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Exponential expressivity in deep neural networks through transient chaos

Ben Poole, Subhaneil Lahiri, Maithra Raghu, Jascha Sohl-Dickstein, Surya Ganguli

We combine Riemannian geometry with the mean field theory of high dimensional chaos to study the nature of signal propagation in generic, deep neural networks with random weights. Our results reveal an order-to-chaos expressivity phase transition, with networks in the chaotic phase computing nonlinear functions whose global curvature grows exponentially with depth but not width. We prove this generic class of deep random functions cannot be efficiently computed by any shallow network, going beyond prior work restricted to the analysis of single functions. Moreover, we formalize and quantitatively demonstrate the long conjectured idea that deep networks can disentangle highly curved manifolds in input space into flat manifolds in hidden space. Our theoretical analysis of the expressive power of deep networks broadly applies to arbitrary nonlinearities, and provides a quantitative underpinning for previously abstract notions about the geometry of deep functions.

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On the Expressive Power of Deep Neural Networks

Maithra Raghu, Ben Poole, Jon Kleinberg, Surya Ganguli, Jascha Sohl-Dickstein

We propose a new approach to the problem of neural network expressivity, which seeks to characterize how structural properties of a neural network family affect the functions it is able to compute. Our approach is based on an interrelated set of measures of expressivity, unified by the novel notion of trajectory length, which measures how the output of a network changes as the input sweeps along a one-dimensional path. Our findings can be summarized as follows: (1) The complexity of the computed function grows exponentially with depth. (2) All weights are not equal: trained networks are more sensitive to their lower (initial) layer weights. (3) Regularizing on trajectory length (trajectory regularization) is a simpler alternative to batch normalization, with the same performance.

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Conditional Image Generation with PixelCNN Decoders

Aaron van den Oord, Nal Kalchbrenner, Oriol Vinyals, Lasse Espeholt, Alex Graves, Koray Kavukcuoglu

This work explores conditional image generation with a new image density model based on the PixelCNN architecture. The model can be conditioned on any vector, including descriptive labels or tags, or latent embeddings created by other networks. When conditioned on class labels from the ImageNet database, the model is able to generate diverse, realistic scenes representing distinct animals, objects, landscapes and structures. When conditioned on an embedding produced by a convolutional network given a single image of an unseen face, it generates a variety of new portraits of the same person with different facial expressions, poses and lighting conditions. We also show that conditional PixelCNN can serve as a powerful decoder in an image autoencoder. Additionally, the gated convolutional layers in the proposed model improve the log-likelihood of PixelCNN to match the state-of-the-art performance of PixelRNN on ImageNet, with greatly reduced computational cost.

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Machine Learning meets Data-Driven Journalism: Boosting International Understanding and Transparency in News Coverage

Elena Erdmann, Karin Boczek, Lars Koppers, Gerret von Nordheim, Christian Pölitz, Alejandro Molina, Katharina Morik, Henrik Müller, Jörg Rahnenführer, Kristian Kersting

Migration crisis, climate change or tax havens: Global challenges need global solutions. But agreeing on a joint approach is difficult without a common ground for discussion. Public spheres are highly segmented because news are mainly produced and received on a national level. Gain- ing a global view on international debates about important issues is hindered by the enormous quantity of news and by language barriers. Media analysis usually focuses only on qualitative re- search. In this position statement, we argue that it is imperative to pool methods from machine learning, journalism studies and statistics to help bridging the segmented data of the international public sphere, using the Transatlantic Trade and Investment Partnership (TTIP) as a case study.

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Improving Variational Inference with Inverse Autoregressive Flow

Diederik P. Kingma, Tim Salimans, Rafal Jozefowicz, Xi Chen, Ilya Sutskever, Max Welling

The framework of normalizing flows provides a general strategy for flexible variational inference of posteriors over latent variables. We propose a new type of normalizing flow, inverse autoregressive flow (IAF), that, in contrast to earlier published flows, scales well to high-dimensional latent spaces. The proposed flow consists of a chain of invertible transformations, where each transformation is based on an autoregressive neural network. In experiments, we show that IAF significantly improves upon diagonal Gaussian approximate posteriors. In addition, we demonstrate that a novel type of variational autoencoder, coupled with IAF, is competitive with neural autoregressive models in terms of attained log-likelihood on natural images, while allowing significantly faster synthesis.

