The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> Learning to store information over extended time intervals by recurrent backpropagation takes a very long time, mostly because of insufficient, decaying error backflow. We briefly review Hochreiter's (1991) analysis of this problem, then address it by introducing a novel, efficient, gradient based method called long short-term memory (LSTM). Truncating the gradient where this does not do harm, LSTM can learn to bridge minimal time lags in excess of 1000 discrete-time steps by enforcing constant error flow through constant error carousels within special units. Multiplicative gate units learn to open and close access to the constant error flow. LSTM is local in space and time; its computational complexity per time step and weight is O. 1. Our experiments with artificial data involve local, distributed, real-valued, and noisy pattern representations. In comparisons with real-time recurrent learning, back propagation through time, recurrent cascade correlation, Elman nets, and neural sequence chunking, LSTM leads to many more successful runs, and learns much faster. LSTM also solves complex, artificial long-time-lag tasks that have never been solved by previous recurrent network algorithms. <s> BIB001 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> The recently introduced continuous Skip-gram model is an efficient method for learning high-quality distributed vector representations that capture a large number of precise syntactic and semantic word relationships. In this paper we present several extensions that improve both the quality of the vectors and the training speed. By subsampling of the frequent words we obtain significant speedup and also learn more regular word representations. We also describe a simple alternative to the hierarchical softmax called negative sampling. ::: ::: An inherent limitation of word representations is their indifference to word order and their inability to represent idiomatic phrases. For example, the meanings of "Canada" and "Air" cannot be easily combined to obtain "Air Canada". Motivated by this example, we present a simple method for finding phrases in text, and show that learning good vector representations for millions of phrases is possible. <s> BIB002 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> Deep Neural Networks (DNNs) are powerful models that have achieved excellent performance on difficult learning tasks. Although DNNs work well whenever large labeled training sets are available, they cannot be used to map sequences to sequences. In this paper, we present a general end-to-end approach to sequence learning that makes minimal assumptions on the sequence structure. Our method uses a multilayered Long Short-Term Memory (LSTM) to map the input sequence to a vector of a fixed dimensionality, and then another deep LSTM to decode the target sequence from the vector. Our main result is that on an English to French translation task from the WMT-14 dataset, the translations produced by the LSTM achieve a BLEU score of 34.8 on the entire test set, where the LSTM's BLEU score was penalized on out-of-vocabulary words. Additionally, the LSTM did not have difficulty on long sentences. For comparison, a phrase-based SMT system achieves a BLEU score of 33.3 on the same dataset. When we used the LSTM to rerank the 1000 hypotheses produced by the aforementioned SMT system, its BLEU score increases to 36.5, which is close to the previous state of the art. The LSTM also learned sensible phrase and sentence representations that are sensitive to word order and are relatively invariant to the active and the passive voice. Finally, we found that reversing the order of the words in all source sentences (but not target sentences) improved the LSTM's performance markedly, because doing so introduced many short term dependencies between the source and the target sentence which made the optimization problem easier. <s> BIB003 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> Recent methods for learning vector space representations of words have succeeded in capturing fine-grained semantic and syntactic regularities using vector arithmetic, but the origin of these regularities has remained opaque. We analyze and make explicit the model properties needed for such regularities to emerge in word vectors. The result is a new global logbilinear regression model that combines the advantages of the two major model families in the literature: global matrix factorization and local context window methods. Our model efficiently leverages statistical information by training only on the nonzero elements in a word-word cooccurrence matrix, rather than on the entire sparse matrix or on individual context windows in a large corpus. The model produces a vector space with meaningful substructure, as evidenced by its performance of 75% on a recent word analogy task. It also outperforms related models on similarity tasks and named entity recognition. <s> BIB004 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> In this paper, we propose a novel neural network model called RNN Encoder‐ Decoder that consists of two recurrent neural networks (RNN). One RNN encodes a sequence of symbols into