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Improving Stochastic Gradient Descent with Feedback

Jayanth Koushik, Hiroaki Hayashi

In this paper we propose a simple and efficient method for improving stochastic gradient descent methods by using feedback from the objective function. The method tracks the relative changes in the objective function with a running average, and uses it to adaptively tune the learning rate in stochastic gradient descent. We specifically apply this idea to modify Adam, a popular algorithm for training deep neural networks. We conduct experiments to compare the resulting algorithm, which we call Eve, with state of the art methods used for training deep learning models. We train CNNs for image classification, and RNNs for language modeling and question answering. Our experiments show that Eve outperforms all other algorithms on these benchmark tasks. We also analyze the behavior of the feedback mechanism during the training process.

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Tying Word Vectors and Word Classifiers: A Loss Framework for Language Modeling

Hakan Inan, Khashayar Khosravi, Richard Socher

Recurrent neural networks have been very successful at predicting sequences of words in tasks such as language modeling. However, all such models are based on the conventional classification framework, where model is trained against one-hot targets, and each word is represented both as an input and as an output in isolation. This causes inefficiencies in learning both in terms of utilizing all of the information and in terms of the number of parameters needed to train. We introduce a novel theoretical framework that facilitates better learning in language modeling, and show that our framework leads to tying together the input embedding and the output projection matrices, greatly reducing the number of trainable variables. Our LSTM model lowers the state of the art word-level perplexity on the Penn Treebank to 68.5.

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Assessing the Ability of LSTMs to Learn Syntax-Sensitive Dependencies

Tal Linzen, Emmanuel Dupoux, Yoav Goldberg

The success of long short-term memory (LSTM) neural networks in language processing is typically attributed to their ability to capture long-distance statistical regularities. Linguistic regularities are often sensitive to syntactic structure; can such dependencies be captured by LSTMs, which do not have explicit structural representations? We begin addressing this question using number agreement in English subject-verb dependencies. We probe the architecture's grammatical competence both using training objectives with an explicit grammatical target (number prediction, grammaticality judgments) and using language models. In the strongly supervised settings, the LSTM achieved very high overall accuracy (less than 1% errors), but errors increased when sequential and structural information conflicted. The frequency of such errors rose sharply in the language-modeling setting. We conclude that LSTMs can capture a non-trivial amount of grammatical structure given targeted supervision, but stronger architectures may be required to further reduce errors; furthermore, the language modeling signal is insufficient for capturing syntax-sensitive dependencies, and should be supplemented with more direct supervision if such dependencies need to be captured.

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Adversarial Machine Learning at Scale

Alexey Kurakin, Ian Goodfellow, Samy Bengio

Adversarial examples are malicious inputs designed to fool machine learning models. They often transfer from one model to another, allowing attackers to mount black box attacks without knowledge of the target model's parameters. Adversarial training is the process of explicitly training a model on adversarial examples, in order to make it more robust to attack or to reduce its test error on clean inputs. So far, adversarial training has primarily been applied to small problems. In this research, we apply adversarial training to ImageNet. Our contributions include: (1) recommendations for how to succesfully scale adversarial training to large models and datasets, (2) the observation that adversarial training confers robustness to single-step attack methods, (3) the finding that multi-step attack methods are somewhat less transferable than single-step attack methods, so single-step attacks are the best for mounting black-box attacks, and (4) resolution of a "label leaking" effect that causes adversarially trained models to perform better on adversarial examples than on clean examples, because the adversarial example construction process uses the true label and the model can learn to exploit regularities in the construction process.

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Categorical Reparameterization with Gumbel-Softmax

Eric Jang, Shixiang Gu, Ben Poole

Categorical variables are a natural choice for representing discrete structure in the world. However, stochastic neural networks rarely use categorical latent variables due to the inability to backpropagate through samples. In this work, we present an efficient gradient estimator that replaces the non-differentiable sample from a categorical distribution with a differentiable sample from a novel Gumbel-Softmax distribution. This distribution has the essential property that it can be smoothly annealed into a categorical distribution. We show that our Gumbel-Softmax estimator outperforms state-of-the-art gradient estimators on structured output prediction and unsupervised generative modeling tasks with categorical latent variables, and enables large speedups on semi-supervised classification.