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Strategic Attentive Writer for Learning Macro-Actions

Alexander, Vezhnevets, Volodymyr Mnih, John Agapiou, Simon Osindero, Alex Graves, Oriol Vinyals, Koray Kavukcuoglu

We present a novel deep recurrent neural network architecture that learns to build implicit plans in an end-to-end manner by purely interacting with an environment in reinforcement learning setting. The network builds an internal plan, which is continuously updated upon observation of the next input from the environment. It can also partition this internal representation into contiguous sub- sequences by learning for how long the plan can be committed to - i.e. followed without re-planing. Combining these properties, the proposed model, dubbed STRategic Attentive Writer (STRAW) can learn high-level, temporally abstracted macro- actions of varying lengths that are solely learnt from data without any prior information. These macro-actions enable both structured exploration and economic computation. We experimentally demonstrate that STRAW delivers strong improvements on several ATARI games by employing temporally extended planning strategies (e.g. Ms. Pacman and Frostbite). It is at the same time a general algorithm that can be applied on any sequence data. To that end, we also show that when trained on text prediction task, STRAW naturally predicts frequent n-grams (instead of macro-actions), demonstrating the generality of the approach.

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Progressive Neural Networks

Andrei A. Rusu, Neil C. Rabinowitz, Guillaume Desjardins, Hubert Soyer, James Kirkpatrick, Koray Kavukcuoglu, Razvan Pascanu, Raia Hadsell

Learning to solve complex sequences of tasks--while both leveraging transfer and avoiding catastrophic forgetting--remains a key obstacle to achieving human-level intelligence. The progressive networks approach represents a step forward in this direction: they are immune to forgetting and can leverage prior knowledge via lateral connections to previously learned features. We evaluate this architecture extensively on a wide variety of reinforcement learning tasks (Atari and 3D maze games), and show that it outperforms common baselines based on pretraining and finetuning. Using a novel sensitivity measure, we demonstrate that transfer occurs at both low-level sensory and high-level control layers of the learned policy.

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Learning to learn by gradient descent by gradient descent

Marcin Andrychowicz, Misha Denil, Sergio Gomez, Matthew W. Hoffman, David Pfau, Tom Schaul, Nando de Freitas

The move from hand-designed features to learned features in machine learning has been wildly successful. In spite of this, optimization algorithms are still designed by hand. In this paper we show how the design of an optimization algorithm can be cast as a learning problem, allowing the algorithm to learn to exploit structure in the problems of interest in an automatic way. Our learned algorithms, implemented by LSTMs, outperform generic, hand-designed competitors on the tasks for which they are trained, and also generalize well to new tasks with similar structure. We demonstrate this on a number of tasks, including simple convex problems, training neural networks, and styling images with neural art.

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DeepMath - Deep Sequence Models for Premise Selection

Alex A. Alemi, Francois Chollet, Geoffrey Irving, Christian Szegedy, Josef Urban

We study the effectiveness of neural sequence models for premise selection in automated theorem proving, one of the main bottlenecks in the formalization of mathematics. We propose a two stage approach for this task that yields good results for the premise selection task on the Mizar corpus while avoiding the hand-engineered features of existing state-of-the-art models. To our knowledge, this is the first time deep learning has been applied to theorem proving.

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Rationalizing Neural Predictions

Tao Lei, Regina Barzilay, Tommi Jaakkola

Prediction without justification has limited applicability. As a remedy, we learn to extract pieces of input text as justifications -- rationales -- that are tailored to be short and coherent, yet sufficient for making the same prediction. Our approach combines two modular components, generator and encoder, which are trained to operate well together. The generator specifies a distribution over text fragments as candidate rationales and these are passed through the encoder for prediction. Rationales are never given during training. Instead, the model is regularized by desiderata for rationales. We evaluate the approach on multi-aspect sentiment analysis against manually annotated test cases. Our approach outperforms attention-based baseline by a significant margin. We also successfully illustrate the method on the question retrieval task.

