As a mathematican I'm not outraged in the slightest. If anything, I'm outraged that they need to pay anything to get that data. In an ideal world every published piece of mathematics would be available free for everyone to learn from it -- human or machine.
And calling it theft is utterly ridiculous! From a fundamental rights standpoint or some kind of background intuition about property it is intellectual property protections that are themselves violations of people's property interests (certainly the Lockean conception). Those are laws which prevent me from using my property in certain ways because they mimic what you did with yourself.
And yes, IP makes sense insofar as it is necessary to incentivize innovation. But beyond that it is theft from our common cultural heritage. And there is no plausible argument that preventing people from training on mathematics papers is a necessary incentive for it to be produced.
Ultimately, Rawls has a very good point that every inequality in wealth is unfair and are only justified by the degree to which they incentivize innovation. And trying to demand that companies get permission to train AI on academic papers of all things is -- like the paid gatekeeping that for profit scientific publishers put up in the first place -- definitely isn't necessary to incentivize innovation.
Besides, it really shouldn't matter that it's a machine learning from your work or a person. Especially for Mathematicians who are paid by governments and universities (largely gov supported) to release work for the benefit of society at large.
I agree with you to a considerable degree, but I don't think you go far enough. Why are Google's search algorithms not in the public domain? Why, indeed, are Google and the rest of the Magnificent Seven not regulated public utilities?
Though I think a good incremental change would also be to require that anytime a company goes bankrupt and gets dissolved all IP that is below some threshold value and all data sets that aren't considered sensitive/personal should be placed into the public domain in an easily accessible way.
Ultimately it's about what the incentivizes are and how it affects them. One big reason for patents is exactly to encourage publication and we've gotten some important information google would otherwise have kept secret that way. But good search requires an incentive to keep improving it -- otherwise it gets swamped with SEO bullshit so I don't think it would be wise to force them to give up their secret details especially given that search is relatively close to a perfectly competitive market (little cost for users to switch to a better option easy comparison of quality).
Having said that I think we've let patent and particular copyright protection grow too broad. One can debate about exactly where that line should be but the really obvious case is that extensions -- either temporal or in terms of the expected swath of the sort of uses which you receive compensation from -- is obviously unjustified. So I see trying to protect currently existing content from being used to train an LLM as analagous to the ridiculous Disney pushed retrospective extension of copyright.
Maybe one can make an argument that in some cases going forward it's necessary to give people some kind of compensation if an LLM trains on their work to incentivize creation but that case needs to be made first and since no one was counting on protection from use as training data when they made existing content no reason to extend it into the past. And in the case of academic research copyright seems totally unnecessary in all cases for incentivizing creation.
--
If -- as seems plausible -- AI companies become truly gigantic and generate huge profits then we should tax them and use the money for society at large..
This is not the time for me to talk about incentives and the organization of society. What I perceive is that the system of incentives operating in Silicon Valley has allowed a stratum of despicable people to accumulate extraordinary wealth and power and to use this wealth and power to perform reprehensible acts. Moreover, these people and their industry are central to the developments discussed in this post.
"My challenge to AlphaGeometry — to rediscover the Euler characteristic — still stands after six months, time enough for hundreds of startups to arise and collapse; so I see no need to add a new challenge in view of the latest information."
Whether "neural networks" (aka "perceptrons") are (in principle) capable of handling "Euler characteristic" was addressed in "Perceptrons" by Minsky and Papert (1969):
This is interesting — I hadn't been aware of that, and it certainly shows good taste on the part of Minsky and Papert. But it's not relevant to the challenge, which I repeat here in full:
Forget the pre-installed table of standard constructions in Euclidean geometry. Instead, give AlphaGeometry 2.0 the list of axioms and let it generate its own constructions for as long as it takes. Then wait to see whether it rediscovers the Euler characteristic.
So, starting with nothing but the axioms of Euclidean geometry, to recover the Euler characteristic. Not to compute it using a formula, nor to find a linear relation satisfied by vertices, edges, faces, and holes (whatever AlphaGeometry may mean by that). To discover it just by the sheer exercise of artificial curiosity.
Would Euler discover the characteristic driven purely by un-artificial curiosity, absent the need/motivation to cross the famed bridges in Kaliningrad? Lacatos's answer might be as tinged by their subjective experience as our own.
Euler's formula, the subject of Lakatos's book, is the case g=0 of the Euler characteristic. Finding Euler's formula only for simply connected polyhedra would miss the point of the challenge. Nevertheless, I think the challenge is quite modest; it would be natural to ask the AI to invent derived categories, but I'm not going that far.
Rawls's splendid egalitarian max-min rule (enunciated in "A Theory of Justice" and beyond) has a tantalizing spectral/variational interpretation.
As a mathematican I'm not outraged in the slightest. If anything, I'm outraged that they need to pay anything to get that data. In an ideal world every published piece of mathematics would be available free for everyone to learn from it -- human or machine.
