Probabilistic "Copies" in Generative AI Models

A. Feder Cooper; Mark A. Lemley

REVIEW 3 major objections 3 minor 125 references

Probabilistic "Copies" in Generative AI Models

T0 review · 3 major / 3 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read A language model contains a copyrighted copy only when the work can be pulled out of it with little effort.

desk verdict A thoughtful, novel legal argument that AI model weights are copies only when extraction is easy, but the load-bearing ease-of-extraction threshold is not in the statute and depends on decoding choices. read the letter →

arxiv 2607.14532 v1 pith:3IRB7PF7 submitted 2026-07-16 cs.CY

Mark A. Lemley , A. Feder Cooper This is my paper · ORCID

classification cs.CY

keywords copyrightfixationLLMmemorizationextractionprobabilisticcopygenerativeAIfairusemodelweightstransitoryduration

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

The paper faces a question copyright law has not answered: when a generative model stores a copyrighted work only as probabilistic relationships in its weights, is the model itself a "copy" of that work? The paper argues that the most likely legal answer is functional, not metaphysical: the model contains a copy if, and only if, the work can be extracted from it with relatively little effort. Deterministic or near-deterministic extraction makes the weights a fixed copy; extraction that needs hundreds or thousands of probabilistic attempts does not, even though the occasional output may still infringe. The answer matters because it decides whether the model itself, and every redistributed copy of the model, is an infringing article before any infringing output occurs. The paper is candid that it finds this result unsatisfying as policy and suggests statutory change.

What carries the argument

The load-bearing distinction is between the fixed probability distribution a model's weights define and the decoding procedure that selects outputs from that distribution. The paper's legal test is "ease of extraction": a work is fixed in the model when a deterministic (or near-deterministic, high-probability) decoding path returns it with minimal prompting; a work that appears only after many stochastic attempts is not fixed, because it arises at the moment of generation rather than persisting in the weights. The analogies to compiled code, video games, and lossy compression carry this distinction into copyright doctrine.

What would settle it

A court decision holding that a model contains a "copy" whenever a copyrighted work is demonstrably encoded in its weights, without regard to extraction probability or effort, would falsify the paper's central prediction; likewise, a ruling that generation-on-the-fly from probabilistic weights satisfies the fixation requirement would do so.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that copyright's fixation requirement, applied to LLMs, splits along an ease-of-extraction line. A model is a copy of a work when the work is retrievable directly and repeatably through a simple prompt, because the weights then act like stored instructions for reproducing the work. When the work surfaces only probabilistically, with many non-infringing outputs for every successful reproduction, what is stored is a set of ingredients, not the end product; the output may be an infringing copy at the moment it is generated, but the latent potential for it is not. Consequently, whether a particular model contains a copy of a particular work is a

Load-bearing premise

The argument assumes that a work appearing in output only once in thousands of tries is not "fixed" in the model for a period of more than transitory duration, so the latent encoding in the weights does not by itself make a copy.

Editorial extensions

If this is right

Models that reproducibly generate a whole work from a short prompt are themselves prima facie infringing copies, even if no one ever requests the output.
Every person who downloads and redistributes such an open-weight model makes a new infringing copy of the works encoded in it, expanding exposure for open distribution relative to closed APIs.
Works extractable only probabilistically (say, one success in a thousand tries) do not make the model a copy, even though a lucky output can still be infringing.
If a model is a copy, withdrawal remedies like injunction and destruction become available; and since removing memorized content from trained weights is unreliable, fair use and output-focused rules take on greater weight.
Because extraction methods improve over time, a given model can cross the copy line without its weights changing.