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Matching Networks for One Shot Learning

Oriol Vinyals, Charles Blundell, Timothy Lillicrap, Koray Kavukcuoglu, Daan Wierstra

Learning from a few examples remains a key challenge in machine learning. Despite recent advances in important domains such as vision and language, the standard supervised deep learning paradigm does not offer a satisfactory solution for learning new concepts rapidly from little data. In this work, we employ ideas from metric learning based on deep neural features and from recent advances that augment neural networks with external memories. Our framework learns a network that maps a small labelled support set and an unlabelled example to its label, obviating the need for fine-tuning to adapt to new class types. We then define one-shot learning problems on vision (using Omniglot, ImageNet) and language tasks. Our algorithm improves one-shot accuracy on ImageNet from 87.6% to 93.2% and from 88.0% to 93.8% on Omniglot compared to competing approaches. We also demonstrate the usefulness of the same model on language modeling by introducing a one-shot task on the Penn Treebank.

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External Lexical Information for Multilingual Part-of-Speech Tagging

Benoît Sagot

Morphosyntactic lexicons and word vector representations have both proven useful for improving the accuracy of statistical part-of-speech taggers. Here we compare the performances of four systems on datasets covering 16 languages, two of these systems being feature-based (MEMMs and CRFs) and two of them being neural-based (bi-LSTMs). We show that, on average, all four approaches perform similarly and reach state-of-the-art results. Yet better performances are obtained with our feature-based models on lexically richer datasets (e.g. for morphologically rich languages), whereas neural-based results are higher on datasets with less lexical variability (e.g. for English). These conclusions hold in particular for the MEMM models relying on our system MElt, which benefited from newly designed features. This shows that, under certain conditions, feature-based approaches enriched with morphosyntactic lexicons are competitive with respect to neural methods.

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InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets

Xi Chen, Yan Duan, Rein Houthooft, John Schulman, Ilya Sutskever, Pieter Abbeel

This paper describes InfoGAN, an information-theoretic extension to the Generative Adversarial Network that is able to learn disentangled representations in a completely unsupervised manner. InfoGAN is a generative adversarial network that also maximizes the mutual information between a small subset of the latent variables and the observation. We derive a lower bound to the mutual information objective that can be optimized efficiently, and show that our training procedure can be interpreted as a variation of the Wake-Sleep algorithm. Specifically, InfoGAN successfully disentangles writing styles from digit shapes on the MNIST dataset, pose from lighting of 3D rendered images, and background digits from the central digit on the SVHN dataset. It also discovers visual concepts that include hair styles, presence/absence of eyeglasses, and emotions on the CelebA face dataset. Experiments show that InfoGAN learns interpretable representations that are competitive with representations learned by existing fully supervised methods.

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Improved Techniques for Training GANs

Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, Xi Chen

We present a variety of new architectural features and training procedures that we apply to the generative adversarial networks (GANs) framework. We focus on two applications of GANs: semi-supervised learning, and the generation of images that humans find visually realistic. Unlike most work on generative models, our primary goal is not to train a model that assigns high likelihood to test data, nor do we require the model to be able to learn well without using any labels. Using our new techniques, we achieve state-of-the-art results in semi-supervised classification on MNIST, CIFAR-10 and SVHN. The generated images are of high quality as confirmed by a visual Turing test: our model generates MNIST samples that humans cannot distinguish from real data, and CIFAR-10 samples that yield a human error rate of 21.3%. We also present ImageNet samples with unprecedented resolution and show that our methods enable the model to learn recognizable features of ImageNet classes.

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Memory-Efficient Backpropagation Through Time

Audrūnas Gruslys, Remi Munos, Ivo Danihelka, Marc Lanctot, Alex Graves

We propose a novel approach to reduce memory consumption of the backpropagation through time (BPTT) algorithm when training recurrent neural networks (RNNs). Our approach uses dynamic programming to balance a trade-off between caching of intermediate results and recomputation. The algorithm is capable of tightly fitting within almost any user-set memory budget while finding an optimal execution policy minimizing the computational cost. Computational devices have limited memory capacity and maximizing a computational performance given a fixed memory budget is a practical use-case. We provide asymptotic computational upper bounds for various regimes. The algorithm is particularly effective for long sequences. For sequences of length 1000, our algorithm saves 95\% of memory usage while using only one third more time per iteration than the standard BPTT.

