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This is a lecture note for the course DS-GA 3001 <Natural Language Understanding with Distributed Representation> at the Center for Data Science , New York University in Fall, 2015. As the name of the course suggests, this lecture note introduces readers to a neural network based approach to natural language understanding/processing. In order to make it as self-contained as possible, I spend much time on describing basics of machine learning and neural networks, only after which how they are used for natural languages is introduced. On the language front, I almost solely focus on language modelling and machine translation, two of which I personally find most fascinating and most fundamental to natural language understanding.

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State-of-the-art models for semantic segmentation are based on adaptations of convolutional networks that had originally been designed for image classification. However, dense prediction and image classification are structurally different. In this work, we develop a new convolutional network module that is specifically designed for dense prediction. The presented module uses dilated convolutions to systematically aggregate multi-scale contextual information without losing resolution. The architecture is based on the fact that dilated convolutions support exponential expansion of the receptive field without loss of resolution or coverage. We show that the presented context module increases the accuracy of state-of-the-art semantic segmentation systems. In addition, we examine the adaptation of image classification networks to dense prediction and show that simplifying the adapted network can increase accuracy.

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We propose BlackOut, an approximation algorithm to efficiently train massive recurrent neural network language models (RNNLMs) with million word vocabularies. BlackOut is motivated by using a discriminative loss, and we describe a new sampling strategy which significantly reduces computation while improving stability, sample efficiency, and rate of convergence. One way to understand BlackOut is to view it as an extension of the DropOut strategy to the output layer, wherein we use a discriminative training loss and a weighted sampling scheme. We also establish close connections between BlackOut, importance sampling, and noise contrastive estimation (NCE). Our experiments, on the recently released one billion word language modeling benchmark, demonstrate scalability and accuracy of BlackOut; we outperform the state-of-the art, and achieve the lowest perplexity scores on this dataset. Moreover, unlike other established methods which typically require GPUs or CPU clusters, we show that a carefully implemented version of BlackOut requires only 1-10 days on a single machine to train a RNNLM with a million word vocabulary and billions of parameters on one billion words. Although we describe BlackOut in the context of RNNLM training, it can be used to any networks with large softmax output layers.

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Deep feedforward and recurrent networks have achieved impressive results in many perception and language processing applications. This success is partially attributed to architectural innovations such as convolutional and long short-term memory networks. The main motivation for these architectural innovations is that they capture better domain knowledge, and importantly are easier to optimize than more basic architectures. Recently, more complex architectures such as Neural Turing Machines and Memory Networks have been proposed for tasks including question answering and general computation, creating a new set of optimization challenges. In this paper, we discuss a low-overhead and easy-to-implement technique of adding gradient noise which we find to be surprisingly effective when training these very deep architectures. The technique not only helps to avoid overfitting, but also can result in lower training loss. This method alone allows a fully-connected 20-layer deep network to be trained with standard gradient descent, even starting from a poor initialization. We see consistent improvements for many complex models, including a 72% relative reduction in error rate over a carefully-tuned baseline on a challenging question-answering task, and a doubling of the number of accurate binary multiplication models learned across 7,000 random restarts. We encourage further application of this technique to additional complex modern architectures.

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Recurrent neural networks (RNNs) are notoriously difficult to train. When the eigenvalues of the hidden to hidden weight matrix deviate from absolute value 1, optimization becomes difficult due to the well studied issue of vanishing and exploding gradients, especially when trying to learn long-term dependencies. To circumvent this problem, we propose a new architecture that learns a unitary weight matrix, with eigenvalues of absolute value exactly 1. The challenge we address is that of parametrizing unitary matrices in a way that does not require expensive computations (such as eigendecomposition) after each weight update. We construct an expressive unitary weight matrix by composing several structured matrices that act as building blocks with parameters to be learned. Optimization with this parameterization becomes feasible only when considering hidden states in the complex domain. We demonstrate the potential of this architecture by achieving state of the art results in several hard tasks involving very long-term dependencies.

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Many tasks in computer vision can be cast as a "label changing" problem, where the goal is to make a semantic change to the appearance of an image or some subject in an image in order to alter the class membership. Although successful task-specific methods have been developed for some label changing applications, to date no general purpose method exists. Motivated by this we propose deep manifold traversal, a method that addresses the problem in its most general form: it first approximates the manifold of natural images then morphs a test image along a traversal path away from a source class and towards a target class while staying near the manifold throughout. The resulting algorithm is surprisingly effective and versatile. It is completely data driven, requiring only an example set of images from the desired source and target domains. We demonstrate deep manifold traversal on highly diverse label changing tasks: changing an individual's appearance (age and hair color), changing the season of an outdoor image, and transforming a city skyline towards nighttime.