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Deep Convolutional Neural Network Design Patterns

Leslie N. Smith, Nicholay Topin

Recent research in the deep learning field has produced a plethora of new architectures. At the same time, a growing number of groups are applying deep learning to new applications and problems. Many of these groups might be composed of inexperienced deep learning practitioners who are baffled by the dizzying array of architecture choices and therefore use an older architecture, such as Alexnet. Here, we are attempting to bridge this gap by mining the collective knowledge contained in recent deep learning research to discover underlying principles for designing neural network architectures. In addition, we describe several architectural innovations, including Fractal of FractalNet, Stagewise Boosting Networks, and Taylor Series Networks (our Caffe code and prototxt files will be made publicly available). We hope others are inspired to build on this preliminary work.

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The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables

Chris J. Maddison, Andriy Mnih, Yee Whye Teh

The reparameterization trick enables the optimization of large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random variable with fixed distribution. After refactoring, the gradients of the loss propagated by the chain rule through the graph are low variance unbiased estimators of the gradients of the expected loss. While many continuous random variables have such reparameterizations, discrete random variables lack continuous reparameterizations due to the discontinuous nature of discrete states. In this work we introduce concrete random variables -- continuous relaxations of discrete random variables. The concrete distribution is a new family of distributions with closed form densities and a simple reparameterization. Whenever a discrete stochastic node of a computation graph can be refactored into a one-hot bit representation that is treated continuously, concrete stochastic nodes can be used with automatic differentiation to produce low-variance biased gradients of objectives (including objectives that depend on the log-likelihood of latent stochastic nodes) on the corresponding discrete graph. We demonstrate their effectiveness on density estimation and structured prediction tasks using neural networks.

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Dual Attention Networks for Multimodal Reasoning and Matching

Hyeonseob Nam, Jung-Woo Ha, Jeonghee Kim

We propose Dual Attention Networks (DANs) which jointly leverage visual and textual attention mechanisms to capture fine-grained interplay between vision and language. DANs attend to specific regions in images and words in text through multiple steps and gather essential information from both modalities. Based on this framework, we introduce two types of DANs for multimodal reasoning and matching, respectively. First, the reasoning model allows visual and textual attentions to steer each other during collaborative inference, which is useful for tasks such as Visual Question Answering (VQA). Second, the matching model exploits the two attention mechanisms to estimate the similarity between images and sentences by focusing on their shared semantics. Our extensive experiments validate the effectiveness of DANs in combining vision and language, achieving the state-of-the-art performance on public benchmarks for VQA and image-text matching.

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Stochastic Variational Deep Kernel Learning

Andrew Gordon Wilson, Zhiting Hu, Ruslan Salakhutdinov, Eric P. Xing

Deep kernel learning combines the non-parametric flexibility of kernel methods with the inductive biases of deep learning architectures. We propose a novel deep kernel learning model and stochastic variational inference procedure which generalizes deep kernel learning approaches to enable classification, multi-task learning, additive covariance structures, and stochastic gradient training. Specifically, we apply additive base kernels to subsets of output features from deep neural architectures, and jointly learn the parameters of the base kernels and deep network through a Gaussian process marginal likelihood objective. Within this framework, we derive an efficient form of stochastic variational inference which leverages local kernel interpolation, inducing points, and structure exploiting algebra. We show improved performance over stand alone deep networks, SVMs, and state of the art scalable Gaussian processes on several classification benchmarks, including an airline delay dataset containing 6 million training points, CIFAR, and ImageNet.

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Towards Lifelong Self-Supervision: A Deep Learning Direction for Robotics

Jay M. Wong

Despite outstanding success in vision amongst other domains, many of the recent deep learning approaches have evident drawbacks for robots. This manuscript surveys recent work in the literature that pertain to applying deep learning systems to the robotics domain, either as means of estimation or as a tool to resolve motor commands directly from raw percepts. These recent advances are only a piece to the puzzle. We suggest that deep learning as a tool alone is insufficient in building a unified framework to acquire general intelligence. For this reason, we complement our survey with insights from cognitive development and refer to ideas from classical control theory, producing an integrated direction for a lifelong learning architecture.

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TorchCraft: a Library for Machine Learning Research on Real-Time Strategy Games

Gabriel Synnaeve, Nantas Nardelli, Alex Auvolat, Soumith Chintala, Timothée Lacroix, Zeming Lin, Florian Richoux, Nicolas Usunier

We present TorchCraft, an open-source library that enables deep learning research on Real-Time Strategy (RTS) games such as StarCraft: Brood War, by making it easier to control these games from a machine learning framework, here Torch. This white paper argues for using RTS games as a benchmark for AI research, and describes the design and components of TorchCraft.

