practical tool for zero-shot code attribution, and the paper's open-source release is a valuable contribution to a timely problem. The experimental comparison against detectGPT is a reasonable first step, and the evaluation across contamination levels and sample sizes is informative. However, the theoretical claims are not supported by the practical algorithm: the distribution-testing guarantee in Theorem 3.1 applies only under an exact or η-approximate EVAL oracle and a condition on the reference distribution that is not verified, while the implemented EVAL+ deviates substantially from that oracle. The paper is more convincing as an empirical heuristic study than as an instance of the distribution-testing framework, and the central claim that the method's success 'reflects the strong theoretical foundation' is not justified by the evidence presented.

major comments (5)
  1. [Section 4.1, Algorithm 5] EVAL+ as specified is not a valid approximation to the oracle required by Definition 2.1. In the recursive case (|σ|>d), the second factor EVAL+(σ_{i+1}...σ_n,d) is computed as a standalone token sequence, so the first token of the right part is not conditioned on the left context; the product is therefore not the probability of the concatenated sequence under the autoregressive model. Additionally, different branches of the sum in line 8 double-count the same tokenization; for example, with n=4 and d=2, the full sequence σ1σ2σ3σ4 is counted in both the i=1 and i=2 branches. This contradicts the claimed 'lower bound' output in the algorithm header. Since Anubis uses these values as oracle probabilities in Algorithms 2-4, the theoretical guarantee of Algorithm 1 does not transfer to the implemented method. The authors must either (a) provide a corrected EVAL+ with a proven η-approximation property, or (b) explicitly state that the practical algorithm is a heuristic and remove the distribution-testing guarantee claims.
  2. [Section 3, Theorem 3.1 and Section 4] The condition ||P*||_2 ≤ sqrt(2/|Ω|) is not verified for language models, and the paper does not discuss whether code LLMs such as DeepSeek-Coder or CodeGemma satisfy it. If this condition fails, the theoretical testing guarantee is void. Furthermore, the sample complexity in Theorem 3.1 depends on |Ω|, the support size of the token-sequence domain, which is astronomically large for LLMs; the reported success with ~1000 samples is in apparent conflict with this bound. The authors should either verify the ℓ2-norm condition for their models and reconcile the sample complexity, or explain why the theory is nonetheless predictive for the empirical regime.
  3. [Section 4.1 and Algorithm 6] getCollision(tok, σ, d) enumerates all token sequences in Σ_tok^d, which for d=2 and a typical vocabulary size of ~5×10^4 is about 2.5×10^9 sequences per input sample. The paper does not describe how this enumeration is made tractable in the reported experiments, nor does it specify whether the implementation actually follows this pseudocode. If the implementation does not enumerate all such sequences, the pseudocode is not a faithful description of the evaluated algorithm; if it does, the computational cost appears prohibitive. This is a reproducibility issue that must be resolved.
  4. [Section 5, evaluation methodology] The paper does not explain how an AUROC curve is obtained from Anubis, which is described as a test that outputs a binary accept/reject decision. To compute AUROC, a continuous score must be used to rank positive and negative datasets; the authors should specify whether they use an internal statistic (e.g., the global or local test statistics) or vary a threshold in some other way. Without this, the reported AUROC values are not reproducible.
  5. [Section 3, Algorithm 4 and Appendix A.1] The Local algorithm computes Z = Σ (z1−z2)^2−z1−z2 over max(z1+z2,1), which is not the chi-squared statistic used in the theoretical analysis referenced in the appendix (where the bound is based on an identity-testing result from Canonne et al. 2021). The thresholds in Algorithm 1 (Thresh2) are derived from the theoretical analysis of a different statistic, so applying them to this ad-hoc statistic is not justified. The authors should either prove the correctness of this statistic under the stated guarantees or align the implementation with the analyzed test.
minor comments (6)
  1. [Title and Section 2] The heading 'Preliminiaries' contains a typo; it should be 'Preliminaries'.
  2. [Section 2, Definition 2.1] The definition of an approximate EVAL oracle is stated correctly, but the notation η-estimate could be made more explicit about whether the guarantee is per-query or uniform; the paper later uses the oracle in a way that assumes consistency across queries, which is not guaranteed by the definition as written.
  3. [Section 3, Theorem 3.1] The theorem's sample complexity expression has unbalanced parentheses and the role of the tilde in eO is not explained; please reformat for clarity and state which algorithm achieves the bound.
  4. [Appendix A.1] In the proof, the sentence 'P ∗(∆j)≥ c4ε2 2ℓ ≥ 2c3ε2 ℓ ,2 then we can assume' is garbled; please fix the typesetting and the logical structure. There is also a typo 'fo the buckets considered'.
  5. [Section 2, Language Models as Distributions] The definition of the tokenizer's decoder is inconsistent: Definition 2.3 says dec:Σ_tok→Σ_w, but it is later used on sequences; this should be stated uniformly as dec on token sequences.
  6. [Section 5, Figures 2 and 3] The number of independent runs used to produce the shaded regions and averaged AUROC is not reported; please include this information for statistical interpretability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central AUROC claim is an external benchmark comparison, and the self-cited distribution-testing theorem is independent support.