Reading between the lines

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

Editorial inference: the ease-of-extraction threshold is a moving target, so legal exposure would become partly a function of forensic technique; a model could be declared a copy after a new extraction paper, not after any change in the model.
Editorial inference: a strict reading of the functional test would treat copyright status as a design variable, because developers could keep outputs below the ease threshold by adding stochastic decoding or filters, shifting infringement risk from the model to the output.
Editorial inference: a quantitative operationalization of "relatively little effort" (for example, a threshold on expected number of attempts or on extraction probability) would make the test administrable, but no such number is derivable from the statute.
Editorial inference: if courts instead held that anything fixed in the weights is a copy regardless of extractability, the paper's functional line would be bypassed and nearly every large model would contain copies of some works; that outcome is the contingency the paper treats as the main doctrinal risk.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

What you should know first: this is a serious and genuinely new legal analysis of whether LLM weights can be “copies” under U.S. copyright law. Lemley and Cooper argue that the answer is functional: a model contains a copy of a work only if the work can be extracted with relatively little effort. Deterministic extraction (e.g., Llama 3.1 70B reproducing Harry Potter from a short prompt) makes the weights a fixed copy; probabilistic extraction (1 in 1000 attempts) does not, though the individual outputs may infringe. That mixed conclusion is not in the prior work they cite, and it matters for the many pending lawsuits and for open-weight vs API models.

They also do some things well. The technical account of memorization vs extraction is accurate and accessible, and they correctly warn against misleading metaphors. They identify a real self-contradiction in the statutory definition of “copy” (read literally, an infringing copy must be made by the author). And they are persistently honest about uncertainty, repeatedly qualifying their conclusion as tentative. The paper does not overclaim.

The soft spots are real. The decisive line between “stored instructions” and “ingredients” has no direct case support. Section 101 says a copy is a material object from which the work “can be perceived, reproduced, or otherwise communicated”—no “relatively little effort” qualifier. The paper imports a threshold that the statute doesn’t state, and the buffer-copy cases they analogize to are about transitory duration, not low-probability persistence. The stress-test note’s point is on target: whether the same weights count as a copy can depend on the decoding procedure. The paper itself concedes (footnote 126 / II.C) that a sequence with only 0.1% extraction probability can be deterministically decoded by beam search if it is the argmax. So the “ease of extraction” test flips depending on which search algorithm a user picks—that is not a stable property of the model. And the paper also states that memorized data are encoded in the weights regardless of extractability, which cuts against the functional test. If the work is truly in the material object, a court could find a copy regardless of effort.

The empirical base is also mostly their own preprints, some still unpublished or with placeholder footnotes. That is not disqualifying, but it means the load-bearing evidence is not independently verified.

Verdict: this deserves serious peer review. The argument is well-crafted, the stakes are high, and the paper says something new. A good referee will push on the ease-of-extraction threshold and the decoding-dependence, and the authors should address those before publication. I’d bring it to a reading group interested in copyright/AI, and I’d cite it if I were writing in that area.

Recommendation: accept for peer review with the expectation of substantial revision.

Referee Report

3 major / 3 minor

Summary. This law review article asks whether an LLM's weights contain a 'copy' of a copyrighted work when the model can reproduce the work only probabilistically. The authors distinguish deterministic or near-deterministic extraction (e.g., Llama 3.1 70B reproducing Harry Potter from a short prompt), which they argue makes the weights a fixed copy, from cases requiring many stochastic attempts (e.g., 1 in 1000), which they argue leaves only 'ingredients' and not a copy. They ground the distinction in 17 U.S.C. § 101's fixation requirement, analogize to compiled code, video games, and lossy compression, and conclude that the most likely judicial answer is functional: a model contains a copy of a work if and only if the work can be extracted with relatively little effort. The paper is explicitly tentative and proposes policy alternatives.

