A Survey of Deep Learning for Mathematical Reasoning

Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.

OpenD: A Benchmark for Language-Driven Door and Drawer Opening

We introduce OPEND, a benchmark for learning how to use a hand to open cabinet doors or drawers in a photo-realistic and physics-reliable simulation environment driven by language instruction. To solve the task, we propose a multi-step planner composed of a deep neural network and rule-base controllers. The network is utilized to capture spatial relationships from images and understand semantic meaning from language instructions. Controllers efficiently execute the plan based on the spatial and semantic understanding. We evaluate our system by measuring its zero-shot performance in test data set. Experimental results demonstrate the effectiveness of decision planning by our multi-step planner for different hands, while suggesting that there is significant room for developing better models to address the challenge brought by language understanding, spatial reasoning, and long-term manipulation. We will release OPEND and host challenges to promote future research in this area.

Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning

Mathematical reasoning, a core ability of human intelligence, presents unique challenges for machines in abstract thinking and logical reasoning. Recent large pre-trained language models such as GPT-3 have achieved remarkable progress on mathematical reasoning tasks written in text form, such as math word problems (MWP). However, it is unknown if the models can handle more complex problems that involve math reasoning over heterogeneous information, such as tabular data. To fill the gap, we present Tabular Math Word Problems (TabMWP), a new dataset containing 38,431 open-domain grade-level problems that require mathematical reasoning on both textual and tabular data. Each question in TabMWP is aligned with a tabular context, which is presented as an image, semi-structured text, and a structured table. There are two types of questions: free-text and multi-choice, and each problem is annotated with gold solutions to reveal the multi-step reasoning process. We evaluate different pre-trained models on TabMWP, including the GPT-3 model in a few-shot setting. As earlier studies suggest, since few-shot GPT-3 relies on the selection of in-context examples, its performance is unstable and can degrade to near chance. The unstable issue is more severe when handling complex problems like TabMWP. To mitigate this, we further propose a novel approach, PromptPG, which utilizes policy gradient to learn to select in-context examples from a small amount of training data and then constructs the corresponding prompt for the test example. Experimental results show that our method outperforms the best baseline by 5.31% on the accuracy metric and reduces the prediction variance significantly compared to random selection, which verifies its effectiveness in the selection of in-context examples.

Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering

When answering a question, humans utilize the information available across different modalities to synthesize a consistent and complete chain of thought (CoT). This process is normally a black box in the case of deep learning models like large-scale language models. Recently, science question benchmarks have been used to diagnose the multi-hop reasoning ability and interpretability of an AI system. However, existing datasets fail to provide annotations for the answers, or are restricted to the textual-only modality, small scales, and limited domain diversity. To this end, we present Science Question Answering (SQA), a new benchmark that consists of ~21k multimodal multiple choice questions with a diverse set of science topics and annotations of their answers with corresponding lectures and explanations. We further design language models to learn to generate lectures and explanations as the chain of thought (CoT) to mimic the multi-hop reasoning process when answering SQA questions. SQA demonstrates the utility of CoT in language models, as CoT improves the question answering performance by 1.20% in few-shot GPT-3 and 3.99% in fine-tuned UnifiedQA. We also explore the upper bound for models to leverage explanations by feeding those in the input; we observe that it improves the few-shot performance of GPT-3 by 18.96%. Our analysis further shows that language models, similar to humans, benefit from explanations to learn from fewer data and achieve the same performance with just 40% of the data.

Structure Extraction in Task-Oriented Dialogues with Slot Clustering

Extracting structure information from dialogue data can help us better understand user and system behaviors. In task-oriented dialogues, dialogue structure has often been considered as transition graphs among dialogue states. However, annotating dialogue states manually is expensive and time-consuming. In this paper, we propose a simple yet effective approach for structure extraction in task-oriented dialogues. We first detect and cluster possible slot tokens with a pre-trained model to approximate dialogue ontology for a target domain. Then we track the status of each identified token group and derive a state transition structure. Empirical results show that our approach outperforms unsupervised baseline models by far in dialogue structure extraction. In addition, we show that data augmentation based on extracted structures enriches the surface formats of training data and can achieve a significant performance boost in dialogue response generation.

Triangular Character Animation Sampling with Motion, Emotion, and Relation

Dramatic progress has been made in animating individual characters. However, we still lack automatic control over activities between characters, especially those involving interactions. In this paper, we present a novel energy-based framework to sample and synthesize animations by associating the characters' body motions, facial expressions, and social relations. We propose a Spatial-Temporal And-Or graph (ST-AOG), a stochastic grammar model, to encode the contextual relationship between motion, emotion, and relation, forming a triangle in a conditional random field. We train our model from a labeled dataset of two-character interactions. Experiments demonstrate that our method can recognize the social relation between two characters and sample new scenes of vivid motion and emotion using Markov Chain Monte Carlo (MCMC) given the social relation. Thus, our method can provide animators with an automatic way to generate 3D character animations, help synthesize interactions between Non-Player Characters (NPCs), and enhance machine emotion intelligence (EQ) in virtual reality (VR).

ValueNet: A New Dataset for Human Value Driven Dialogue System

Building a socially intelligent agent involves many challenges, one of which is to teach the agent to speak guided by its value like a human. However, value-driven chatbots are still understudied in the area of dialogue systems. Most existing datasets focus on commonsense reasoning or social norm modeling. In this work, we present a new large-scale human value dataset called ValueNet, which contains human attitudes on 21,374 text scenarios. The dataset is organized in ten dimensions that conform to the basic human value theory in intercultural research. We further develop a Transformer-based value regression model on ValueNet to learn the utility distribution. Comprehensive empirical results show that the learned value model could benefit a wide range of dialogue tasks. For example, by teaching a generative agent with reinforcement learning and the rewards from the value model, our method attains state-of-the-art performance on the personalized dialog generation dataset: Persona-Chat. With values as additional features, existing emotion recognition models enable capturing rich human emotions in the context, which further improves the empathetic response generation performance in the EmpatheticDialogues dataset. To the best of our knowledge, ValueNet is the first large-scale text dataset for human value modeling, and we are the first one trying to incorporate a value model into emotionally intelligent dialogue systems. The dataset is available at https://liang-qiu.github.io/ValueNet/.

Learning from the Tangram to Solve Mini Visual Tasks

Current pre-training methods in computer vision focus on natural images in the daily-life context. However, abstract diagrams such as icons and symbols are common and important in the real world. This work is inspired by Tangram, a game that requires replicating an abstract pattern from seven dissected shapes. By recording human experience in solving tangram puzzles, we present the Tangram dataset and show that a pre-trained neural model on the Tangram helps solve some mini visual tasks based on low-resolution vision. Extensive experiments demonstrate that our proposed method generates intelligent solutions for aesthetic tasks such as folding clothes and evaluating room layouts. The pre-trained feature extractor can facilitate the convergence of few-shot learning tasks on human handwriting and improve the accuracy in identifying icons by their contours. The Tangram dataset is available at https://github.com/yizhouzhao/Tangram.

IconQA: A New Benchmark for Abstract Diagram Understanding and Visual Language 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.