We propose Text2Math, a model for semantically parsing text into math expressions. The model can be used to solve different math related problems including arithmetic word problems and equation parsing problems. Unlike previous approaches, we tackle the problem from an end-to-end structured prediction perspective where our algorithm aims to predict the complete math expression at once as a tree structure, where minimal manual efforts are involved in the process. Empirical results on benchmark datasets demonstrate the efficacy of our approach.
With increasing popularity in online learning, a surge of E-learning platforms have emerged to facilitate education opportunities for k-12 (from kindergarten to 12th grade) students and with this, a wealth of information on their learning logs are getting recorded. However, it remains unclear how to make use of these detailed learning behavior data to improve the design of learning materials and gain deeper insight into students' thinking and learning styles. In this work, we propose a visual analytics system to analyze student learning behaviors on a K-12 mathematics E-learning platform. It supports both correlation analysis between different attributes and a detailed visualization of user mouse-movement logs. Our case studies on a real dataset show that our system can better guide the design of learning resources (e.g., math questions) and facilitate quick interpretation of students' problem-solving and learning styles.
Reading comprehension models have been successfully applied to extractive text answers, but it is unclear how best to generalize these models to abstractive numerical answers. We enable a BERT-based reading comprehension model to perform lightweight numerical reasoning. We augment the model with a predefined set of executable 'programs' which encompass simple arithmetic as well as extraction. Rather than having to learn to manipulate numbers directly, the model can pick a program and execute it. On the recent Discrete Reasoning Over Passages (DROP) dataset, designed to challenge reading comprehension models, we show a 33% absolute improvement by adding shallow programs. The model can learn to predict new operations when appropriate in a math word problem setting (Roy and Roth, 2015) with very few training examples.
In this paper we propose a deep neural network model with an encoder-decoder architecture that translates images of math formulas into their LaTeX markup sequences. The encoder is a convolutional neural network (CNN) that transforms images into a group of feature maps. To better capture the spatial relationships of math symbols, the feature maps are augmented with 2D positional encoding before being unfolded into a vector. The decoder is a stacked bidirectional long short-term memory (LSTM) model integrated with the soft attention mechanism, which works as a language model to translate the encoder output into a sequence of LaTeX tokens. The neural network is trained in two steps. The first step is token-level training using the Maximum-Likelihood Estimation (MLE) as the objective function. At completion of the token-level training, the sequence-level training objective function is employed to optimize the overall model based on the policy gradient algorithm from reinforcement learning. Our design also overcomes the exposure bias problem by closing the feedback loop in the decoder during sequence-level training, i.e., feeding in the predicted token instead of the ground truth token at every time step. The model is trained and evaluated on the IM2LATEX-100K dataset and shows state-of-the-art performance on both sequence-based and image-based evaluation metrics.
This paper proposes a Transformer-based model to generate equations for math word problems. It achieves much better results than RNN models when copy and align mechanisms are not used, and can outperform complex copy and align RNN models. We also show that training a Transformer jointly in a generation task with two decoders, left-to-right and right-to-left, is beneficial. Such a Transformer performs better than the one with just one decoder not only because of the ensemble effect, but also because it improves the encoder training procedure. We also experiment with adding reinforcement learning to our model, showing improved performance compared to MLE training.
There is a general trend towards solving problems suited to deep learning with more complex deep learning architectures trained on larger training sets. This requires longer compute times and greater data parallelization or model parallelization. Both data and model parallelism have been historically faster in parameter server architectures, but data parallelism is starting to be faster in ring architectures due to algorithmic improvements. In this paper, we analyze the math behind ring architectures and make an informed adaptation of dynamic scheduling to ring architectures. To do so, we formulate a non-convex, non-linear, NP-hard integer programming problem and a new efficient doubling heuristic for its solution. We build upon Horovod: an open source ring architecture framework over TensorFlow. We show that Horovod jobs have a low cost to stop and restart and that stopping and restarting ring architecture jobs leads to faster completion times. These two facts make dynamic scheduling of ring architecture jobs feasible. Lastly, we simulate a scheduler using these runs and show a more than halving of average job time on some workload patterns.
From massive face-recognition-based surveillance and machine-learning-based decision systems predicting crime recidivism rates, to the move towards automated health diagnostic systems, artificial intelligence (AI) is being used in scenarios that have serious consequences in people's lives. However, this rapid permeation of AI into society has not been accompanied by a thorough investigation of the sociopolitical issues that cause certain groups of people to be harmed rather than advantaged by it. For instance, recent studies have shown that commercial face recognition systems have much higher error rates for dark skinned women while having minimal errors on light skinned men. A 2016 ProPublica investigation uncovered that machine learning based tools that assess crime recidivism rates in the US are biased against African Americans. Other studies show that natural language processing tools trained on newspapers exhibit societal biases (e.g. finishing the analogy "Man is to computer programmer as woman is to X" by homemaker). At the same time, books such as Weapons of Math Destruction and Automated Inequality detail how people in lower socioeconomic classes in the US are subjected to more automated decision making tools than those who are in the upper class. Thus, these tools are most often used on people towards whom they exhibit the most bias. While many technical solutions have been proposed to alleviate bias in machine learning systems, we have to take a holistic and multifaceted approach. This includes standardization bodies determining what types of systems can be used in which scenarios, making sure that automated decision tools are created by people from diverse backgrounds, and understanding the historical and political factors that disadvantage certain groups who are subjected to these tools.
