Zhicheng Yang
2024
ATG: Benchmarking Automated Theorem Generation for Generative Language Models
Xiaohan Lin
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Qingxing Cao
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Yinya Huang
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Zhicheng Yang
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Zhengying Liu
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Zhenguo Li
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Xiaodan Liang
Findings of the Association for Computational Linguistics: NAACL 2024
Humans can develop new theorems to explore broader and more complex mathematical results.While current generative language models (LMs) have achieved significant improvement in automatically proving theorems, their ability to generate new or reusable theorems is still under-explored. Without the new theorems, current LMs struggle to prove harder theorems that are distant from the given hypotheses with the exponentially growing search space.More advanced theorem proving is if an agent (for instance, a generative LM) can leverage its creativity to generate new but also reasonable theorems that properly substitute part of a proof and also be saved as reusable knowledge for future theorem proving.Therefore, this paper proposes an Automated Theorem Generation (ATG) benchmark that evaluates whether an agent can automatically generate valuable (and possibly brand new) theorems that are applicable for downstream theorem proving as reusable knowledge. Specifically, we construct the ATG benchmark by splitting the Metamath library into three sets: axioms, library, and problem based on their proving depth.We conduct extensive experiments to investigate whether current LMs can generate theorems in the library and benefit the problem theorems proving. The results demonstrate that high-quality ATG data facilitates models’ performances on downstream ATP. However, there is still room for current LMs to develop better ATG and generate more advanced and human-like theorems. We hope the new ATG challenge can shed some light on advanced complex theorem proving.
2022
Unbiased Math Word Problems Benchmark for Mitigating Solving Bias
Zhicheng Yang
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Jinghui Qin
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Jiaqi Chen
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Xiaodan Liang
Findings of the Association for Computational Linguistics: NAACL 2022
In this paper, we revisit the solving bias when evaluating models on current Math Word Problem (MWP) benchmarks. However, current solvers exist solving bias which consists of data bias and learning bias due to biased dataset and improper training strategy. Our experiments verify MWP solvers are easy to be biased by the biased training datasets which do not cover diverse questions for each problem narrative of all MWPs, thus a solver can only learn shallow heuristics rather than deep semantics for understanding problems. Besides, an MWP can be naturally solved by multiple equivalent equations while current datasets take only one of the equivalent equations as ground truth, forcing the model to match the labeled ground truth and ignoring other equivalent equations. Here, we first introduce a novel MWP dataset named UnbiasedMWP which is constructed by varying the grounded expressions in our collected data and annotating them with corresponding multiple new questions manually. Then, to further mitigate learning bias, we propose a Dynamic Target Selection (DTS) Strategy to dynamically select more suitable target expressions according to the longest prefix match between the current model output and candidate equivalent equations which are obtained by applying commutative law during training. The results show that our UnbiasedMWP has significantly fewer biases than its original data and other datasets, posing a promising benchmark for fairly evaluating the solvers’ reasoning skills rather than matching nearest neighbors. And the solvers trained with our DTS achieve higher accuracies on multiple MWP benchmarks. The source code is available at https://github.com/yangzhch6/UnbiasedMWP.
LogicSolver: Towards Interpretable Math Word Problem Solving with Logical Prompt-enhanced Learning
Zhicheng Yang
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Jinghui Qin
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Jiaqi Chen
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Liang Lin
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Xiaodan Liang
Findings of the Association for Computational Linguistics: EMNLP 2022
Recently, deep learning models have made great progress in MWP solving on answer accuracy. However, they are uninterpretable since they mainly rely on shallow heuristics to achieve high performance without understanding and reasoning the grounded math logic. To address this issue and make a step towards interpretable MWP solving, we first construct a high-quality MWP dataset named InterMWP which consists of 11,495 MWPs and annotates interpretable logical formulas based on algebraic knowledge as the grounded linguistic logic of each solution equation. Different from existing MWP datasets, our InterMWP benchmark asks for a solver to not only output the solution expressions but also predict the corresponding logical formulas. We further propose a novel approach with logical prompt and interpretation generation, called LogicSolver. For each MWP, our LogicSolver first retrieves some highly-correlated algebraic knowledge and then passes them to the backbone model as prompts to improve the semantic representations of MWPs. With these improved semantic representations, our LogicSolver generates corresponding solution expressions and interpretable knowledge formulas in accord with the generated solution expressions, simultaneously. Experimental results show that our LogicSolver has stronger logical formula-based interpretability than baselines while achieving higher answer accuracy with the help of logical prompts, simultaneously. The source code and dataset will be available at https://github.com/yangzhch6/InterMWP.
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Co-authors
- Xiaodan Liang 3
- Jinghui Qin 2
- Jiaqi Chen 2
- Liang Lin 1
- Xiaohan Lin 1
- show all...