So, one way to prove that the data played no part is to trace and show that it wasn't used in the training process at all. If the data was never used in training, then it couldn't have played a part in the training process.

You're right; if the data was used in training, then it gets much trickier; it would be very difficult to show whether some particular data had a significant effect on the outcome.

This is one of the big problems with giant models like these; it becomes nearly impossible to discern what is and isn't plagiarism, or copyright violation.

It would in theory be possible to have things like n-gram databases or rolling hashes of training data, somewhat similar to OLMoTrace (https://arxiv.org/abs/2504.07096), which would allow for detecting whether particular documents ended up in the training data or not (you'd have to keep this for every model used in the whole training chain, as synthetic data generated by earlier models could be influenced by training data that wasn't included in later models). I'm sure there are practical issues with providing such a tool, but I think that it's necessary if you want to be able to categorically say "no, this document has never been present in the training data of this model."

Or look at it the other way: if your model wasn't influenced by things in your training data, why include them in the first place? Clearly, you train on all of these documents because they influence the model. Yes, it's hard to trace the exact influence of each one. But if they're not affecting the output, then why not just stop training on them? You could just not train on any private documents; only train on public, traceable data.

But instead, you choose to train on these private documents, so you have to admit, your model and its outputs are influenced by them.

> As a parallel example, can we prove the phase of the moon had no impact on the NS solution? No, not without a bunch experiments run at different phases of the moon.

That reads as incredibly dismissive and condescending. What makes you think you’re in a position to communicate like that when engaging on such a sensitive topic?

I think there is a much easier way to prove that the ChatGPT usage of Tristan Buckmaster and Levent Alpöge (possibly also the ChatGPT usage of Córdoba and Martínez-Zoroa, if they use it) had no influence on OpenAI solving the Navier-Stokes problem.

If the internal OpenAI model is as capable as you claim (being able to solve a Millenium problem without using unpublished insights built on years of work from mathematicians), then it should be able to demonstrate this capability again.

How about OpenAI solves another Millenium problem within the next two weeks, that doesn't coincide with the parallel discovery/solution of other teams of mathematicians, using ChatGPT for preliminary proofs & write-ups.

So you definitely did train on their data, you just think it is unlikely that it impacted the final model significantly?

> identify any of their de-identified data that came from their usage of ChatGPT

"de-identified" seems more of a euphemism than normal in this context, given the very unique work they were doing.

(a) identify any of their de-identified data that came from their usage of ChatGPT.

You don't need his login information, you just need to identify if anyone was approaching the NS problem using his method. Nobody else on earth (presumably) besides him, his team, and at best OpenAI were approaching the problem this way.

Why wouldn't contamination be possible? I can believe the data is de identified so you couldn't simply prompt the model to "follow this guy's approach", but it's entirely plausible that there is a very tiny amount of data about this approach in your dataset, and it comes precisely from this researcher.

Please answer this question: do you or do you not train your models on anonymized user data, where those users have opted out of such training?

The blog post appears to imply the answer to this is yes, as otherwise I assume it would be impossible for this contamination to have happened.

"There's no reason to believe that anything they did in ChatGPT led to our solution"

do you think that the model's proof was unrelated to being fed a solution that was close to completion?

any comment on openai allegedly trying to drop attribution for alpöge and then threatening buckmaster?

That's such a shit parallel example that it borders on dishonest.

There are hundreds of incredibly strong scientific priors that would have to be disproven for the moon to contribute to the solution.

If a model was trained on this data, even if it was trained using methods that lead you to believe it unlikely to have learned details about the proof (e.g., maybe it was only used to train some kind of reward model, which played a minor role in the overall training and would thus be very unlikely to transfer details of a proof), you wouldn't have to disprove large swathes of known science to be wrong.

What about ripping off the prompts?

It is, perhaps worth considering that the reputational community might not care about the difficulty for the AI builder to verify pedigree.