a fixedlength vector representation, and the other decodes the representation into another sequence of symbols. The encoder and decoder of the proposed model are jointly trained to maximize the conditional probability of a target sequence given a source sequence. The performance of a statistical machine translation system is empirically found to improve by using the conditional probabilities of phrase pairs computed by the RNN Encoder‐Decoder as an additional feature in the existing log-linear model. Qualitatively, we show that the proposed model learns a semantically and syntactically meaningful representation of linguistic phrases. <s> BIB005 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> We propose the task of free-form and open-ended Visual Question Answering (VQA). Given an image and a natural language question about the image, the task is to provide an accurate natural language answer. Mirroring real-world scenarios, such as helping the visually impaired, both the questions and answers are open-ended. Visual questions selectively target different areas of an image, including background details and underlying context. As a result, a system that succeeds at VQA typically needs a more detailed understanding of the image and complex reasoning than a system producing generic image captions. Moreover, VQA is amenable to automatic evaluation, since many open-ended answers contain only a few words or a closed set of answers that can be provided in a multiple-choice format. We provide a dataset containing ~0.25M images, ~0.76M questions, and ~10M answers (www.visualqa.org), and discuss the information it provides. Numerous baselines for VQA are provided and compared with human performance. <s> BIB006 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> Answering natural language questions over a knowledge base is an important and challenging task. Most of existing systems typically rely on hand-crafted features and rules to conduct question understanding and/or answer ranking. In this paper, we introduce multi-column convolutional neural networks (MCCNNs) to understand questions from three different aspects (namely, answer path, answer context, and answer type) and learn their distributed representations. Meanwhile, we jointly learn low-dimensional embeddings of entities and relations in the knowledge base. Question-answer pairs are used to train the model to rank candidate answers. We also leverage question paraphrases to train the column networks in a multi-task learning manner. We use FREEBASE as the knowledge base and conduct extensive experiments on the WEBQUESTIONS dataset. Experimental results show that our method achieves better or comparable performance compared with baseline systems. In addition, we develop a method to compute the salience scores of question words in different column networks. The results help us intuitively understand what MCCNNs learn. <s> BIB007 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> Sequence to sequence learning has recently emerged as a new paradigm in supervised learning. To date, most of its applications focused on only one task and not much work explored this framework for multiple tasks. This paper examines three multi-task learning (MTL) settings for sequence to sequence models: (a) the oneto-many setting - where the encoder is shared between several tasks such as machine translation and syntactic parsing, (b) the many-to-one setting - useful when only the decoder can be shared, as in the case of translation and image caption generation, and (c) the many-to-many setting - where multiple encoders and decoders are shared, which is the case with unsupervised objectives and translation. Our results show that training on a small amount of parsing and image caption data can improve the translation quality between English and German by up to 1.5 BLEU points over strong single-task baselines on the WMT benchmarks. Furthermore, we have established a new state-of-the-art result in constituent parsing with 93.0 F1. Lastly, we reveal interesting properties of the two unsupervised learning objectives, autoencoder and skip-thought, in the MTL context: autoencoder helps less in terms of perplexities but more on BLEU scores compared to skip-thought. <s> BIB008 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> In recent years, the task of event recognition from videos has attracted increasing interest in multimedia area. While most of the existing research was mainly focused on exploring visual cues to handle relatively small-granular events, it is difficult to directly analyze video content without any prior knowledge. Therefore, synthesizing both the visual and semantic analysis is a natural way for video event understanding. In this paper, we study the problem of Web video event recognition, where Web videos often describe large-granular events and carry limited textual information. Key challenges include how to accurately represent event semantics from incomplete textual information and how to effectively explore the correlation between visual and textual cues for video event understanding. We propose a novel framework to perform complex event recognition from Web videos. In order to compensate the insufficient