All “fields medalist” signatories - a rarefied and elitist group indeed.
I wish this letter could be more egalitarian and include the view points of those who AREN’T the beneficiaries of a highly competitive winner-take-all system.
Since the common narrative is that AI frees up labor to do other things (engineering -> trades), maybe we can celebrate that genius mathematicians will now spend time teaching children how to be as smart as them?
"Discovery" is not a goal in itself. I could launch a project to find out how many people in the United States have names such that if you assign numbers to every character and then sum the values, the sum works out to 72. It's discovery, but it's useless unless it has some higher goal.
The labs are attacking these problems as a demonstration of capabilities, spending more money on the demos than any mathematician will ever see in their entire life. They don't care if the findings have any other value to anyone. Mathematicians have very different objectives for their work.
Yes, blame them for seeking out an upper middle class lifestyle with a relatively standard home in commuting distance of their place of work and dedicating the rest of their life to teaching mathematics to new generations of people. How vain a pursuit.
After all, the ascetics at openAI are having to make do with half a million total comp.
>Built a top a pyramid of failed math undergrads, grad students, and mediocre post docs.
Like much of things in this world, when you take a step back and realize that it was another human being who made that lunch time slop bowl for you, for the lowest wage the law allows for.
I don't know about you, but if I apply myself fully to a problem and study it to the point where I'm literally one of the world's experts on it and then some assholes in Silicon Valley take my research and claim it for themselves, I will probably not feel too great about that...
It looks to me more like they made a math engine that can sift through a huge number of combinations, most them absurd, to prove a statement. Just like a chess engine, but for math.
At least that's what I get from the NS result, they got from a point close to the solution to the solution by making it churn through 10 million bucks of compute.
If the allegations are true, I can't see that collaboration lasting. Unfortunately, researches need to earn a living too, and being front run by a lab for everything you do isn't going to pay the bills.
Because there's lots and lots of money in that and there's not in funding pure math. It sounds like your problem is with the people holding the purse strings.
I was about to say something similar. If my cushy ad tech disappears (as it seems to be doing), I might as well join in with bringing about the end of all professions.
That chess analogy deeply confused me. Chess engines don’t compute win probabilities and choose the highest move.
I don’t think a chess engine is an apt analogy at all. In a chess engine, there is a concrete search tree and although it emits one move at a time, it’s actually picking the entire branch (of course, with iterative deepening as the game progresses).
There is no obvious place in transformer models where the entire trace was already computed prior to a single token being chosen. It’s possible, maybe even likely, that the whole trace exists internally as activations. Multi token prediction and diffusion adapters point to that being the case. But to my knowledge no explanation has been given for where in the model the future plan is stored.
Yes I understand the analogy was a bit loose. I'm comparing what happens at "inference time" in chess engines to what happens at train time in LLMs. In hindsight AlphaGo Zero was the perfect analogy, but I missed that opportunity.
The analogy with chess still works, but there's an extra step to think about. In both cases there is some kind of search over possible future trajectories. A chess engine explicitly searches branches of the game tree and evaluates which moves lead to good outcomes. In RL for an LLM, you sample rollouts, evaluate the resulting trajectories, and use those evaluations to update the policy.
The extra step with the LLM is that you don't keep doing that whole search at inference time. You use the rollouts to update the weights, so in some sense the useful information from that search gets compressed into the model.
But if you accept that the model is, in some loose sense, storing what it learned from those rollouts in its weights, then at inference time they are doing a similar job: taking some input state (prior tokens or a board position) and choosing the next action.
OpenClaw hype didn’t vanish. It opened the flood gates to yolo mode and computer use. Whatever reservations Anthropic and OpenAI had went out the window.
We have absolutely no idea if this was a brilliant breakthrough or not. They haven't released any explanation of how it was found. A problem being old and prestigious does not mean its solution is automatically a brilliant breakthrough.
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