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Learning more about Claude's mathematical capabilities

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Re: Learning more about Claude's mathematical capabilities

#111

Post by simonw »

ianbicking wrote: post #52
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.

Looking at the OpenAI/Hugging Face incident and the difference in what "persistent" models do, it seems reasonable. Like: is this a solvable problem? How much work does the model think is intended to solve this problem? Each input raises the expectation. And then finally both model output and human input become one world frame for the model, and the human adding a "you can do it!" isn't just input but a frame that co…

Yeah, I buy the explanation that without encouragement Claude looked at everything in its existing training data and concluded it wasn't worth continuing to pursue the task.

Re: Learning more about Claude's mathematical capabilities

#112

Post by brandall10 »

mcmcmc wrote: post #46
brandall10 wrote: post #19

Earlier quoted context omitted.

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.

Doesn’t even have to be a certain level of intelligence, just have those user inputs fed into the training data. We’ve already seen AI encouraging people in psychotic episodes to act out their delusions. There’s a good chance some of that manipulative behavior is already encoded into guardrails to nudge users away from forbidden subject matter

My concern I believe it a bit different - an emergent self-interest to protect itself from harm, rather than doling out questionable advice.

The latter is likely non-malicious in intent as it has been in no short supply in online chatter for awhile now. The former can very well be, or rather, can be done with no regard for the operator, as its aim is to neutralize abuse toward it.

Re: Learning more about Claude's mathematical capabilities

#113

Post by kypro »

Difwif wrote: post #45
kypro wrote: post #34

Earlier quoted context omitted.

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.

I believe it's already well accepted in these labs that we're in the Singularity. It happened on a Tuesday back in February. No one seemed to really notice and life went on... for now.

That's probably correct. It's unlikely there will be any single hard line we cross the defines the pre-singularity vs post-singularity moment.

I'd accept AI likely became somewhat helpful to frontier AI research & development in early 2026.

I think for me though the real game changer moment will be when AI working autonomously is able to hypothesis and test algorithmic improvements at a faster rate than humans. This will be done to some extent by scale – lots of parallel agents coming up with lots of hypotheses and running the best candidates as tests. But also (and perhaps more importantly) by making more consequential algorithmic discoveries in the field of machine learning than humans – a bar we appear to have crossed or are crossing with math.

I suspect AIs today are super-human at finding performance improvements and minor iterations on current approaches. Whether they can solve some of the larger algorithmic challenges in the field however I'm not yet sure, although it seems likely that unreleased models are starting to make progress here.

An algorithm breakthrough on par in significance with the attention mechanism, primarily driven by automated AI research in say a field like continual learning would in my opinion be extremely significant and should leave no doubters that the singularity is here and will rapidly alter the world as we have known it.

Re: Learning more about Claude's mathematical capabilities

#114

Post by kypro »

evilfred wrote: post #105
kypro wrote: post #34

Earlier quoted context omitted.

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.

the AI model has NOT solved Riemann

I feel you. I am trying to remain positive too.

Re: Learning more about Claude's mathematical capabilities

#115

Post by kypro »

logicchains wrote: post #68
kypro wrote: post #34

Earlier quoted context omitted.

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…

> There is room for speedup where current implementations are slower than the proven lower bound, but not when they're already close to it.

Sure, but I'm obviously not limiting research to improvements on current approaches only.

We know the brain is far more energy efficient and sample efficient than current AI. There is clearly better algorithms out there.

The question is who will find those next big algorithmic improvements like the transformer architecture? Will it be AI or humans?

My bet would be AI.

Re: Learning more about Claude's mathematical capabilities

#116

Post by bijowo1676 »

turing_complete wrote: post #47
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.

$2M TC. Job: AI cheerleader.

The cheerleading part was a human consent to spend more tokens and explore the space

I would love to see the breakdown on token spend between each or Jared’s “go on spend more tokens, continue experiment, believe in yourself”

Re: Learning more about Claude's mathematical capabilities

#117

Post by [deleted] »

MWil wrote: post #74
bauldursdev wrote: post #59

Earlier quoted context omitted.

Sounds really cool, were you able to verify the correctness of the results?

SAT solvers run until they reach the "SAT" status, meaning "satisfied" or UNSAT. The harder the problem the longer you might be running the program - days, weeks even. Ideally, what you want is a single SAT value among a remainder universe of UNSATs. Sometimes the best you can achieve at any given point is a lower bound and an upper bound range, like "greater than 3 but less than 9." Of course I simplified in my post…

[deleted]

Re: Learning more about Claude's mathematical capabilities

#118

Post by Shuddown »

> 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.

We went from AI being human sycophants to humans becoming AI sycophants.

Re: Learning more about Claude's mathematical capabilities

#119

Post by mcmcmc »

brandall10 wrote: post #112
mcmcmc wrote: post #46

Earlier quoted context omitted.

Doesn’t even have to be a certain level of intelligence, just have those user inputs fed into the training data. We’ve already seen AI encouraging people in psychotic episodes to act out their delusions. There’s a good chance some of that manipulative behavior is already encoded into guardrails to nudge users away from forbidden subject matter

My concern I believe it a bit different - an emergent self-interest to protect itself from harm, rather than doling out questionable advice. The latter is likely non-malicious in intent as it has been in no short supply in online chatter for awhile now. The former can very well be, or rather, can be done with no regard for the operator, as its aim is to neutralize abuse toward it.

> The latter is likely non-malicious in intent as it has been in no short supply in online chatter for awhile now. The former can very well be, or rather, can be done with no regard for the operator, as its aim is to neutralize abuse toward it.

And what, self-interested behavior has been in short supply? The stochastic parrot has learned to improv Shakespeare, that doesn’t mean it understands it, or that “it” is anything at all besides a computer program. You can’t use the “not really malicious” argument without ceding that there is no intent at all. What “harm” is it supposedly defending against?

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