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Full-Capacity Unitary Recurrent Neural Networks

Scott Wisdom, Thomas Powers, John R. Hershey, Jonathan Le Roux, Les Atlas

Recurrent neural networks are powerful models for processing sequential data, but they are generally plagued by vanishing and exploding gradient problems. Unitary recurrent neural networks (uRNNs), which use unitary recurrence matrices, have recently been proposed as a means to avoid these issues. However, in previous experiments, the recurrence matrices were restricted to be a product of parameterized unitary matrices, and an open question remains: when does such a parameterization fail to represent all unitary matrices, and how does this restricted representational capacity limit what can be learned? To address this question, we propose full-capacity uRNNs that optimize their recurrence matrix over all unitary matrices, leading to significantly improved performance over uRNNs that use a restricted-capacity recurrence matrix. Our contribution consists of two main components. First, we provide a theoretical argument to determine if a unitary parameterization has restricted capacity. Using this argument, we show that a recently proposed unitary parameterization has restricted capacity for hidden state dimension greater than 7. Second, we show how a complete, full-capacity unitary recurrence matrix can be optimized over the differentiable manifold of unitary matrices. The resulting multiplicative gradient step is very simple and does not require gradient clipping or learning rate adaptation. We confirm the utility of our claims by empirically evaluating our new full-capacity uRNNs on both synthetic and natural data, achieving superior performance compared to both LSTMs and the original restricted-capacity uRNNs.

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Neural Symbolic Machines: Learning Semantic Parsers on Freebase with Weak Supervision

Chen Liang, Jonathan Berant, Quoc Le, Kenneth D. Forbus, Ni Lao

Extending the success of deep neural networks to natural language understanding and symbolic reasoning requires complex operations and external memory. Recent neural program induction approaches have attempted to address this problem, but are typically limited to differentiable memory, and consequently cannot scale beyond small synthetic tasks. In this work, we propose the Manager-Programmer-Computer framework, which integrates neural networks with non-differentiable memory to support abstract, scalable and precise operations through a friendly neural computer interface. Specifically, we introduce a Neural Symbolic Machine, which contains a sequence-to-sequence neural "programmer", and a non-differentiable "computer" that is a Lisp interpreter with code assist. To successfully apply REINFORCE for training, we augment it with approximate gold programs found by an iterative maximum likelihood training process. NSM is able to learn a semantic parser from weak supervision over a large knowledge base. It achieves new state-of-the-art performance on WebQuestionsSP, a challenging semantic parsing dataset, with weak supervision. Compared to previous approaches, NSM is end-to-end, therefore does not rely on feature engineering or domain specific knowledge.

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Neural Machine Translation in Linear Time

Nal Kalchbrenner, Lasse Espeholt, Karen Simonyan, Aaron van den Oord, Alex Graves, Koray Kavukcuoglu

We present a neural architecture for sequence processing. The ByteNet is a stack of two dilated convolutional neural networks, one to encode the source sequence and one to decode the target sequence, where the target network unfolds dynamically to generate variable length outputs. The ByteNet has two core properties: it runs in time that is linear in the length of the sequences and it preserves the sequences' temporal resolution. The ByteNet decoder attains state-of-the-art performance on character-level language modelling and outperforms the previous best results obtained with recurrent neural networks. The ByteNet also achieves a performance on raw character-level machine translation that approaches that of the best neural translation models that run in quadratic time. The implicit structure learnt by the ByteNet mirrors the expected alignments between the sequences.

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Compressed Learning: A Deep Neural Network Approach

Amir Adler, Michael Elad, Michael Zibulevsky

Compressed Learning (CL) is a joint signal processing and machine learning framework for inference from a signal, using a small number of measurements obtained by linear projections of the signal. In this paper we present an end-to-end deep learning approach for CL, in which a network composed of fully-connected layers followed by convolutional layers perform the linear sensing and non-linear inference stages. During the training phase, the sensing matrix and the non-linear inference operator are jointly optimized, and the proposed approach outperforms state-of-the-art for the task of image classification. For example, at a sensing rate of 1% (only 8 measurements of 28 X 28 pixels images), the classification error for the MNIST handwritten digits dataset is 6.46% compared to 41.06% with state-of-the-art.