full rationale

The claimed derivation chain is not circular. The theoretical guarantee in Theorem 3.1 is explicitly adapted from Canonne et al. (2022), a prior distribution-testing result whose stated assumptions (a fully specified reference distribution and access to an EVAL oracle) do not include the paper's attribution target; it is therefore independent evidence rather than a conclusion that is assumed into existence. Although the first author is a co-author of that cited work, the theorem is not invoked as an unverifiable uniqueness principle and does not forbid competing approaches. The practical pipeline replaces the idealized EVAL oracle with EVAL+, and the empirical evaluation compares Anubis against detectGPT on code samples derived from the external HumanEval benchmark, so the reported AUROC does not reduce to a fitted parameter or to the paper's own test thresholds. The paper does not report the numerical values of epsilon_1, epsilon_2, and c_1 through c_4, but there is no quoted evidence that these were tuned on the evaluation set, so hidden calibration remains only a speculative concern. The apparent invalidity of EVAL+ as a true probability oracle is a correctness and robustness issue, not a circularity: the test decisions may lose their statistical grounding, but they are not equivalent to their inputs by construction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the accuracy of the EVAL+ probability estimator and the transfer of an idealized testing theorem to a real, high-dimensional setting. The free parameters (tau_Delta0, d, and the unreported threshold constants) are choices the reader cannot audit from the paper alone. No new entities are postulated.

free parameters (3)
  • tau_Delta0 (leftover fraction) = 0.05
    Hyperparameter controlling the Monte Carlo bucket estimation; paper reports low sensitivity but does not derive an optimal value.
  • d (EVAL+ depth) = 2
    Depth parameter for tokenizer collision search; set to 2 for tractability, which truncates the enumeration of alternative token sequences and likely biases the probability estimate.
  • Threshold constants epsilon1, epsilon2, c1, c2, c3, c4 = not reported
    The accept/reject thresholds in Algorithm 1 depend on these constants; the paper does not state their values in the experiments, so they are unspecified free parameters that can affect AUROC.
assumptions (4)
  • standard math DKW inequality bounds the l-infinity error of the empirical CDF for i.i.d. samples (Lemma 2.2).
    Used to set the Global test threshold in Algorithm 3; requires independence of samples drawn from P*.
  • domain assumption The LLM token distribution factorizes via the chain rule as Ltok(sigma) = Prod_i Ltok(sigma_i | sigma_<i).
    Standard for next-token LLMs; invoked in Section 2 and used by EVAL+ when computing token probabilities.
  • ad hoc to paper The reference distribution satisfies ||P*||_2 <= sqrt(2/|Omega|), and the bucketing approximation preserves the testing guarantee.
    Theorem 3.1 requires this norm bound, which is not verified for LLM distributions; the Monte Carlo bucket estimation in Section 4 is not analyzed.
  • ad hoc to paper EVAL+ provides an eta-approximate EVAL oracle (Definition 2.1).
    The practical algorithm relies on EVAL+ as the EVAL oracle, but Algorithm 5 states it returns a lower bound and has no proven approximation guarantee.

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Pith. "Pith review of Zero-Shot Attribution for Large Language Models: A Distribution Testing Approach." pith.science (2026). https://pith.science/paper/E32HWFM5

@misc{pith2026250620197,
  author       = {Pith},
  title        = {Pith review of: Zero-Shot Attribution for Large Language Models: A Distribution Testing Approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E32HWFM5}},
  note         = {Machine review of arXiv:2506.20197}
}
abstract

A growing fraction of all code is sampled from Large Language Models (LLMs). We investigate the problem of attributing code generated by language models using hypothesis testing to leverage established techniques and guarantees. Given a set of samples $S$ and a suspect model $\mathcal{L}^*$, our goal is to assess the likelihood of $S$ originating from $\mathcal{L}^*$. Due to the curse of dimensionality, this is intractable when only samples from the LLM are given: to circumvent this, we use both samples and density estimates from the LLM, a form of access commonly available. We introduce $\mathsf{Anubis}$, a zero-shot attribution tool that frames attribution as a distribution testing problem. Our experiments on a benchmark of code samples show that $\mathsf{Anubis}$ achieves high AUROC scores ( $\ge0.9$) when distinguishing between LLMs like DeepSeek-Coder, CodeGemma, and Stable-Code using only $\approx 2000$ samples.

Figures

Figures reproduced from arXiv: 2506.20197 by the authors.

Figure 1
Figure 1. Overview of our framework Anubis. Given a sample set S and a target model L ∗ , Anubis computes the probability of S under L ∗ and partitions the samples into buckets. Anubis then measures the distance between the bucket distribution and the occurrence disparity within each bucket to make a final decision. To address this issue, we adopt a framework from oracle-enhanced distribution testing, a sub￾field of testing t… view at source ↗
Figure 2
Figure 2. The AUROC of Anubis and detectGPT was evaluated against the target LLMs – DEEPSEEK-CODER and CODEGEMMA. The AUROC values are averaged over multiple runs across different datasets with the same contamination level γ%. The shaded regions indicate the uncertainty across independent runs. The dashed line represents detectGPT, while the solid line represents Anubis. RQ1 For a target model L ∗ , parameters LB%, UB%, and a… view at source ↗
Figure 3
Figure 3. The AUROC of Anubis when the number of samples is varied from 500 to 2000, evaluated against DEEPSEEK-CODER and CODEGEMMA. LB% is set to 0 in all cases. The colour intensity represents the AUROC value, with darker shades indicating higher AUROC. for that sample. To make detectGPT work for the dataset, we aggregated the scores for all samples to evaluate the overall attribution for the dataset. Evaluation metric. Fol… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Tokenizers are non-invertible. The GPT2 tokenizer encodes the string “a!=b” [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

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