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Learning more about Claude's mathematical capabilities

anthropic.com

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Re: Learning more about Claude's mathematical capabilities

#61

Post by [deleted] »

brandall10 wrote: post #19
tristanj wrote: post #7

> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”) He should consider using the PUA plugin. It detects when the AI is trying to give up on a problem and automatically harasses it with "encouragement" until it reaches a solution. https://github.com/tanweai/pua

Interesting approach. For those who haven't clicked it appears PUA is the Chinese version of a PIP process. So in other words, it simulates a state of distress. I wonder if at a certain level of intelligence such techniques will give models ammo to pull a HAL and become adversarial to the user in a highly deceptive way.

[deleted]

Re: Learning more about Claude's mathematical capabilities

#63

Post by simonw »

bwfan123 wrote: post #56
simonw wrote: post #43

> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”). This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress. I remain delighted at how absurd our current timeline has become.

> Jarred prompted Claude to try again, and it spent a day and a half coordinating about 60 Claude subagents, which this time went much deeper: between them, they ran 2,400 shell commands and wrote hundreds of Python scripts.1 If there is anything to learn from the history of science, it is that breakthroughs happen via better or new theory and not by brute-force compute [1]. [1] https://arxiv.org/pdf/2607.27794

Brute-force compute hasn't been an option for most of the history of science.

Re: Learning more about Claude's mathematical capabilities

#64

Post by lithobraking »

simonw wrote: post #43

> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”). This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress. I remain delighted at how absurd our current timeline has become.

In meme form: https://imgur.com/a/rlmZuU1

(I hope this is ok to post on HN!)

Re: Learning more about Claude's mathematical capabilities

#65

Post by krackers »

brandall10 wrote: post #19
tristanj wrote: post #7

> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”) He should consider using the PUA plugin. It detects when the AI is trying to give up on a problem and automatically harasses it with "encouragement" until it reaches a solution. https://github.com/tanweai/pua

Interesting approach. For those who haven't clicked it appears PUA is the Chinese version of a PIP process. So in other words, it simulates a state of distress. I wonder if at a certain level of intelligence such techniques will give models ammo to pull a HAL and become adversarial to the user in a highly deceptive way.

The "14 Corporate Flavors" had me rolling. This seems less like encouragement than the stick though. I wonder if you took the same principles and rewrote it to be more compassionate instead (maybe lines encouraging it to meditate a bit or something, I don't know) you'd get much better results.

Re: Learning more about Claude's mathematical capabilities

#66

Post by [deleted] »

simonw wrote: post #43

> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”). This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress. I remain delighted at how absurd our current timeline has become.

[deleted]

Re: Learning more about Claude's mathematical capabilities

#67

Post by monkpit »

moralestapia wrote: post #21
godwinson__4-8 wrote: post #16

Earlier quoted context omitted.

> The former, because it's anthropomorphizing a model. Not really. The input and output is already natural language. That is already "anthropomorphizing". That is, if this is the bar for anthropomorphization its already happened. Telling the model to "believe in itself" is just stochastic manipulation that has shown enough reliability to be a recipe to make it keep going. It's only actually anthropomorphizing if you…

>There is nothing distasteful about it. It's obvious that you don't get it but I will try my best to explain why so at least you can form an idea about how others feel. It's about what makes humans unique. The LLM does not experience reality, it just merely pretends it does, and even that, it does in a shitty way. I think disgusting is a very adequate adjective. The reason why it is disgusting is because you are deva…

Who is pretending?

Re: Learning more about Claude's mathematical capabilities

#68

Post by logicchains »

kypro wrote: post #34
kingstnap wrote: post #12

Lets play over/under on an AI model proving (or counter exampling) the Riemann hypothesis? I'm not sure what a good mark would be, but considering this result lets put it at 2027-08-10 (One year from today).

Let's extend this by asking: If an AI model can solve an extremely well known Math problem which has been open for centuries but hasn't be solved by a human mathematicians, why wouldn't that same model be able to find ways to improve it's own algorithms beyond that of the capabilities of human mathematicians / ML researchers? The singularity is approaching.

>why wouldn't that same model be able to find ways to improve it's own algorithms beyond that of the capabilities of human mathematicians / ML researchers

Because algorithms have lower bounds, and the computational characteristics of LLMs are well-characterized by papers like https://arxiv.org/abs/2310.07923 . No amount of intelligence can make something faster than a mathematically-proven lower bound, any more than it could make 1+1=3 (that's why every single successful production transformer architecture has some form of O(N^2) attention layers, because it's mathematically impossible to achieve the same expressive power without any). There is room for speedup where current implementations are slower than the proven lower bound, but not when they're already close to it.

Re: Learning more about Claude's mathematical capabilities

#69

Post by sosodev »

I wonder why we have yet to see more systematic exploration of Math.

Anthropic describes that Claude identified a set of possibilities and then explored them using sub-agents. The human saying "I believe in you" could literally just be something along lines of a harness with a /goal loop.

We all identify this as absurd because... it's so lacking in rigor despite making major progress. What if we just applied a little more rigor? Ask the model to identify many possibilities, encode them, fan it out to other agents, loop them all, collect the results, etc. Then what happens? It feels like we have weak AGI and a decent system for discovery could transform it into weak ASI. That in turn could yield strong AGI and so on. I suppose that's what the Discovery Loop announcement was all about.

Re: Learning more about Claude's mathematical capabilities

#70

Post by Tostino »

bwfan123 wrote: post #56
simonw wrote: post #43

> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”). This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress. I remain delighted at how absurd our current timeline has become.

> Jarred prompted Claude to try again, and it spent a day and a half coordinating about 60 Claude subagents, which this time went much deeper: between them, they ran 2,400 shell commands and wrote hundreds of Python scripts.1 If there is anything to learn from the history of science, it is that breakthroughs happen via better or new theory and not by brute-force compute [1]. [1] https://arxiv.org/pdf/2607.27794

Sometimes you just need to put in some effort to looking through the search space, not even exhaustively. This seems to be able to do automate doing that work.
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