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Key-Value Memory Networks for Directly Reading Documents

Alexander Miller, Adam Fisch, Jesse Dodge, Amir-Hossein Karimi, Antoine Bordes, Jason Weston

Directly reading documents and being able to answer questions from them is an unsolved challenge. To avoid its inherent difficulty, question answering (QA) has been directed towards using Knowledge Bases (KBs) instead, which has proven effective. Unfortunately KBs often suffer from being too restrictive, as the schema cannot support certain types of answers, and too sparse, e.g. Wikipedia contains much more information than Freebase. In this work we introduce a new method, Key-Value Memory Networks, that makes reading documents more viable by utilizing different encodings in the addressing and output stages of the memory read operation. To compare using KBs, information extraction or Wikipedia documents directly in a single framework we construct an analysis tool, WikiMovies, a QA dataset that contains raw text alongside a preprocessed KB, in the domain of movies. Our method reduces the gap between all three settings. It also achieves state-of-the-art results on the existing WikiQA benchmark.

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Edinburgh Neural Machine Translation Systems for WMT 16

Rico Sennrich, Barry Haddow, Alexandra Birch

We participated in the WMT 2016 shared news translation task by building neural translation systems for four language pairs, each trained in both directions: English<->Czech, English<->German, English<->Romanian and English<->Russian. Our systems are based on an attentional encoder-decoder, using BPE subword segmentation for open-vocabulary translation with a fixed vocabulary. We experimented with using automatic back-translations of the monolingual News corpus as additional training data, pervasive dropout, and target-bidirectional models. All reported methods give substantial improvements, and we see improvements of 4.3--11.2 BLEU over our baseline systems. In the human evaluation, our systems were the (tied) best constrained system for 7 out of 8 translation directions in which we participated.

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Safe and Efficient Off-Policy Reinforcement Learning

Rémi Munos, Tom Stepleton, Anna Harutyunyan, Marc G. Bellemare

In this work, we take a fresh look at some old and new algorithms for off-policy, return-based reinforcement learning. Expressing these in a common form, we derive a novel algorithm, Retrace($\lambda$), with three desired properties: (1) low variance; (2) safety, as it safely uses samples collected from any behaviour policy, whatever its degree of "off-policyness"; and (3) efficiency, as it makes the best use of samples collected from near on-policy behaviour policies. We analyse the contractive nature of the related operator under both off-policy policy evaluation and control settings and derive online sample-based algorithms. To our knowledge, this is the first return-based off-policy control algorithm converging a.s. to $Q^*$ without the GLIE assumption (Greedy in the Limit with Infinite Exploration). As a corollary, we prove the convergence of Watkins' Q($\lambda$), which was still an open problem. We illustrate the benefits of Retrace($\lambda$) on a standard suite of Atari 2600 games.

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Convolution by Evolution: Differentiable Pattern Producing Networks

Chrisantha Fernando, Dylan Banarse, Malcolm Reynolds, Frederic Besse, David Pfau, Max Jaderberg, Marc Lanctot, Daan Wierstra

In this work we introduce a differentiable version of the Compositional Pattern Producing Network, called the DPPN. Unlike a standard CPPN, the topology of a DPPN is evolved but the weights are learned. A Lamarckian algorithm, that combines evolution and learning, produces DPPNs to reconstruct an image. Our main result is that DPPNs can be evolved/trained to compress the weights of a denoising autoencoder from 157684 to roughly 200 parameters, while achieving a reconstruction accuracy comparable to a fully connected network with more than two orders of magnitude more parameters. The regularization ability of the DPPN allows it to rediscover (approximate) convolutional network architectures embedded within a fully connected architecture. Such convolutional architectures are the current state of the art for many computer vision applications, so it is satisfying that DPPNs are capable of discovering this structure rather than having to build it in by design. DPPNs exhibit better generalization when tested on the Omniglot dataset after being trained on MNIST, than directly encoded fully connected autoencoders. DPPNs are therefore a new framework for integrating learning and evolution.

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Learning Language Games through Interaction

Sida I. Wang, Percy Liang, Christopher D. Manning

We introduce a new language learning setting relevant to building adaptive natural language interfaces. It is inspired by Wittgenstein's language games: a human wishes to accomplish some task (e.g., achieving a certain configuration of blocks), but can only communicate with a computer, who performs the actual actions (e.g., removing all red blocks). The computer initially knows nothing about language and therefore must learn it from scratch through interaction, while the human adapts to the computer's capabilities. We created a game in a blocks world and collected interactions from 100 people playing it. First, we analyze the humans' strategies, showing that using compositionality and avoiding synonyms correlates positively with task performance. Second, we compare computer strategies, showing how to quickly learn a semantic parsing model from scratch, and that modeling pragmatics further accelerates learning for successful players.

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