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FrontierMath: A benchmark for evaluating advanced mathematical reasoning in AI

epochai.org

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Re: FrontierMath: A benchmark for evaluating advanced mathematical reasoning in AI

#11

Post by sebzim4500 »

agucova wrote: post #2

For some context on why this is important: this benchmark was designed to be extremely challenging for LLMs, with problems requiring several hours or days of work by expert mathematicians. Currently, LLMs solve 2% of problems in the set (which is kept private to prevent contamination). They even provide a quote from Terence Tao, which helped create the benchmark (alongside other Field medalists and IMO question write…

>Surprisingly, prediction markets [1] are putting 62% on AI achieving > 85% performance on the benchmark before 2028.

Or they know the ancient technique of training on the test set. I know most of the questions are kept secret, but they are being regularly sent over the API to every LLM provider.

Re: FrontierMath: A benchmark for evaluating advanced mathematical reasoning in AI

#12

Post by light_hue_1 »

agucova wrote: post #2

For some context on why this is important: this benchmark was designed to be extremely challenging for LLMs, with problems requiring several hours or days of work by expert mathematicians. Currently, LLMs solve 2% of problems in the set (which is kept private to prevent contamination). They even provide a quote from Terence Tao, which helped create the benchmark (alongside other Field medalists and IMO question write…

If I was going to bet, I would bet yes, they will reach above 85% performance.

The problem with all benchmarks, one that we just don't how to solve, is leakage. Systematically, LLMs are much better at benchmarks created before they were trained than after. There are countless papers that show significant leakage between training and test sets for models.

This is in part why so many LLMs are so strong according to benchmarks, particularly older popular benchmarks, but then prove to be so weak in practice when you try them out.

In addition to leakage, people also over-tune their LLMs to specific datasets. They also go out and collect more data that looks like the dataset they want to perform well on.

There's a lot of behind the scenes talk about unethical teams that collect data which doesn't technically overlap test sets, but is extremely close. You can detect this if you look at the pattern of errors these models make. But no one wants to go out and accuse specific teams, at least not for now.

Re: FrontierMath: A benchmark for evaluating advanced mathematical reasoning in AI

#13

Post by dr_dshiv »

light_hue_1 wrote: post #9
firebaze wrote: post #6

Earlier quoted context omitted.

I'm not sure if it is feasible to provide all relevant sources to someone who doesn't follow a field. It is quite common knowledge that LLMs in their current form have no ability to recurse directly over a prompt, which inherently limits their reasoning ability.

This is just totally false. That's exactly what countless techniques related to chain of thought do.

It’s sometimes like, are these critics using the tools? It’s a strange schism at the moment.

Re: FrontierMath: A benchmark for evaluating advanced mathematical reasoning in AI

#14

Post by nerdponx »

light_hue_1 wrote: post #12
agucova wrote: post #2

For some context on why this is important: this benchmark was designed to be extremely challenging for LLMs, with problems requiring several hours or days of work by expert mathematicians. Currently, LLMs solve 2% of problems in the set (which is kept private to prevent contamination). They even provide a quote from Terence Tao, which helped create the benchmark (alongside other Field medalists and IMO question write…

If I was going to bet, I would bet yes, they will reach above 85% performance. The problem with all benchmarks, one that we just don't how to solve, is leakage. Systematically, LLMs are much better at benchmarks created before they were trained than after. There are countless papers that show significant leakage between training and test sets for models. This is in part why so many LLMs are so strong according to ben…

Could you run the benchmark by bootstrapping (average of repeated subsampling), instead of a straight-across performance score, and regain some leakage resistance that way? As well as a better simulation of "out of sample" data, at least for a little while.

Re: FrontierMath: A benchmark for evaluating advanced mathematical reasoning in AI

#15

Post by llm_trw »

light_hue_1 wrote: post #9
firebaze wrote: post #6

Earlier quoted context omitted.

I'm not sure if it is feasible to provide all relevant sources to someone who doesn't follow a field. It is quite common knowledge that LLMs in their current form have no ability to recurse directly over a prompt, which inherently limits their reasoning ability.

This is just totally false. That's exactly what countless techniques related to chain of thought do.

The closest explanation to how chain of through works is suppressing the probability of a termination token.

People have found that even letting llms generate gibberish tokens produces better final outputs. Which isn't a surprise when you realise that the only way a llm can do computation is by outputting tokens.

Re: FrontierMath: A benchmark for evaluating advanced mathematical reasoning in AI

#16

Post by nerdponx »

benchmarkist wrote: post #8

Very cool. It'll be nice to have a benchmark that can be used to validate abstract reasoning capabilities because the hype is really starting to get out of hand.

I wonder if the best benchmark is a Prolog program that generates tests of logical reasoning. You could have a functionally infinite stream of test cases!

Re: FrontierMath: A benchmark for evaluating advanced mathematical reasoning in AI

#17

Post by llm_trw »

dr_dshiv wrote: post #13
light_hue_1 wrote: post #9

Earlier quoted context omitted.

This is just totally false. That's exactly what countless techniques related to chain of thought do.

It’s sometimes like, are these critics using the tools? It’s a strange schism at the moment.

It's my job to build these tools. I'm well aware of their strengths and shortcomings.

Re: FrontierMath: A benchmark for evaluating advanced mathematical reasoning in AI

#18

Post by mkl »

benchmarkist wrote: post #7
llm_trw wrote: post #3

Earlier quoted context omitted.

These benchmarks are entirely pointless. The people making them are specialists attempting to apply their skills to areas unrelated to LLM performance, a bit like a sprinter making a training regimen for a fighter jet. What matters is the data structures that underlie the problem space - graph traversal. First, finding a path between two nodes; second, identifying the most efficient path; and third, deriving implicit…

It will be a useful benchmark to validate claims by people like Sam Altman about having achieved AGI.

Most humans can't solve these problems, so it's certainly possible to imagine a legitimate AGI that can't either.

Re: FrontierMath: A benchmark for evaluating advanced mathematical reasoning in AI

#19

Post by llm_trw »

dr_dshiv wrote: post #4
llm_trw wrote: post #3

Earlier quoted context omitted.

These benchmarks are entirely pointless. The people making them are specialists attempting to apply their skills to areas unrelated to LLM performance, a bit like a sprinter making a training regimen for a fighter jet. What matters is the data structures that underlie the problem space - graph traversal. First, finding a path between two nodes; second, identifying the most efficient path; and third, deriving implicit…

> they’re merely regurgitating memorized information Source?

If a model can't inately reason over 5 steps in a simple task but produces a flawless 500 step proof you either have divine intervention or memorisation.

Re: FrontierMath: A benchmark for evaluating advanced mathematical reasoning in AI

#20

Post by westurner »

ScholarlyArticle: "FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI" (2024) https://arxiv.org/abs/2411.04872 .. https://epochai.org/frontiermath/the-benchmark :

> [Not even 2%]

> Abstract: We introduce FrontierMath, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. The questions cover most major branches of modern mathematics -- from computationally intensive problems in number theory and real analysis to abstract questions in algebraic geometry and category theory. Solving a typical problem requires multiple hours of effort from a researcher in the relevant branch of mathematics, and for the upper end questions, multiple days. FrontierMath uses new, unpublished problems and automated verification to reliably evaluate models while minimizing risk of data contamination. Current state-of-the-art AI models solve under 2% of problems, revealing a vast gap between AI capabilities and the prowess of the mathematical community. As AI systems advance toward expert-level mathematical abilities, FrontierMath offers a rigorous testbed that quantifies their progress.

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