Numerical reasoning over text is a challenging task of Artificial Intelligence (AI), requiring reading comprehension and numerical reasoning abilities. Previous approaches use numerical reasoning programs to represent the reasoning process. However, most works do not separate the generation of operators and operands, which are key components of a numerical reasoning program, thus limiting their ability to generate such programs for complicated tasks. In this paper, we introduce the numEricaL reASoning with adapTive symbolIc Compiler (ELASTIC) model, which is constituted of the RoBERTa as the Encoder and a Compiler with four modules: Reasoning Manager, Operator Generator, Operands Generator, and Memory Register. ELASTIC is robust when conducting complicated reasoning. Also, it is domain agnostic by supporting the expansion of diverse operators without caring about the number of operands it contains. Experiments show that ELASTIC achieves 68.96 and 65.21 of execution accuracy and program accuracy on the FinQA dataset and 83.00 program accuracy on the MathQA dataset, outperforming previous state-of-the-art models significantly.
Compositional generalization refers to a model's capability to generalize to newly composed input data based on the data components observed during training. It has triggered a series of compositional generalization analysis on different tasks as generalization is an important aspect of language and problem solving skills. However, the similar discussion on math word problems (MWPs) is limited. In this manuscript, we study compositional generalization in MWP solving. Specifically, we first introduce a data splitting method to create compositional splits from existing MWP datasets. Meanwhile, we synthesize data to isolate the effect of compositions. To improve the compositional generalization in MWP solving, we propose an iterative data augmentation method that includes diverse compositional variation into training data and could collaborate with MWP methods. During the evaluation, we examine a set of methods and find all of them encounter severe performance loss on the evaluated datasets. We also find our data augmentation method could significantly improve the compositional generalization of general MWP methods. Code is available at https://github.com/demoleiwang/CGMWP.
Pretrained large language models (LLMs) are widely used in many sub-fields of natural language processing (NLP) and generally known as excellent few-shot learners with task-specific exemplars. Notably, chain of thought (CoT) prompting, a recent technique for eliciting complex multi-step reasoning through step-by-step answer examples, achieved the state-of-the-art performances in arithmetics and symbolic reasoning, difficult system-2 tasks that do not follow the standard scaling laws for LLMs. While these successes are often attributed to LLMs' ability for few-shot learning, we show that LLMs are decent zero-shot reasoners by simply adding "Let's think step by step" before each answer. Experimental results demonstrate that our Zero-shot-CoT, using the same single prompt template, significantly outperforms zero-shot LLM performances on diverse benchmark reasoning tasks including arithmetics (MultiArith, GSM8K, AQUA-RAT, SVAMP), symbolic reasoning (Last Letter, Coin Flip), and other logical reasoning tasks (Date Understanding, Tracking Shuffled Objects), without any hand-crafted few-shot examples, e.g. increasing the accuracy on MultiArith from 17.7% to 78.7% and GSM8K from 10.4% to 40.7% with large InstructGPT model (text-davinci-002), as well as similar magnitudes of improvements with another off-the-shelf large model, 540B parameter PaLM. The versatility of this single prompt across very diverse reasoning tasks hints at untapped and understudied fundamental zero-shot capabilities of LLMs, suggesting high-level, multi-task broad cognitive capabilities may be extracted by simple prompting. We hope our work not only serves as the minimal strongest zero-shot baseline for the challenging reasoning benchmarks, but also highlights the importance of carefully exploring and analyzing the enormous zero-shot knowledge hidden inside LLMs before crafting finetuning datasets or few-shot exemplars.
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 is available at https://github.com/yangzhch6/InterMWP.
Solving math word problems requires deductive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without explicitly performing relational reasoning between quantities in the given context. While empirically effective, such approaches typically do not provide explanations for the generated expressions. In this work, we view the task as a complex relation extraction problem, proposing a novel approach that presents explainable deductive reasoning steps to iteratively construct target expressions, where each step involves a primitive operation over two quantities defining their relation. Through extensive experiments on four benchmark datasets, we show that the proposed model significantly outperforms existing strong baselines. We further demonstrate that the deductive procedure not only presents more explainable steps but also enables us to make more accurate predictions on questions that require more complex reasoning.