expressive power of visual cues, we construct an event knowledge base by deeply mining semantic information from ubiquitous Web documents. This event knowledge base is capable of describing each event with comprehensive semantics. By utilizing this base, the textual cues for a video can be significantly enriched. Furthermore, we introduce a two-view adaptive regression model, which explores the intrinsic correlation between the visual and textual cues of the videos to learn reliable classifiers. Extensive experiments on two real-world video data sets show the effectiveness of our proposed framework and prove that the event knowledge base indeed helps improve the performance of Web video event recognition. <s> BIB009 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional annotations or predefined templates. We develop a theory for expression trees that can be used to represent and evaluate the target arithmetic expressions; we use it to uniquely decompose the target arithmetic problem to multiple classification problems; we then compose an expression tree, combining these with world knowledge through a constrained inference framework. Our classifiers gain from the use of quantity schemas that supports better extraction of features. Experimental results show that our method outperforms existing systems, achieving state of the art performance on benchmark datasets of arithmetic word problems. <s> BIB010 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> Math word problems provide a natural abstraction to a range of natural language understanding problems that involve reasoning about quantities, such as interpreting election results, news about casualties, and the financial section of a newspaper. Units associated with the quantities often provide information that is essential to support this reasoning. This paper proposes a principled way to capture and reason about units and shows how it can benefit an arithmetic word problem solver. This paper presents the concept of Unit Dependency Graphs (UDGs), which provides a compact representation of the dependencies between units of numbers mentioned in a given problem. Inducing the UDG alleviates the brittleness of the unit extraction system and allows for a natural way to leverage domain knowledge about unit compatibility, for word problem solving. We introduce a decomposed model for inducing UDGs with minimal additional annotations, and use it to augment the expressions used in the arithmetic word problem solver of (Roy and Roth 2015) via a constrained inference framework. We show that introduction of UDGs reduces the error of the solver by over 10 %, surpassing all existing systems for solving arithmetic word problems. In addition, it also makes the system more robust to adaptation to new vocabulary and equation forms . <s> BIB011 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> Recent progress in using long short-term memory (LSTM) for image captioning has motivated the exploration of their applications for video captioning. By taking a video as a sequence of features, an LSTM model is trained on video-sentence pairs and learns to associate a video to a sentence. However, most existing methods compress an entire video shot or frame into a static representation, without considering attention mechanism which allows for selecting salient features. Furthermore, existing approaches usually model the translating error, but ignore the correlations between sentence semantics and visual content. To tackle these issues, we propose a novel end-to-end framework named aLSTMs, an attention-based LSTM model with semantic consistency, to transfer videos to natural sentences. This framework integrates attention mechanism with LSTM to capture salient structures of video, and explores the correlation between multimodal representations (i.e., words and visual content) for generating sentences with rich semantic content. Specifically, we first propose an attention mechanism that uses the dynamic weighted sum of local two-dimensional convolutional neural network representations. Then, an LSTM decoder takes these visual features at time $t$ and the word-embedding feature at time $t$ $-$ 1 to generate important words. Finally, we use multimodal embedding to map the visual and sentence features into a joint space to guarantee the semantic consistence of the sentence description and the video visual content. Experiments on the benchmark datasets demonstrate that our method using single feature can achieve competitive or even better results than the state-of-the-art baselines for video captioning in both BLEU and METEOR. <s> BIB012 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> This paper proposes a new model for extracting an interpretable sentence embedding by introducing self-attention. Instead of using a vector, we use a 2-D matrix to represent the embedding, with each row of the matrix attending on a different part of the sentence. We also propose a self-attention mechanism and a special regularization term for the model. As a side effect, the embedding comes with an easy way of visualizing what specific parts of the sentence are encoded into the embedding. We evaluate our model on 3 different tasks: author