Spoken language proficiency is critically important for children's growth and personal development. Due to the limited and imbalanced educational resources in China, elementary students barely have chances to improve their oral language skills in classes. Verbal fluency tasks (VFTs) were invented to let the students practice their spoken language proficiency after school. VFTs are simple but concrete math related questions that ask students to not only report answers but speak out the entire thinking process. In spite of the great success of VFTs, they bring a heavy grading burden to elementary teachers. To alleviate this problem, we develop Dolphin, a spoken language proficiency assessment system for Chinese elementary education. Dolphin is able to automatically evaluate both phonological fluency and semantic relevance of students' VFT answers. We conduct a wide range of offline and online experiments to demonstrate the effectiveness of Dolphin. In our offline experiments, we show that Dolphin improves both phonological fluency and semantic relevance evaluation performance when compared to state-of-the-art baselines on real-world educational data sets. In our online A/B experiments, we test Dolphin with 183 teachers from 2 major cities (Hangzhou and Xi'an) in China for 10 weeks and the results show that VFT assignments grading coverage is improved by 22\%.
Significant work is being done to develop the math and tools necessary to build provable defenses, or at least bounds, against adversarial attacks of neural networks. In this work, we argue that tools from control theory could be leveraged to aid in defending against such attacks. We do this by example, building a provable defense against a weaker adversary. This is done so we can focus on the mechanisms of control theory, and illuminate its intrinsic value.
We present an open source math-aware Question Answering System based on Ask Platypus. Our system returns as a single mathematical formula for a natural language question in English or Hindi. This formulae originate from the knowledge-base Wikidata. We translate these formulae to computable data by integrating the calculation engine sympy into our system. This way, users can enter numeric values for the variables occurring in the formula. Moreover, the system loads numeric values for constants occurring in the formula from Wikidata. In a user study, our system outperformed a commercial computational mathematical knowledge engine by 13%. However, the performance of our system heavily depends on the size and quality of the formula data available in Wikidata. Since only a few items in Wikidata contained formulae when we started the project, we facilitated the import process by suggesting formula edits to Wikidata editors. With the simple heuristic that the first formula is significant for the article, 80% of the suggestions were correct.
Identifying academic plagiarism is a pressing task for educational and research institutions, publishers, and funding agencies. Current plagiarism detection systems reliably find instances of copied and moderately reworded text. However, reliably detecting concealed plagiarism, such as strong paraphrases, translations, and the reuse of nontextual content and ideas is an open research problem. In this paper, we extend our prior research on analyzing mathematical content and academic citations. Both are promising approaches for improving the detection of concealed academic plagiarism primarily in Science, Technology, Engineering and Mathematics (STEM). We make the following contributions: i) We present a two-stage detection process that combines similarity assessments of mathematical content, academic citations, and text. ii) We introduce new similarity measures that consider the order of mathematical features and outperform the measures in our prior research. iii) We compare the effectiveness of the math-based, citation-based, and text-based detection approaches using confirmed cases of academic plagiarism. iv) We demonstrate that the combined analysis of math-based and citation-based content features allows identifying potentially suspicious cases in a collection of 102K STEM documents. Overall, we show that analyzing the similarity of mathematical content and academic citations is a striking supplement for conventional text-based detection approaches for academic literature in the STEM disciplines.
We introduce a new framework for unifying and systematizing the performance analysis of first-order black-box optimization algorithms for unconstrained convex minimization. The low-cost iteration complexity enjoyed by first-order algorithms renders them particularly relevant for applications in machine learning and large-scale data analysis. Relying on sum-of-squares (SOS) optimization, we introduce a hierarchy of semidefinite programs that give increasingly better convergence bounds for higher levels of the hierarchy. Alluding to the power of the SOS hierarchy, we show that the (dual of the) first level corresponds to the Performance Estimation Problem (PEP) introduced by Drori and Teboulle [Math. Program., 145(1):451--482, 2014], a powerful framework for determining convergence rates of first-order optimization algorithms. Consequently, many results obtained within the PEP framework can be reinterpreted as degree-1 SOS proofs, and thus, the SOS framework provides a promising new approach for certifying improved rates of convergence by means of higher-order SOS certificates. To determine analytical rate bounds, in this work we use the first level of the SOS hierarchy and derive new result{s} for noisy gradient descent with inexact line search methods (Armijo, Wolfe, and Goldstein).
We propose a new domain adaptation method for Combinatory Categorial Grammar (CCG) parsing, based on the idea of automatic generation of CCG corpora exploiting cheaper resources of dependency trees. Our solution is conceptually simple, and not relying on a specific parser architecture, making it applicable to the current best-performing parsers. We conduct extensive parsing experiments with detailed discussion; on top of existing benchmark datasets on (1) biomedical texts and (2) question sentences, we create experimental datasets of (3) speech conversation and (4) math problems. When applied to the proposed method, an off-the-shelf CCG parser shows significant performance gains, improving from 90.7% to 96.6% on speech conversation, and from 88.5% to 96.8% on math problems.
