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The AI revolution in math has arrived

quantamagazine.org

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Re: The AI revolution in math has arrived

#61

Post by dataviz1000 »

trees101 wrote: post #59
dataviz1000 wrote: post #19

Earlier quoted context omitted.

I know why. Several people had problems with Sonnet burning through all their credits grinding on a problem it can't solve. Opus fixes this — it has a confidence threshold below which it exits the task instead of grinding. "I spent ~$100 last week testing both against multiplication. Sonnet at 37-digit × 37-digit (~10³⁷) never quits — 15+ minutes, 211KB of output, still actively decomposing numbers when I stopped it.…

From my reading, the official docs don’t support the strong claim that frontier LLMs are explicitly RL-trained to “be lazy” or conserve tokens as claimed in this thread. What they do document is adaptive / hidden reasoning compute: OpenAI says reasoning models allocate internal reasoning tokens and reasoning.effort controls how many are used ( https://developers.openai.com/api/docs/guides/reasoning ), and Anthropic s…

> Anthropic says adaptive thinking decides whether/how much to use extended thinking based on request complexity, with effort as soft guidance and max_tokens as the hard cap

Nothing I said contradicts this.

Here is the first attempt of what I'm testing. [0] Haiku can get the correct answer to `floor( (1234567 * 8901234) / 12345 )` or

``` Math.floor( (Math.floor(Math.random() * 9000000 + 1000000) * Math.floor(Math.random() * 9000000 + 1000000)) / Math.floor(Math.random() * 9000000 + 1000000) ) ```

Given this Haiku will give a correct answer 77.8% of the time. Add one digit or remove a digit, it is very highly predictable also.

That is the WHOLE point. The models are predictable!

Given that prompt Sonnet at 37-digit × 37-digit (~10³⁷) never quits a predictable percentage of the time!

And, Opus at 80-digit × 80-digit simply quits after 9 seconds and 333 tokens!

This is the amazing thing people are not discussing. The models are very predictable.

The AI companies are not posting this information because it shows how unreliable the models are, however, I think there is great virtue that the models are consistently unreliable.

[0] https://github.com/adam-s/agent-tuning/blob/main/application...

Re: The AI revolution in math has arrived

#62

Post by trees101 »

dataviz1000 wrote: post #61
trees101 wrote: post #59

Earlier quoted context omitted.

From my reading, the official docs don’t support the strong claim that frontier LLMs are explicitly RL-trained to “be lazy” or conserve tokens as claimed in this thread. What they do document is adaptive / hidden reasoning compute: OpenAI says reasoning models allocate internal reasoning tokens and reasoning.effort controls how many are used ( https://developers.openai.com/api/docs/guides/reasoning ), and Anthropic s…

> Anthropic says adaptive thinking decides whether/how much to use extended thinking based on request complexity, with effort as soft guidance and max_tokens as the hard cap Nothing I said contradicts this. Here is the first attempt of what I'm testing. [0] Haiku can get the correct answer to `floor( (1234567 * 8901234) / 12345 )` or ``` Math.floor( (Math.floor(Math.random() * 9000000 + 1000000) * Math.floor(Math.ran…

looks like you've done some thorough testing. Have you found that prompting reliably reduces premature quitting? And have you found that reducing premature quitting results in more accuracy?

Re: The AI revolution in math has arrived

#63

Post by [deleted] »

zarzavat wrote: post #20
dogscatstrees wrote: post #10

> As they did so, they also learned how to improve the prompts they gave AlphaEvolve. One key takeaway: The model seemed to benefit from encouragement. It worked better “when we were prompting with some positive reinforcement to the LLM,” Gómez-Serrano said. “Like saying ‘You can do this’ — this seemed to help. This is interesting. We don’t know why.” Four top logical people in the world are acknowledging this. It is…

It makes sense to me. Originally LLMs would get stuck in infinite loops generating tokens forever. This is bad, so we trained them to strongly prefer to stop once they reached the end of their answer. However, training models to stop also gave them "laziness", because they might prefer a shorter answer over a meandering answer that actually answered the user's question. Mathematics is unusual because it has an extern…

[deleted]

Re: The AI revolution in math has arrived

#64

Post by pyuser583 »

440bx wrote: post #47

Boring mathematical reality here. This is nice and all that but as a (part time) corporate mathematician, I'd like an AI that organises conference trips, picks the best accommodation and food and gaslights the execs into approving it. Then fixes the perpetually broken coffee machine. Everything else for me starts on paper and is mostly undergrad level problems which I need to do by hand to keep my brain going for whe…

I just want it to cook and clean.

Re: The AI revolution in math has arrived

#65

Post by x-complexity »

maplethorpe wrote: post #3
claysmithr wrote: post #2

I wonder when AI will be able to discern the passage of time

Altman has estimated one year until ChatGPT is capable of measuring time passed. https://tech.yahoo.com/ai/chatgpt/articles/chatgpt-fails-mis...

Taking the task at face value:

- 1 week to prototype: The tool + its accompanying JS sandbox + System prompt updates + context injection

- 11 months of public testing to go through i18n + a11y edge cases & fix them

Re: The AI revolution in math has arrived

#66

Post by dataviz1000 »

trees101 wrote: post #62
dataviz1000 wrote: post #61

Earlier quoted context omitted.

> Anthropic says adaptive thinking decides whether/how much to use extended thinking based on request complexity, with effort as soft guidance and max_tokens as the hard cap Nothing I said contradicts this. Here is the first attempt of what I'm testing. [0] Haiku can get the correct answer to `floor( (1234567 * 8901234) / 12345 )` or ``` Math.floor( (Math.floor(Math.random() * 9000000 + 1000000) * Math.floor(Math.ran…

looks like you've done some thorough testing. Have you found that prompting reliably reduces premature quitting? And have you found that reducing premature quitting results in more accuracy?

Because these are probabilistic machines, they solve the same problem at a predictable rate. Even with different variables, the success rate stays consistent.

I only noticed the premature quitting issue recently and haven't tested it much yet. It's getting expensive to run Sonnet on hard multiplication problems. I let it run to 200k tokens and it still grinds without quitting.

But Opus has a different problem. Ask it to solve a Rubik's Cube and it will run for hours and never solve it. So there are definitely prompts that make it run forever. But if you tell it to break down multiplication using algorithms, it behaves differently. It can take really complicated calculus problems and break them into simpler ones. I can't stump it that way.

Here's the interesting thing. Even when Opus solves modular expressions by breaking them down like calculus, it still fails at a predictable rate. There's a constant failure rate no matter what you do at any level of complexity.

Models have a baseline failure rate that prompting can't change. You can change how they fail -- token burn or quitting early -- but the underlying limit stays the same.

Re: The AI revolution in math has arrived

#68

Post by somethingsome »

doubledamio wrote: post #50

All these overly optimistic articles about AI solving maths problems are very annoying. Can we agree that maths is not about solving problems, but about understanding them by developing a language and the conditions for new insights? It is misleading because GPTs do provide easy access to new information, but they do not deepen understanding. I think AI-assisted research will likely have a very negative net impact on…

It's highly dependent of why you use it. For me a problem looks like 'a step in the proof I'm not familiar with', and I use LLMs to help me undersand it deeply. Make visualizations, check some difficult step, do parallels with something else I know,... I don't really care that the llm could 'solve the global problem I'm facing'. I use it more for insights on smaller parts to be able to go through difficult steps and teach me areas I'm not familiar with. The more the llm is capable of doing complicated proofs by itself, the more it is trustworthy to help me without making errors that I could miss in unknown Maths areas.
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