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In this paper we present a method for learning a discriminative classifier from unlabeled or partially labeled data. Our approach is based on an objective function that trades-off mutual information between observed examples and their predicted categorical class distribution, against robustness of the classifier to an adversarial generative model. The resulting algorithm can either be interpreted as a natural generalization of the generative adversarial networks (GAN) framework or as an extension of the regularized information maximization (RIM) framework to robust classification against an optimal adversary. We empirically evaluate our method - which we dub categorical generative adversarial networks (or CatGAN) - on synthetic data as well as on challenging image classification tasks, demonstrating the robustness of the learned classifiers. We further qualitatively assess the fidelity of samples generated by the adversarial generator that is learned alongside the discriminative classifier, and identify links between the CatGAN objective and discriminative clustering algorithms (such as RIM).

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Hypernymy, textual entailment, and image captioning can be seen as special cases of a single visual-semantic hierarchy over words, sentences, and images. In this paper we advocate for explicitly modeling the partial order structure of this hierarchy. Towards this goal, we introduce a general method for learning ordered representations, and show how it can be applied to a variety of tasks involving images and language. We show that the resulting representations improve performance over current approaches for hypernym prediction and image-caption retrieval.

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The standard recurrent neural network language model (RNNLM) generates sentences one word at a time and does not work from an explicit global sentence representation. In this work, we introduce and study an RNN-based variational autoencoder generative model that incorporates distributed latent representations of entire sentences. This factorization allows it to explicitly model holistic properties of sentences such as style, topic, and high-level syntactic features. Samples from the prior over these sentence representations remarkably produce diverse and well-formed sentences through simple deterministic decoding. By examining paths through this latent space, we are able to generate coherent novel sentences that interpolate between known sentences. We present techniques for solving the difficult learning problem presented by this model, demonstrate its effectiveness in imputing missing words, explore many interesting properties of the model's latent sentence space, and present negative results on the use of the model in language modeling.

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We propose the neural programmer-interpreter (NPI): a recurrent and compositional neural network that learns to represent and execute programs. NPI has three learnable components: a task-agnostic recurrent core, a persistent key-value program memory, and domain-specific encoders that enable a single NPI to operate in multiple perceptually diverse environments with distinct affordances. By learning to compose lower-level programs to express higher-level programs, NPI reduces sample complexity and increases generalization ability compared to sequence-to-sequence LSTMs. The program memory allows efficient learning of additional tasks by building on existing programs. NPI can also harness the environment (e.g. a scratch pad with read-write pointers) to cache intermediate results of computation, lessening the long-term memory burden on recurrent hidden units. In this work we train the NPI with fully-supervised execution traces; each program has example sequences of calls to the immediate subprograms conditioned on the input. Rather than training on a huge number of relatively weak labels, NPI learns from a small number of rich examples. We demonstrate the capability of our model to learn several types of compositional programs: addition, sorting, and canonicalizing 3D models. Furthermore, a single NPI learns to execute these programs and all 21 associated subprograms.

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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.

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Experience replay lets online reinforcement learning agents remember and reuse experiences from the past. In prior work, experience transitions were uniformly sampled from a replay memory. However, this approach simply replays transitions at the same frequency that they were originally experienced, regardless of their significance. In this paper we develop a framework for prioritizing experience, so as to replay important transitions more frequently, and therefore learn more efficiently. We use prioritized experience replay in Deep Q-Networks (DQN), a reinforcement learning algorithm that achieved human-level performance across many Atari games. DQN with prioritized experience replay achieves a new state-of-the-art, outperforming DQN with uniform replay on 41 out of 49 games.

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We tackle image question answering (ImageQA) problem by learning a convolutional neural network (CNN) with a dynamic parameter layer whose weights are determined adaptively based on questions. For the adaptive parameter prediction, we employ a separate parameter prediction network, which consists of gated recurrent unit (GRU) taking a question as its input and a fully-connected layer generating a set of candidate weights as its output. However, it is challenging to construct a parameter prediction network for a large number of parameters in the fully-connected dynamic parameter layer of the CNN. We reduce the complexity of this problem by incorporating a hashing technique, where the candidate weights given by the parameter prediction network are selected using a predefined hash function to determine individual weights in the dynamic parameter layer. The proposed network---joint network with the CNN for ImageQA and the parameter prediction network---is trained end-to-end through back-propagation, where its weights are initialized using a pre-trained CNN and GRU. The proposed algorithm illustrates the state-of-the-art performance on all available public ImageQA benchmarks.