If OpenAI's answer to this problem is "We can't know," then the rational conclusion may very well be "If I seek to have my reputation attached to the discovery of the solution, it is not sane to use the AI as an assistive tool, lest it scoop me on my own work using my own work. After all, they don't know it doesn't do that..."

If the model has access to the "anonymized" data from chats, and the model is capable of building its own context from data that it can search through, including this data. Then it looks pretty damning. An independent review of the data traces from CoT and tool use involved in producing the result should make it clear one way or the other. Seems like discovery in a civil lawsuit could be very productive.

> As a parallel example, can we prove the phase of the moon had no impact on the NS solution? No, not without a bunch experiments run at different phases of the moon.

The _gall_ to say something like this. Do you perhaps think we are all stupid?? This very blogpost claims not to know if their work was used as input for this model. I don't even understand how that is possible, surely you can know if something is part of the training data, even if you are in the dark about what impact it actually made, qualitatively. The moon....

> Knowing most of the recipes we use, there's really no reason to think such contamination happened.

Yeah sorry but I don't trust you. I don't trust people or companies that have shown themselves to be dishonest before. Especially when the previous paragraph is comparing plagiarism and training data contamination with, _the phases of the moon_.

Might even be you're actually telling the truth, but the boy that cried wolf and all that.

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As an aside, I would bet very good money at how most (all?) these companies are flouting their ZDR.

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Yeah, I'm sure it's completely automated.

But that doesn't preclude being able to index and track what the sources of data are. For your data sets, I would hope you are including source information for where the data came frome. And at OpenAI's scale, I would presume they are doing some amount of rolling hashing or similar to weed out duplication, training on too much duplicate data can cause problems.

AllenAI have at least attempted to add some amount of traceability to their models with OLMoTrace (https://arxiv.org/abs/2504.07096), by letting you find n-gram matches from the outputs in their training data. It's not the most useful, there's a reason that LLMs use full fledged attention mechanisms and not just n-grams, a lot of times the n-gram matches it finds aren't all that related to the given output, it might be better to supplement this index with a vector search or other ways of keeping track of what training data would have most influenced particular parts of the output.

But anyhow, this is something that is an important question, and the big labs should be working on to make their products more trustworthy. Instead, they are hiding information about how they train, hiding their reasoning traces, and just producing output with no information on what might have influenced the training.

The question is not "does OpenAI know", it's "can OpenAI attest that the usage of their products for confidential data is not going to cause that sensitive data to become known to their models". And right now the answer I'm reading is that OpenAI can't attest to that.

Aye, but do they train on user data in these circumstances or not? If they do, then almost certainly the model was influenced by the input of the allegedly plagiarised material.

> could trace whether that data was used

The point of de-identifying data is to ensure you can't trace who it came from. It would be a serious privacy violation if they could.

There are two different things:

- was item X in the training data

- did the inclusion of X in the training data lead to Y

I understand why the second is hard, but why is the first one hard?

Whether they opted out would help assess the degree of wrongdoing, but regardless, using their own data to try to scoop them is unethical.

Also highlights that it ought to be opt-in

I believe jrflo was saying that OpenAI watches the chats of everyone from Anthropic because watching what Anthropic employees type into their personal ChatGPT accounts is a critical source of intelligence on is happening inside of Anthropic.

I would be surprised if OpenAI isn't doing that. OpenAI will take any advantage they can get. If an employee at their primary adversary is typing useful intelligence into OpenAIs website, a website that does not promise privacy from OpenAI, the only reason they wouldn't weaponize that information against Anthropic is ethics or fair play.

I don't think he was defecting or leaking directly, just that it's entirely possible that this information got to OpenAI as a rumor rather than them directly spying on mathematicians chat logs.

I suspect this controversy will blow the case for ZDR wide open. Whatever the facts (possibly unknowable), it's going to become a very public lesson that data sovereignty was never about "having nothing to hide".

If this is what they do to academic pure mathematicians, where the stakes are so low (financially)—just imagine the sort of front-running that could be happening in other places.

Hahaha, how exactly is an individual user supposed to get a ZDR agreement?