And calling it theft is utterly ridiculous! From a fundamental rights standpoint or some kind of background intuition about property it is intellectual property protections that are themselves violations of people's property interests (certainly the Lockean conception). Those are laws which prevent me from using my property in certain ways because they mimic what you did with yourself.
And yes, IP makes sense insofar as it is necessary to incentivize innovation. But beyond that it is theft from our common cultural heritage. And there is no plausible argument that preventing people from training on mathematics papers is a necessary incentive for it to be produced.
Ultimately, Rawls has a very good point that every inequality in wealth is unfair and are only justified by the degree to which they incentivize innovation. And trying to demand that companies get permission to train AI on academic papers of all things is -- like the paid gatekeeping that for profit scientific publishers put up in the first place -- definitely isn't necessary to incentivize innovation.
Besides, it really shouldn't matter that it's a machine learning from your work or a person. Especially for Mathematicians who are paid by governments and universities (largely gov supported) to release work for the benefit of society at large.
I agree with you to a considerable degree, but I don't think you go far enough. Why are Google's search algorithms not in the public domain? Why, indeed, are Google and the rest of the Magnificent Seven not regulated public utilities?
Though I think a good incremental change would also be to require that anytime a company goes bankrupt and gets dissolved all IP that is below some threshold value and all data sets that aren't considered sensitive/personal should be placed into the public domain in an easily accessible way.
Ultimately it's about what the incentivizes are and how it affects them. One big reason for patents is exactly to encourage publication and we've gotten some important information google would otherwise have kept secret that way. But good search requires an incentive to keep improving it -- otherwise it gets swamped with SEO bullshit so I don't think it would be wise to force them to give up their secret details especially given that search is relatively close to a perfectly competitive market (little cost for users to switch to a better option easy comparison of quality).
Having said that I think we've let patent and particular copyright protection grow too broad. One can debate about exactly where that line should be but the really obvious case is that extensions -- either temporal or in terms of the expected swath of the sort of uses which you receive compensation from -- is obviously unjustified. So I see trying to protect currently existing content from being used to train an LLM as analagous to the ridiculous Disney pushed retrospective extension of copyright.
Maybe one can make an argument that in some cases going forward it's necessary to give people some kind of compensation if an LLM trains on their work to incentivize creation but that case needs to be made first and since no one was counting on protection from use as training data when they made existing content no reason to extend it into the past. And in the case of academic research copyright seems totally unnecessary in all cases for incentivizing creation.
--
If -- as seems plausible -- AI companies become truly gigantic and generate huge profits then we should tax them and use the money for society at large..
This is not the time for me to talk about incentives and the organization of society. What I perceive is that the system of incentives operating in Silicon Valley has allowed a stratum of despicable people to accumulate extraordinary wealth and power and to use this wealth and power to perform reprehensible acts. Moreover, these people and their industry are central to the developments discussed in this post.
By the way, for some reason the photo that belonged at the top of this post was missing when it was published; it has now been restored.
"My challenge to AlphaGeometry — to rediscover the Euler characteristic — still stands after six months, time enough for hundreds of startups to arise and collapse; so I see no need to add a new challenge in view of the latest information."
Whether "neural networks" (aka "perceptrons") are (in principle) capable of handling "Euler characteristic" was addressed in "Perceptrons" by Minsky and Papert (1969):
https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society/volume-78/issue-1/Review--Marvin-Minsky-and-Seymour-Papert-Perceptrons-An-Introduction/bams/1183533389.full
This is interesting — I hadn't been aware of that, and it certainly shows good taste on the part of Minsky and Papert. But it's not relevant to the challenge, which I repeat here in full:
Forget the pre-installed table of standard constructions in Euclidean geometry. Instead, give AlphaGeometry 2.0 the list of axioms and let it generate its own constructions for as long as it takes. Then wait to see whether it rediscovers the Euler characteristic.
So, starting with nothing but the axioms of Euclidean geometry, to recover the Euler characteristic. Not to compute it using a formula, nor to find a linear relation satisfied by vertices, edges, faces, and holes (whatever AlphaGeometry may mean by that). To discover it just by the sheer exercise of artificial curiosity.
Would Euler discover the characteristic driven purely by un-artificial curiosity, absent the need/motivation to cross the famed bridges in Kaliningrad? Lacatos's answer might be as tinged by their subjective experience as our own.
Euler's formula, the subject of Lakatos's book, is the case g=0 of the Euler characteristic. Finding Euler's formula only for simply connected polyhedra would miss the point of the challenge. Nevertheless, I think the challenge is quite modest; it would be natural to ask the AI to invent derived categories, but I'm not going that far.
Speaking of the recent news, are you planning to shed light on the interactions between "trillion dollar companies"
https://www.nytimes.com/2024/08/29/technology/telegram-encryption-pavel-durov.html
and Arakelov geometry
https://arxiv.org/abs/0704.2030