Current visual question answering (VQA) tasks mainly consider answering human-annotated questions for natural images. However, aside from natural images, abstract diagrams with semantic richness are still understudied in visual understanding and reasoning research. In this work, we introduce a new challenge of Icon Question Answering (IconQA) with the goal of answering a question in an icon image context. We release IconQA, a large-scale dataset that consists of 107,439 questions and three sub-tasks: multi-image-choice, multi-text-choice, and filling-in-the-blank. The IconQA dataset is inspired by real-world diagram word problems that highlight the importance of abstract diagram understanding and comprehensive cognitive reasoning. Thus, IconQA requires not only perception skills like object recognition and text understanding, but also diverse cognitive reasoning skills, such as geometric reasoning, commonsense reasoning, and arithmetic reasoning. To facilitate potential IconQA models to learn semantic representations for icon images, we further release an icon dataset Icon645 which contains 645,687 colored icons on 377 classes. We conduct extensive user studies and blind experiments and reproduce a wide range of advanced VQA methods to benchmark the IconQA task. Also, we develop a strong IconQA baseline Patch-TRM that applies a pyramid cross-modal Transformer with input diagram embeddings pre-trained on the icon dataset. IconQA and Icon645 are available at https://iconqa.github.io.
In this article, we tackle the math word problem, namely, automatically answering a mathematical problem according to its textual description. Although recent methods have demonstrated their promising results, most of these methods are based on template-based generation scheme which results in limited generalization capability. To this end, we propose a novel human-like analogical learning method in a recall and learn manner. Our proposed framework is composed of modules of memory, representation, analogy, and reasoning, which are designed to make a new exercise by referring to the exercises learned in the past. Specifically, given a math word problem, the model first retrieves similar questions by a memory module and then encodes the unsolved problem and each retrieved question using a representation module. Moreover, to solve the problem in a way of analogy, an analogy module and a reasoning module with a copy mechanism are proposed to model the interrelationship between the problem and each retrieved question. Extensive experiments on two well-known datasets show the superiority of our proposed algorithm as compared to other state-of-the-art competitors from both overall performance comparison and micro-scope studies.
Standard accuracy metrics have shown that Math Word Problem (MWP) solvers have achieved high performance on benchmark datasets. However, the extent to which existing MWP solvers truly understand language and its relation with numbers is still unclear. In this paper, we generate adversarial attacks to evaluate the robustness of state-of-the-art MWP solvers. We propose two methods Question Reordering and Sentence Paraphrasing to generate adversarial attacks. We conduct experiments across three neural MWP solvers over two benchmark datasets. On average, our attack method is able to reduce the accuracy of MWP solvers by over 40 percentage points on these datasets. Our results demonstrate that existing MWP solvers are sensitive to linguistic variations in the problem text. We verify the validity and quality of generated adversarial examples through human evaluation.
Developing automatic Math Word Problem (MWP) solvers has been an interest of NLP researchers since the 1960s. Over the last few years, there are a growing number of datasets and deep learning-based methods proposed for effectively solving MWPs. However, most existing methods are benchmarked soly on one or two datasets, varying in different configurations, which leads to a lack of unified, standardized, fair, and comprehensive comparison between methods. This paper presents MWPToolkit, the first open-source framework for solving MWPs. In MWPToolkit, we decompose the procedure of existing MWP solvers into multiple core components and decouple their models into highly reusable modules. We also provide a hyper-parameter search function to boost the performance. In total, we implement and compare 17 MWP solvers on 4 widely-used single equation generation benchmarks and 2 multiple equations generation benchmarks. These features enable our MWPToolkit to be suitable for researchers to reproduce advanced baseline models and develop new MWP solvers quickly. Code and documents are available at https://github.com/LYH-YF/MWPToolkit.
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.
The problem of designing NLP solvers for math word problems (MWP) has seen sustained research activity and steady gains in the test accuracy. Since existing solvers achieve high performance on the benchmark datasets for elementary level MWPs containing one-unknown arithmetic word problems, such problems are often considered "solved" with the bulk of research attention moving to more complex MWPs. In this paper, we restrict our attention to English MWPs taught in grades four and lower. We provide strong evidence that the existing MWP solvers rely on shallow heuristics to achieve high performance on the benchmark datasets. To this end, we show that MWP solvers that do not have access to the question asked in the MWP can still solve a large fraction of MWPs. Similarly, models that treat MWPs as bag-of-words can also achieve surprisingly high accuracy. Further, we introduce a challenge dataset, SVAMP, created by applying carefully chosen variations over examples sampled from existing datasets. The best accuracy achieved by state-of-the-art models is substantially lower on SVAMP, thus showing that much remains to be done even for the simplest of the MWPs.
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.