Significance. The paper is the first sustained attempt to connect the ML literature on probabilistic memorization and extraction to the statutory definition of 'copy.' If its functional test were accepted, it would create a work-by-work, model-by-model evidentiary inquiry and would expose open-weight models to greater direct-infringement risk than closed models. The paper's honest hedging and careful technical explanation of decoding procedures are strengths. However, the central legal premise — that 'relatively little effort' is the correct reading of § 101's 'can be perceived, reproduced, or otherwise communicated' — is asserted rather than demonstrated, and the proposed test is not a stable property of the model.

major comments (3)

[Part II.A and Conclusion] The central test — a model contains a copy 'if, but only if, the work can be extracted with relatively little effort' — reads an ease-of-extraction threshold into § 101 that the statute does not contain. The definition of 'copies' speaks of material objects 'from which the work can be perceived, reproduced, or otherwise communicated,' with no qualifier about probability, persistence of effort, or determinism. The paper itself concedes in Part I.B that memorized training data are encoded in the weights 'regardless of whether they can be extracted' and that extraction is 'a symptom of memorization, not its cause.' If the work is encoded in a permanent material object, repeated stochastic sampling can reproduce it, so 'can be reproduced' is literally satisfied. The buffer-copy cases (Cartoon Network, CoStar) concern transitory duration, not low-probability persistence. No case is cited for
[Part II.C (0.1% extraction and beam search)] The proposed ease-of-extraction test is not a stable property of the model; it varies with the user-chosen decoding procedure. The paper acknowledges (footnote 126 and surrounding text) that a sequence with extraction probability 1/1000 may nonetheless be returned deterministically by beam search if it is the highest-probability continuation. Thus the same weights would be a 'copy' for a weakly memorized passage when decoded with beam search, but 'ingredients' when decoded by stochastic sampling. The legal status of a fixed material object would flip based on which algorithm a litigant runs. Fixation doctrine asks whether the embodiment is sufficiently permanent, not whether a particular machine or device retrieves it conveniently. This instability undermines the functional test as a matter of statutory interpretation.
[Part II.B] The analogies to compiled code, lossy compression, and video games do not support the conclusion that probabilistic extraction is not fixation. All of the analogies involve deterministic or effectively deterministic systems, and the paper itself distinguishes video games on precisely that ground. But the paper's own technical account in Part I.A shows that an LLM is a fixed set of weights defining a fixed probability distribution; output variability arises from the decoding procedure, not from the model. A memorized sequence is encoded with high fidelity in those fixed weights. The 'on the fly' framing thus conflates the act of generating a particular output with the persistence of encoded information in the model. The internal tension between the technical premise (encoded regardless of extractability) and the legal conclusion (no copy unless easily extracted) is not resolved.

minor comments (3)

[Figure 2 caption] The caption reports a '99.2% match' but does not specify the metric or the alignment method. Clarify whether this is character-level, token-level, or something else, since the claim of 'near-exact' is central to the Harry Potter example.
[Footnotes 119 and 126] The discussion of 1/1000 probability and deterministic beam search is crucial and arguably contradicts the paper's clean dichotomy. It should be moved into the main text and engaged directly, rather than appearing as a caveat in footnotes.
[References] Several load-bearing empirical sources are unpublished preprints or are cited as 'Cooper Untitled,' 'Extractable Memorization From First Principles' (arXiv:2607.12649), and other 2026 manuscripts. For reproducibility, the authors should either cite peer-reviewed versions or provide a stable artifact/DOI.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the statutory analysis and functional test are independent of the empirical extraction evidence, though key empirical examples rely on the authors' own preprints.

full rationale

The paper's central claim is a legal prediction: courts will likely treat a model as containing a copy only when the work can be extracted with relatively little effort (Conclusion, II.C). That claim is constructed from statutory text (17 U.S.C. § 101), case law on fixation (Cartoon Network, CoStar, Kelley, video-game and compiled-code analogies), and policy arguments in Part II, not from the empirical extraction results in Part I. The extraction findings (e.g., Llama 3.1 70B generating Harry Potter) are used as illustrative evidence, not as the definitional ground of the legal conclusion. The paper expressly concedes that memorized data are encoded in weights even when not extractable (I.B), so the 'copy' determination does not collapse into the presence of an encoded work; it is instead a separate normative/doctrinal line-drawing exercise. The heavy reliance on the authors' own preprints (Extracting Books, Near-Verbatim, Extractable Memorization From First Principles) means the empirical illustrations are not independently verified within the paper, but those preprints are empirical, falsifiable studies of extraction probabilities and do not themselves assume the copyright conclusion. No equation or construction makes a 'prediction' equal to its input. Therefore no specific circular step is exhibited; the paper is best characterized as relying on self-cited empirical support within an otherwise independent legal derivation.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

