Summary of Mathgap: Out-of-distribution Evaluation on Problems with Arbitrarily Complex Proofs, by Andreas Opedal et al.
MathGAP: Out-of-Distribution Evaluation on Problems with Arbitrarily Complex Proofs
by Andreas Opedal, Haruki Shirakami, Bernhard Schölkopf, Abulhair Saparov, Mrinmaya Sachan
First submitted to arxiv on: 17 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Computation and Language (cs.CL)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper investigates how well large language models (LLMs) generalize to more complex arithmetic word problems, which have not been thoroughly studied. The existing evaluation data has largely been seen by the most capable models during training, and current benchmarks do not capture the complexity of problem proofs. To overcome these limitations, the authors present a data-generation framework called MathGAP, which generates problem statements and chain-of-thought reasoning traces according to specifications about their arithmetic proof structure. This allows for systematic studies on easy-to-hard generalization with respect to complexity of proof trees. The results show that LLMs significantly decrease in performance as proofs get deeper and wider, with a more pronounced effect in complex, nonlinear proof structures. However, the models remain capable of solving some complex problems, suggesting that reasoning generalization is noisy. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how well computer models can solve hard math problems. Right now, these models are really good at simple math problems, but it’s unclear if they can handle more complicated ones. The problem is that most of the data used to train these models has already been seen by them during training, and there aren’t many benchmarks to test their skills. To fix this, the authors created a new way to generate math problems with complex solutions. They found that as the math problems get harder, the computer models get worse at solving them. However, they’re still able to solve some really tough ones. |
Keywords
» Artificial intelligence » Generalization