A practical automatic textual math word problems (MWPs) solver should be able to solve various textual MWPs while most existing works only focused on one-unknown linear MWPs. Herein, we propose a simple but efficient method called Universal Expression Tree (UET) to make the first attempt to represent the equations of various MWPs uniformly. Then a semantically-aligned universal tree-structured solver (SAU-Solver) based on an encoder-decoder framework is proposed to resolve multiple types of MWPs in a unified model, benefiting from our UET representation. Our SAU-Solver generates a universal expression tree explicitly by deciding which symbol to generate according to the generated symbols' semantic meanings like human solving MWPs. Besides, our SAU-Solver also includes a novel subtree-level semanticallyaligned regularization to further enforce the semantic constraints and rationality of the generated expression tree by aligning with the contextual information. Finally, to validate the universality of our solver and extend the research boundary of MWPs, we introduce a new challenging Hybrid Math Word Problems dataset (HMWP), consisting of three types of MWPs. Experimental results on several MWPs datasets show that our model can solve universal types of MWPs and outperforms several state-of-the-art models.
Automatically solving math word problems is a critical task in the field of natural language processing. Recent models have reached their performance bottleneck and require more high-quality data for training. We propose a novel data augmentation method that reverses the mathematical logic of math word problems to produce new high-quality math problems and introduce new knowledge points that can benefit learning the mathematical reasoning logic. We apply the augmented data on two SOTA math word problem solving models and compare our results with a strong data augmentation baseline. Experimental results show the effectiveness of our approach. We release our code and data at https://github.com/yiyunya/RODA.
Recent progress in pre-trained neural language models has significantly improved the performance of many natural language processing (NLP) tasks. In this paper we propose a new model architecture DeBERTa (Decoding-enhanced BERT with disentangled attention) that improves the BERT and RoBERTa models using two novel techniques. The first is the disentangled attention mechanism, where each word is represented using two vectors that encode its content and position, respectively, and the attention weights among words are computed using disentangled matrices on their contents and relative positions, respectively. Second, an enhanced mask decoder is used to incorporate absolute positions in the decoding layer to predict the masked tokens in model pre-training. In addition, a new virtual adversarial training method is used for fine-tuning to improve models' generalization. We show that these techniques significantly improve the efficiency of model pre-training and the performance of both natural language understanding (NLU) and natural langauge generation (NLG) downstream tasks. Compared to RoBERTa-Large, a DeBERTa model trained on half of the training data performs consistently better on a wide range of NLP tasks, achieving improvements on MNLI by +0.9% (90.2% vs. 91.1%), on SQuAD v2.0 by +2.3% (88.4% vs. 90.7%) and RACE by +3.6% (83.2% vs. 86.8%). Notably, we scale up DeBERTa by training a larger version that consists of 48 Transform layers with 1.5 billion parameters. The significant performance boost makes the single DeBERTa model surpass the human performance on the SuperGLUE benchmark (Wang et al., 2019a) for the first time in terms of macro-average score (89.9 versus 89.8), and the ensemble DeBERTa model sits atop the SuperGLUE leaderboard as of January 6, 2021, out performing the human baseline by a decent margin (90.3 versus 89.8).
The celebrated Seq2Seq technique and its numerous variants achieve excellent performance on many tasks such as neural machine translation, semantic parsing, and math word problem solving. However, these models either only consider input objects as sequences while ignoring the important structural information for encoding, or they simply treat output objects as sequence outputs instead of structural objects for decoding. In this paper, we present a novel Graph-to-Tree Neural Networks, namely Graph2Tree consisting of a graph encoder and a hierarchical tree decoder, that encodes an augmented graph-structured input and decodes a tree-structured output. In particular, we investigated our model for solving two problems, neural semantic parsing and math word problem. Our extensive experiments demonstrate that our Graph2Tree model outperforms or matches the performance of other state-of-the-art models on these tasks.
Solving math word problems is a challenging task that requires accurate natural language understanding to bridge natural language texts and math expressions. Motivated by the intuition about how human generates the equations given the problem texts, this paper presents a neural approach to automatically solve math word problems by operating symbols according to their semantic meanings in texts. This paper views the process of generating equation as a bridge between the semantic world and the symbolic world, where the proposed neural math solver is based on an encoder-decoder framework. In the proposed model, the encoder is designed to understand the semantics of problems, and the decoder focuses on tracking semantic meanings of the generated symbols and then deciding which symbol to generate next. The preliminary experiments are conducted in a dataset Math23K, and our model significantly outperforms both the state-of-the-art single model and the best non-retrieval-based model over about 10% accuracy, demonstrating the effectiveness of bridging the symbolic and semantic worlds from math word problems.