Zhenwen Liang


2024

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MinT: Boosting Generalization in Mathematical Reasoning via Multi-view Fine-tuning
Zhenwen Liang | Dian Yu | Xiaoman Pan | Wenlin Yao | Qingkai Zeng | Xiangliang Zhang | Dong Yu
Proceedings of the 2024 Joint International Conference on Computational Linguistics, Language Resources and Evaluation (LREC-COLING 2024)

Reasoning in mathematical domains remains a significant challenge for relatively small language models (LMs). Many current methods focus on specializing LMs in mathematical reasoning and rely heavily on distilling knowledge from powerful yet inefficient large LMs (LLMs). In this work, we explore a new direction that avoids over-reliance on LLM teachers, introducing a multi-view fine-tuning method that efficiently exploits existing mathematical problem datasets with diverse annotation styles. Our approach uniquely considers the various annotation formats as different “views” that may help each other and leverage them in training the model. By postpending distinct instructions to input questions, models can learn to generate solutions in diverse formats in a flexible manner. Experimental results show that our strategy enables relatively small LMs to outperform prior approaches that heavily rely on knowledge distillation, as well as carefully established baselines. Additionally, the proposed method grants the models promising generalization ability across various views and datasets, and the capability to learn from inaccurate or incomplete noisy data. We hope our multi-view training paradigm could inspire future studies in other machine reasoning domains.

2023

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Don’t be Blind to Questions: Question-Oriented Math Word Problem Solving
Zhenwen Liang | Jipeng Zhang | Xiangliang Zhang
Proceedings of the 13th International Joint Conference on Natural Language Processing and the 3rd Conference of the Asia-Pacific Chapter of the Association for Computational Linguistics (Volume 1: Long Papers)

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Compositional Mathematical Encoding for Math Word Problems
Zhenwen Liang | Jipeng Zhang | Kehan Guo | Xiaodong Wu | Jie Shao | Xiangliang Zhang
Findings of the Association for Computational Linguistics: ACL 2023

Solving math word problem (MWP) remains a challenging task, as it requires to understand both the semantic meanings of the text and the mathematical logic among quantities, i.e., for both semantics modal and quantity modal learning. Current MWP encoders work in a uni-modal setting and map the given problem description to a latent representation, then for decoding. The generalizability of these MWP encoders is thus limited because some problems are semantics-demanding and others are quantity-demanding. To address this problem, we propose a Compositional Math Word Problem Solver (C-MWP) which works in a bi-modal setting encoding in an interactive way. Extensive experiments validate the effectiveness of C-MWP and show its superiority over state-of-the-art models on public benchmarks.

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UniMath: A Foundational and Multimodal Mathematical Reasoner
Zhenwen Liang | Tianyu Yang | Jipeng Zhang | Xiangliang Zhang
Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing

While significant progress has been made in natural language processing (NLP), existing methods exhibit limitations in effectively interpreting and processing diverse mathematical modalities. Therefore, we introduce UniMath, a versatile and unified system designed for multimodal mathematical reasoning tasks. Tackling complex problem-solving in arithmetic, geometry, and table-based math, UniMath utilizes a fine-tuned T5 model augmented with a variational autoencoder (VAE)-based image tokenizer. By jointly training and evaluating the model on three diverse datasets - SVAMP, GeoQA, and TableMWP, UniMath achieves state-of-the-art performance. The model’s generalization ability is further demonstrated via fine-tuning on two additional datasets, MathQA and Geo-Proving. Through comprehensive evaluations, we showcase that joint training across diverse math tasks improves overall model performance and enhances its ability to generalize across different mathematical reasoning tasks. This pioneering approach provides a blueprint and inspires further efforts on unified mathematical reasoning with deep learning systems.

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Let GPT be a Math Tutor: Teaching Math Word Problem Solvers with Customized Exercise Generation
Zhenwen Liang | Wenhao Yu | Tanmay Rajpurohit | Peter Clark | Xiangliang Zhang | Ashwin Kalyan
Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing

In this paper, we present a novel approach for distilling math word problem solving capabilities from large language models (LLMs) into smaller, more efficient student models. Our approach is designed to consider the student model’s weaknesses and foster a tailored learning experience by generating targeted exercises aligned with educational science principles, such as knowledge tracing and personalized learning. Concretely, we let GPT-3 be a math tutor and run two steps iteratively: 1) assessing the student model’s current learning status on a GPT-generated exercise book, and 2) improving the student model by training it with tailored exercise samples generated by GPT-3. Experimental results reveal that our approach outperforms LLMs (e.g., GPT-3 and PaLM) in accuracy across three distinct benchmarks while employing significantly fewer parameters. Furthermore, we provide a comprehensive analysis of the various components within our methodology to substantiate their efficacy.