We introduce a large-scale dataset of math word problems and an interpretable neural math problem solver that learns to map problems to operation programs. Due to annotation challenges, current datasets in this domain have been either relatively small in scale or did not offer precise operational annotations over diverse problem types. We introduce a new representation language to model precise operation programs corresponding to each math problem that aim to improve both the performance and the interpretability of the learned models. Using this representation language, our new dataset, MathQA, significantly enhances the AQuA dataset with fully-specified operational programs. We additionally introduce a neural sequence-to-program model enhanced with automatic problem categorization. Our experiments show improvements over competitive baselines in our MathQA as well as the AQuA dataset. The results are still significantly lower than human performance indicating that the dataset poses new challenges for future research. Our dataset is available at: https://math-qa.github.io/math-QA/
This work addresses a classic problem of online prediction with expert advice. We assume an adversarial opponent, and we consider both the finite-horizon and random-stopping versions of this zero-sum, two-person game. Focusing on an appropriate continuum limit and using methods from optimal control, we characterize the value of the game as the viscosity solution of a certain nonlinear partial differential equation. The analysis also reveals the predictor's and the opponent's minimax optimal strategies. Our work provides, in particular, a continuum perspective on recent work of Gravin, Peres, and Sivan (Proc SODA 2016). Our techniques are similar to those of Kohn and Serfaty (Comm Pure Appl Math 2010), where scaling limits of some two-person games led to elliptic or parabolic PDEs.
Over the last decades, a class of important mathematical results have required an ever increasing amount of human effort to carry out. For some, the help of computers is now indispensable. We analyze the implications of this trend towards "big mathematics", its relation to human cognition, and how machine support for big math can be organized. The central contribution of this position paper is an information model for "doing mathematics", which posits that humans very efficiently integrate four aspects: inference, computation, tabulation, and narration around a well-organized core of mathematical knowledge. The challenge for mathematical software systems is that these four aspects need to be integrated as well. We briefly survey the state of the art.
This paper explains the math behind a generative adversarial network (GAN) model and why it is hard to be trained. Wasserstein GAN is intended to improve GANs' training by adopting a smooth metric for measuring the distance between two probability distributions.
The deep network model, with the majority built on neural networks, has been proved to be a powerful framework to represent complex data for high performance machine learning. In recent years, more and more studies turn to nonneural network approaches to build diverse deep structures, and the Deep Stacking Network (DSN) model is one of such approaches that uses stacked easy-to-learn blocks to build a parameter-training-parallelizable deep network. In this paper, we propose a novel SVM-based Deep Stacking Network (SVM-DSN), which uses the DSN architecture to organize linear SVM classifiers for deep learning. A BP-like layer tuning scheme is also proposed to ensure holistic and local optimizations of stacked SVMs simultaneously. Some good math properties of SVM, such as the convex optimization, is introduced into the DSN framework by our model. From a global view, SVM-DSN can iteratively extract data representations layer by layer as a deep neural network but with parallelizability, and from a local view, each stacked SVM can converge to its optimal solution and obtain the support vectors, which compared with neural networks could lead to interesting improvements in anti-saturation and interpretability. Experimental results on both image and text data sets demonstrate the excellent performances of SVM-DSN compared with some competitive benchmark models.
Sequencing items in adaptive learning systems typically relies on a large pool of interactive assessment items (questions) that are analyzed into a hierarchy of skills or Knowledge Components (KCs). Educational data mining techniques can be used to analyze students performance data in order to optimize the mapping of items to KCs. Standard methods that map items into KCs using item-similarity measures make the implicit assumption that students performance on items that depend on the same skill should be similar. This assumption holds if the latent trait (mastery of the underlying skill) is relatively fixed during students activity, as in the context of testing, which is the primary context in which these measures were developed and applied. However, in adaptive learning systems that aim for learning, and address subject matters such as K6 Math that consist of multiple sub-skills, this assumption does not hold. In this paper we propose a new item-similarity measure, termed Kappa Learning (KL), which aims to address this gap. KL identifies similarity between items under the assumption of learning, namely, that learners mastery of the underlying skills changes as they progress through the items. We evaluate Kappa Learning on data from a computerized tutor that teaches Fractions for 4th grade, with experts tagging as ground truth, and on simulated data. Our results show that clustering that is based on Kappa Learning outperforms clustering that is based on commonly used similarity measures (Cohen Kappa, Yule, and Pearson).
Convolution Neural Networks is one of the most powerful tools in the present era of science. There has been a lot of research done to improve their performance and robustness while their internal working was left unexplored to much extent. They are often defined as black boxes that can map non-linear data very effectively. This paper tries to show how CNN has learned to look at an image. The proposed algorithm exploits the basic math of CNN to backtrack the important pixels it is considering to predict. This is a simple algorithm which does not involve any training of its own over a pre-trained CNN which can classify.