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PaperclipPerfector  1mo ago (text post)   33494 thread views

Culture War Roundup for the week of March 31, 2025

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Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad

Abstract: Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with the leading model, o3-mini, achieving scores comparable to top human competitors. However, these benchmarks evaluate models solely based on final numerical answers, neglecting rigorous reasoning and proof generation which are essential for real-world mathematical tasks. To address this, we introduce the first comprehensive evaluation of full-solution reasoning for challenging mathematical problems. Using expert human annotators, we evaluated several state-of-the-art reasoning models on the six problems from the 2025 USAMO within hours of their release. Our results reveal that all tested models struggled significantly, achieving less than 5% on average. Through detailed analysis of reasoning traces, we identify the most common failure modes and find several unwanted artifacts arising from the optimization strategies employed during model training. Overall, our results suggest that current LLMs are inadequate for rigorous mathematical reasoning tasks, highlighting the need for substantial improvements in reasoning and proof generation capabilities.

Background: The 'official' American competitive high school math circuit has several levels, progressing from AMC 10/12 (25 question, multiple choice, 75 minutes total) to AIME (15 questions, 3 hours, answers are in the form of positive 3 digit integers) to USAMO (2 days, 6 proof-based questions total, 3 questions with 4.5 hours per day), with difficulty increasing commensurate with the decrease in # of questions. While most AIME questions can be ground out using a standard set of high school/introductory college level math knowledge and tricks, the USAMO requires more depth of understanding and specialized techniques. For example, problem 1 (theoretically, the easiest) is as follows:

Let k and d be positive integers. Prove that there exists a positive integer N such that for every odd integer n > N , the digits in the base-2n representation of n^k are all greater than d.

This problem can be solved fairly simply using induction on k.

I've also noticed this when plugging grad-level QM questions into Gemini/ChatGPT. No matter how many times I tell it that it's wrong, it will repeatedly apologize and make the same mistake, usually copied from some online textbook or solution set without being able to adapt the previous solution to the new context.

It's not a proof, and in order to be "a bluff" there would've had to have been an intent to decieve.

Last week @2rafa asked "When will the AI penny drop? and the answer i would have liked to give at at the time was "when the footprint of a decent tokenizer gets small enough to run organically" or "when the equipment available to the hobbiest and semi-pro comunity catches up with the requirements of a decent tokenizer".

Until that happens specific questions will be doomed to be answered unspecifically.

The broad consensus (which i agree with) within the robotics and machine learning communities is that the existing generative models are ill-suited for any task requiring autonomy or rigor and that this is not a problem that can be fixed by throwing more FLOPs at it.

Why are you talking about the footprint of a tokenizer? Tokenization is cheap compared to actually evaluating the LLM.

Tokenization is cheap compared to actually evaluating the LLM.

Processing tokens is cheap. Generating tokens is expensive.

Evaluating a model can range from relatively cheap to cripplingly expensive depending on the metrics chosen and level of rigor required.

I agree with everything you wrote in this reply. But your reply seems to have nothing to do with your message I originally replied to. Why were you mentioning the cost of tokenization?

Because the collection and tokenization of reference material is currently a significant bottleneck. The democratization of it, or ability to do so organically would make a number of different approaches substantially more feasible. It also introduces the posibility of a Jobs or Zuckerberg type bootstrapping an AI in thier garage.

Is this a bit? Yes collecting a dataset is tons of work, but tokenizing it is trivial.

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