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In this paper, we propose the "adversarial autoencoder" (AAE), which is a probabilistic autoencoder that uses the recently proposed generative adversarial networks (GAN) to perform variational inference by matching the aggregated posterior of the hidden code vector of the autoencoder with an arbitrary prior distribution. Matching the aggregated posterior to the prior ensures that generating from any part of prior space results in meaningful samples. As a result, the decoder of the adversarial autoencoder learns a deep generative model that maps the imposed prior to the data distribution. We show how the adversarial autoencoder can be used in applications such as semi-supervised classification, disentangling style and content of images, unsupervised clustering, dimensionality reduction and data visualization. We performed experiments on MNIST, Street View House Numbers and Toronto Face datasets and show that adversarial autoencoders achieve competitive results in generative modeling and semi-supervised classification tasks.

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Unlike human learning, machine learning often fails to handle changes between training (source) and test (target) input distributions. Such domain shifts, common in practical scenarios, severely damage the performance of conventional machine learning methods. Supervised domain adaptation methods have been proposed for the case when the target data have labels, including some that perform very well despite being "frustratingly easy" to implement. However, in practice, the target domain is often unlabeled, requiring unsupervised adaptation. We propose a simple, effective, and efficient method for unsupervised domain adaptation called CORrelation ALignment (CORAL). CORAL minimizes domain shift by aligning the second-order statistics of source and target distributions, without requiring any target labels. Even though it is extraordinarily simple--it can be implemented in four lines of Matlab code--CORAL performs remarkably well in extensive evaluations on standard benchmark datasets.

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We propose an image super-resolution method (SR) using a deeply-recursive convolutional network (DRCN). Our network has a very deep recursive layer (up to 16 recursions). Increasing recursion depth can improve performance without introducing new parameters for additional convolutions. Albeit advantages, learning a DRCN is very hard with a standard gradient descent method due to exploding/vanishing gradients. To ease the difficulty of training, we propose two extensions: recursive-supervision and skip-connection. Our method outperforms previous methods by a large margin.

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Recent work has shown that deep neural networks are capable of approximating both value functions and policies in reinforcement learning domains featuring continuous state and action spaces. However, to the best of our knowledge no previous work has succeeded at using deep neural networks in structured (parameterized) continuous action spaces. To fill this gap, this paper focuses on learning within the domain of simulated RoboCup soccer, which features a small set of discrete action types, each of which is parameterized with continuous variables. The best learned agent can score goals more reliably than the 2012 RoboCup champion agent. As such, this paper represents a successful extension of deep reinforcement learning to the class of parameterized action space MDPs.

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In recent years significant progress has been made in successfully training recurrent neural networks (RNNs) on sequence learning problems involving long range temporal dependencies. The progress has been made on three fronts: (a) Algorithmic improvements involving sophisticated optimization techniques, (b) network design involving complex hidden layer nodes and specialized recurrent layer connections and (c) weight initialization methods. In this paper, we focus on recently proposed weight initialization with identity matrix for the recurrent weights in a RNN. This initialization is specifically proposed for hidden nodes with Rectified Linear Unit (ReLU) non linearity. We offer a simple dynamical systems perspective on weight initialization process, which allows us to propose a modified weight initialization strategy. We show that this initialization technique leads to successfully training RNNs composed of ReLUs. We demonstrate that our proposal produces comparable or better solution for three toy problems involving long range temporal structure: the addition problem, the multiplication problem and the MNIST classification problem using sequence of pixels. In addition, we present results for a benchmark action recognition problem.

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This paper shows that simply prescribing "none of the above" labels to unlabeled data has a beneficial regularization effect to supervised learning. We call it universum prescription by the fact that the prescribed labels cannot be one of the supervised labels. In spite of its simplicity, universum prescription obtained competitive results in training deep convolutional networks for CIFAR-10, CIFAR-100, STL-10 and ImageNet datasets. A qualitative justification of these approaches using Rademacher complexity is presented. The effect of a regularization parameter -- probability of sampling from unlabeled data -- is also studied empirically.

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Probabilistic generative models can be used for compression, denoising, inpainting, texture synthesis, semi-supervised learning, unsupervised feature learning, and other tasks. Given this wide range of applications, it is not surprising that a lot of heterogeneity exists in the way these models are formulated, trained, and evaluated. As a consequence, direct comparison between models is often difficult. This article reviews mostly known but often underappreciated properties relating to the evaluation and interpretation of generative models with a focus on image models. In particular, we show that three of the currently most commonly used criteria---average log-likelihood, Parzen window estimates, and visual fidelity of samples---are largely independent of each other when the data is high-dimensional. Good performance with respect to one criterion therefore need not imply good performance with respect to the other criteria. Our results show that extrapolation from one criterion to another is not warranted and generative models need to be evaluated directly with respect to the application(s) they were intended for. In addition, we provide examples demonstrating that Parzen window estimates should generally be avoided.

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