2022

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ArMATH: a Dataset for Solving Arabic Math Word Problems
Reem Alghamdi | Zhenwen Liang | Xiangliang Zhang
Proceedings of the Thirteenth Language Resources and Evaluation Conference

This paper studies solving Arabic Math Word Problems by deep learning. A Math Word Problem (MWP) is a text description of a mathematical problem that can be solved by deriving a math equation to reach the answer. Effective models have been developed for solving MWPs in English and Chinese. However, Arabic MWPs are rarely studied. This paper contributes the first large-scale dataset for Arabic MWPs, which contains 6,000 samples of primary-school math problems, written in Modern Standard Arabic (MSA). Arabic MWP solvers are then built with deep learning models and evaluated on this dataset. In addition, a transfer learning model is built to let the high-resource Chinese MWP solver promote the performance of the low-resource Arabic MWP solver. This work is the first to use deep learning methods to solve Arabic MWP and the first to use transfer learning to solve MWP across different languages. The transfer learning enhanced solver has an accuracy of 74.15%, which is 3% higher than the solver without using transfer learning. We make the dataset and solvers available in public for encouraging more research of Arabic MWPs: https://github.com/reem-codes/ArMATH

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MWP-BERT: Numeracy-Augmented Pre-training for Math Word Problem Solving
Zhenwen Liang | Jipeng Zhang | Lei Wang | Wei Qin | Yunshi Lan | Jie Shao | Xiangliang Zhang
Findings of the Association for Computational Linguistics: NAACL 2022

Math word problem (MWP) solving faces a dilemma in number representation learning. In order to avoid the number representation issue and reduce the search space of feasible solutions, existing works striving for MWP solving usually replace real numbers with symbolic placeholders to focus on logic reasoning. However, different from common symbolic reasoning tasks like program synthesis and knowledge graph reasoning, MWP solving has extra requirements in numerical reasoning. In other words, instead of the number value itself, it is the reusable numerical property that matters more in numerical reasoning. Therefore, we argue that injecting numerical properties into symbolic placeholders with contextualized representation learning schema can provide a way out of the dilemma in the number representation issue here. In this work, we introduce this idea to the popular pre-training language model (PLM) techniques and build MWP-BERT, an effective contextual number representation PLM. We demonstrate the effectiveness of our MWP-BERT on MWP solving and several MWP-specific understanding tasks on both English and Chinese benchmarks.

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Analogical Math Word Problems Solving with Enhanced Problem-Solution Association
Zhenwen Liang | Jipeng Zhang | Xiangliang Zhang
Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing

Math word problem (MWP) solving is an important task in question answering which requires human-like reasoning ability. Analogical reasoning has long been used in mathematical education, as it enables students to apply common relational structures of mathematical situations to solve new problems. In this paper, we propose to build a novel MWP solver by leveraging analogical MWPs, which advance the solver’s generalization ability across different kinds of MWPs. The key idea, named analogy identification, is to associate the analogical MWP pairs in a latent space, i.e., encoding an MWP close to another analogical MWP, while leaving away from the non-analogical ones. Moreover, a solution discriminator is integrated into the MWP solver to enhance the association between an MWP and its true solution. The evaluation results verify that our proposed analogical learning strategy promotes the performance of MWP-BERT on Math23k over the state-of-the-art model Generate2Rank, with 5 times fewer parameters in the encoder. We also find that our model has a stronger generalization ability in solving difficult MWPs due to the analogical learning from easy MWPs.

2021

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Data-Efficient Language Shaped Few-shot Image Classification
Zhenwen Liang | Xiangliang Zhang
Findings of the Association for Computational Linguistics: EMNLP 2021

Many existing works have demonstrated that language is a helpful guider for image understanding by neural networks. We focus on a language-shaped learning problem in a few-shot setting, i.e., using language to improve few-shot image classification when language descriptions are only available during training. We propose a data-efficient method that can make the best usage of the few-shot images and the language available only in training. Experimental results on dataset ShapeWorld and Birds show that our method outperforms other state-of-the-art baselines in language-shaped few-shot learning area, especially when training data is more severely limited. Therefore, we call our approach data-efficient language-shaped learning (DF-LSL).