Training Verifiers to Solve Math Word Problems
FreeImproving math reasoning with verifiers
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About Training Verifiers to Solve Math Word Problems
Training Verifiers to Solve Math Word Problems is a research paper that introduces GSM8K, a dataset of 8,500 high-quality, linguistically diverse grade school math word problems. The paper proposes a method to improve multi-step mathematical reasoning in large language models by training verifiers to judge the correctness of model-generated solutions. At test time, the model generates many candidate solutions, and the verifier selects the highest-ranked one. This verification approach significantly improves performance on GSM8K and scales more effectively with additional data compared to standard finetuning baselines.
Key Features
Introduces GSM8K, a dataset of 8,500 grade school math word problems
Trains a verifier model to judge correctness of generated solutions
Generates many candidate solutions at test time and selects the best via verifier ranking
Shows verification scales better with more data than standard finetuning
Diagnoses failure modes of large transformer models on multi-step math reasoning
Pros & Cons
Pros
- Verification significantly boosts performance on math word problems
- Scales effectively with increased data
- Open dataset (GSM8K) enables reproducible research
- Conceptually simple approach that leverages existing language models
Cons
- Large transformer models still fail on many simple math problems without verification
- Requires generating many candidate solutions, which may be computationally expensive
- Method is research-oriented and not a ready-to-use product
- Performance improvements depend on the quality of the base model and verifier
Best For
Solving grade school math word problemsImproving multi-step reasoning in language modelsEvaluating model-generated solutions for correctnessEducational AI for math tutoring
FAQ
What is GSM8K?
GSM8K is a dataset of 8,500 high-quality, linguistically diverse grade school math word problems introduced in this paper to support research on multi-step mathematical reasoning.
How does the verification method work?
A verifier model is trained to judge the correctness of candidate solutions. At test time, the language model generates many candidate solutions, and the verifier ranks them, selecting the highest-ranked one.
What are the main findings of the paper?
The paper finds that even large transformer models struggle with multi-step math reasoning, but using a verifier significantly improves performance and scales better with increased data compared to finetuning alone.