No new physical or technical entity is postulated; 'probabilistic copy' is a legal characterization, not an entity. The two free parameters are the ease-of-extraction thresholds used to distinguish copies from non-copies. The axioms are the technical and interpretive premises needed to connect memorization science to fixation doctrine.

free parameters (2)

Ease-of-extraction threshold ('relatively little effort') = Not quantified; calibrated by examples: >95% extraction probability for Harry Potter, ~0.1% for the middle class, 1-in-1
The legal conclusion turns on distinguishing straightforward from probabilistic extraction, but no statutory or case-law basis fixes this threshold; it is chosen by the authors from their own extraction results.
Extraction probability threshold for 'copy' = >95% for deterministic copy; ~0.1% via beam search; 1/1000 as illustrative probabilistic case
Used to classify works as copied versus not copied in the model; these numbers come from the authors' empirical studies, not from the law.

assumptions (4)

domain assumption Memorized training data are encoded in model weights, and extraction is a symptom of that encoding.
Invoked in Part I.B; central to linking empirical extraction to legal copy analysis; relies on the ML literature, including the authors' own papers.
domain assumption The Copyright Act's fixation requirement demands a stable embodiment from which the work can be perceived or reproduced; on-the-fly probabilistic generation does not satisfy it.
Parts II.B-II.C; the conclusion depends on interpreting 'sufficiently permanent or stable' as excluding probabilistic outputs; case law on point is analogical, not direct.
domain assumption A compressed or encoded representation counts as a copy if it is deterministic and reliably reproducible.
Part II.B; used to analogize model weights to compiled code and video game content, and to distinguish Microsoft Word as a non-copy.
domain assumption Failure to extract a work does not prove it is absent from the model.
Part I.B; the paper uses this to hedge its negative examples like Sandman Slim, but the premise also makes the proposed legal test inherently provisional.

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Cite this review

Pith. "Pith review of Probabilistic "Copies" in Generative AI Models." pith.science (2026). https://pith.science/paper/3IRB7PF7

@misc{pith2026260714532,
  author       = {Pith},
  title        = {Pith review of: Probabilistic "Copies" in Generative AI Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3IRB7PF7}},
  note         = {Machine review of arXiv:2607.14532}
}

read the original abstract

Recent work shows that it is possible to extract verbatim or near-verbatim text of some copyrighted works from some large language models (LLMs or models). That is evidence that the model weights encode the works in some form - that the model has "memorized" those works from its training data. But LLMs don't store information in the same format as familiar databases. Rather, their weights store statistical relationships between tokens that have been learned from the training data, and those relationships inform a generation process that is often probabilistic rather than deterministic. In the case of memorization, those relationships are strong enough that, in many circumstances, the model might generate a copyrighted work from its training data with some probability. Copyright law has not previously had to decide whether storing information that might or might not produce output similar to a copyrighted work is itself a copy of the work. The answer to the question is important, because it may determine the legality of many LLMs. The statute and case law are largely unhelpful. We argue that copyright law will likely take a functional approach to the question, finding that LLMs contain a copy of a particular work only if it is straightforward to extract that work in outputs. That result is unsatisfying as a policy matter, and we suggest potential changes to the law, but it is the most likely outcome under current law.

Figures

Figures reproduced from arXiv: 2607.14532 by the authors.

**Figure 1.** Illustrating autoregressive generation. The input prompt is “Mr. and Mrs. Durs,” for which the (autoregressive) LLM produces a distribution over the next tokens in its vocabulary (all possible tokens it can generate). At each generation step, the decoding procedure illustrated here selects the highest-probability token as the one to generate. In this example, the top-ranked token has enormous probability at each ste… view at source ↗

**Figure 3.** We know that this book was in Llama’s training data, [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗

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