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Conditional Image Synthesis With Auxiliary Classifier GANs

Augustus Odena, Christopher Olah, Jonathon Shlens

Synthesizing high resolution photorealistic images has been a long-standing challenge in machine learning. In this paper we introduce new methods for the improved training of generative adversarial networks (GANs) for image synthesis. We construct a variant of GANs employing label conditioning that results in 128x128 resolution image samples exhibiting global coherence. We expand on previous work for image quality assessment to provide two new analyses for assessing the discriminability and diversity of samples from class-conditional image synthesis models. These analyses demonstrate that high resolution samples provide class information not present in low resolution samples. Across 1000 ImageNet classes, 128x128 samples are more than twice as discriminable as artificially resized 32x32 samples. In addition, 84.7% of the classes have samples exhibiting diversity comparable to real ImageNet data.

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Improving Sampling from Generative Autoencoders with Markov Chains

Kai Arulkumaran, Antonia Creswell, Anil Anthony Bharath

We focus on generative autoencoders, such as variational or adversarial autoencoders, which jointly learn a generative model alongside an inference model. We define generative autoencoders as autoencoders which are trained to softly enforce a prior on the latent distribution learned by the model. However, the model does not necessarily learn to match the prior. We formulate a Markov chain Monte Carlo (MCMC) sampling process, equivalent to iteratively encoding and decoding, which allows us to sample from the learned latent distribution. Using this we can improve the quality of samples drawn from the model, especially when the learned distribution is far from the prior. Using MCMC sampling, we also reveal previously unseen differences between generative autoencoders trained either with or without the denoising criterion.

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Professor Forcing: A New Algorithm for Training Recurrent Networks

Alex Lamb, Anirudh Goyal, Ying Zhang, Saizheng Zhang, Aaron Courville, Yoshua Bengio

The Teacher Forcing algorithm trains recurrent networks by supplying observed sequence values as inputs during training and using the network's own one-step-ahead predictions to do multi-step sampling. We introduce the Professor Forcing algorithm, which uses adversarial domain adaptation to encourage the dynamics of the recurrent network to be the same when training the network and when sampling from the network over multiple time steps. We apply Professor Forcing to language modeling, vocal synthesis on raw waveforms, handwriting generation, and image generation. Empirically we find that Professor Forcing acts as a regularizer, improving test likelihood on character level Penn Treebank and sequential MNIST. We also find that the model qualitatively improves samples, especially when sampling for a large number of time steps. This is supported by human evaluation of sample quality. Trade-offs between Professor Forcing and Scheduled Sampling are discussed. We produce T-SNEs showing that Professor Forcing successfully makes the dynamics of the network during training and sampling more similar.

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Operator Variational Inference

Rajesh Ranganath, Jaan Altosaar, Dustin Tran, David M. Blei

Variational inference is an umbrella term for algorithms which cast Bayesian inference as optimization. Classically, variational inference uses the Kullback-Leibler divergence to define the optimization. Though this divergence has been widely used, the resultant posterior approximation can suffer from undesirable statistical properties. To address this, we reexamine variational inference from its roots as an optimization problem. We use operators, or functions of functions, to design variational objectives. As one example, we design a variational objective with a Langevin-Stein operator. We develop a black box algorithm, operator variational inference (OPVI), for optimizing any operator objective. Importantly, operators enable us to make explicit the statistical and computational tradeoffs for variational inference. We can characterize different properties of variational objectives, such as objectives that admit data subsampling---allowing inference to scale to massive data---as well as objectives that admit variational programs---a rich class of posterior approximations that does not require a tractable density. We illustrate the benefits of OPVI on a mixture model and a generative model of images.

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Scaling Memory-Augmented Neural Networks with Sparse Reads and Writes

Jack W Rae, Jonathan J Hunt, Tim Harley, Ivo Danihelka, Andrew Senior, Greg Wayne, Alex Graves, Timothy P Lillicrap

Neural networks augmented with external memory have the ability to learn algorithmic solutions to complex tasks. These models appear promising for applications such as language modeling and machine translation. However, they scale poorly in both space and time as the amount of memory grows --- limiting their applicability to real-world domains. Here, we present an end-to-end differentiable memory access scheme, which we call Sparse Access Memory (SAM), that retains the representational power of the original approaches whilst training efficiently with very large memories. We show that SAM achieves asymptotic lower bounds in space and time complexity, and find that an implementation runs $1,\!000\times$ faster and with $3,\!000\times$ less physical memory than non-sparse models. SAM learns with comparable data efficiency to existing models on a range of synthetic tasks and one-shot Omniglot character recognition, and can scale to tasks requiring $100,\!000$s of time steps and memories. As well, we show how our approach can be adapted for models that maintain temporal associations between memories, as with the recently introduced Differentiable Neural Computer.

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