Chain-of-thought prompting, by including intermediate reasoning steps in few-shot examples, elicits strong reasoning abilities in large language models on arithmetic, commonsense, and symbolic tasks.
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Measuring Mathematical Problem Solving With the MATH Dataset
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abstract
Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are able to increase accuracy on MATH, our results show that accuracy remains relatively low, even with enormous Transformer models. Moreover, we find that simply increasing budgets and model parameter counts will be impractical for achieving strong mathematical reasoning if scaling trends continue. While scaling Transformers is automatically solving most other text-based tasks, scaling is not currently solving MATH. To have more traction on mathematical problem solving we will likely need new algorithmic advancements from the broader research community.
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- abstract Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are
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representative citing papers
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Reinforcement Learning from Denoising Feedback
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Post-Optimization Adaptive Rank Allocation for LoRA
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Learning Uncertainty from Sequential Internal Dispersion in Large Language Models
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Acceptance Dynamics Across Cognitive Domains in Speculative Decoding
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Empirical Evidence of Complexity-Induced Limits in Large Language Models on Finite Discrete State-Space Problems with Explicit Validity Constraints
Large reasoning models exhibit reasoning collapse, with accuracy dropping sharply beyond task-specific complexity thresholds in controlled versions of nine classical reasoning tasks using strict validity validators.
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Adapt to Thrive! Adaptive Power-Mean Policy Optimization for Improved LLM Reasoning
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