profiling, sentiment classification, and textual entailment. Results show that our model yields a significant performance gain compared to other sentence embedding methods in all of the 3 tasks. <s> BIB013 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> 3-D convolutional neural networks (3-D-convNets) have been very recently proposed for action recognition in videos, and promising results are achieved. However, existing 3-D-convNets has two “artificial” requirements that may reduce the quality of video analysis: 1) It requires a fixed-sized (e.g., 112 $\times$ 112) input video; and 2) most of the 3-D-convNets require a fixed-length input (i.e., video shots with fixed number of frames). To tackle these issues, we propose an end-to-end pipeline named Two-stream 3-D-convNet Fusion , which can recognize human actions in videos of arbitrary size and length using multiple features. Specifically, we decompose a video into spatial and temporal shots. By taking a sequence of shots as input, each stream is implemented using a spatial temporal pyramid pooling (STPP) convNet with a long short-term memory (LSTM) or CNN-E model, softmax scores of which are combined by a late fusion. We devise the STPP convNet to extract equal-dimensional descriptions for each variable-size shot, and we adopt the LSTM/CNN-E model to learn a global description for the input video using these time-varying descriptions. With these advantages, our method should improve all 3-D CNN-based video analysis methods. We empirically evaluate our method for action recognition in videos and the experimental results show that our method outperforms the state-of-the-art methods (both 2-D and 3-D based) on three standard benchmark datasets (UCF101, HMDB51 and ACT datasets). <s> BIB014 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> DL-Based Methods <s> We explore contemporary, data-driven techniques for solving math word problems over recent large-scale datasets. We show that well-tuned neural equation classifiers can outperform more sophisticated models such as sequence to sequence and self-attention across these datasets. Our error analysis indicates that, while fully data driven models show some promise, semantic and world knowledge is necessary for further advances. <s> BIB015
In recent years, deep learning (DL) has witnessed great success in a wide spectrum of "smart" applications, such as video captioning BIB012 , video event recognition BIB009 , human action regnition BIB014 , visual question answering BIB006 , and question answering with knowledge base BIB007 . The main advantage is that with sufficient amount of training data, DL is able to learn an effective feature representation in a data-driven manner without human intervention. It is not surprising to notice that several efforts have been attempted to apply DL for math word problem solving. Deep Neural Solver (DNS)  is the first deep learning based algorithm that does not rely on hand-crafted features. This is a milestone contribution because all the previous methods (including MathDQN) require human intelligence to help extract features that are effective. The deep model used in DNS is a typical sequence to sequence (seq2seq) model BIB003 , BIB008 ,  . The words in the problem are vectorized into features through word embedding techniques BIB002 , BIB004 . In the encoding layer, GRU BIB005 is used as the Recurrent Neural Network (RNN) to capture word dependency because compared to LSTM BIB001 , GRU has fewer parameters in the model and is less likely to be over-fitting in small datasets. This seq2seq model translates math word problems to equation templates, followed by a number mapping step to fill the slots in the equation with the quantities extracted from the text. To ensure that the output equations by the model are syntactically correct, five rules are pre-defined as validity constraints. For example, if the i th character in the output sequence is an operator in {+, −, ×, ÷}, then the model cannot result in c ∈ {+, −, ×, ÷, ), =} for the (i + 1) th character. To further improve the accuracy, DNS enhances the model in two ways. First, it builds a LSTM-based binary classification model to determine whether a number is relevant. This is similar to the relevance model trained in ExpressionTree BIB010 and UNITDEP BIB011 . The difference is that DNS uses LSTM as the classifier with unsupervised word-embedding features whereas ExpressionTree and UNITDEP use SVM with handcrafted features. Second, the seq2seq model is integrated with a similarity-based method  introduced in Section 3.2. Given a pre-defined threshold, the similarity-based retrieval strategy is selected as the solver if the maximal similarity score is higher than the threshold. Otherwise, the seq2seq model is used to solve the problem. Another follow-up of DNS was proposed recently in BIB015 . Instead of using GRU and LSTM, the math solver examines the performance of other seq2seq models when applied in mapping the problem text to equation templates. In particular, two models including BiLSTM BIB001 and structured self-attention BIB013 , were examined respectively for the equation template classification task. Results show that both models achieve comparable performance.