ICLR 2017 Papers

We introduce a method to stabilize Generative Adversarial Networks (GANs) by defining the generator objective with respect to an unrolled optimization of the discriminator. This allows training to be adjusted between using the optimal discriminator in the generator's objective, which is ideal but infeasible in practice, and using the current value of the discriminator, which is often unstable and leads to poor solutions. We show how this technique solves the common problem of mode collapse, stabilizes training of GANs with complex recurrent generators, and increases diversity and coverage of the data distribution by the generator.

Two potential bottlenecks on the expressiveness of recurrent neural networks (RNNs) are their ability to store information about the task in their parameters, and to store information about the input history in their units. We show experimentally that all common RNN architectures achieve nearly the same per-task and per-unit capacity bounds with careful training, for a variety of tasks and stacking depths. They can store an amount of task information which is linear in the number of parameters, and is approximately 5 bits per parameter. They can additionally store approximately one real number from their input history per hidden unit. We further find that for several tasks it is the per-task parameter capacity bound that determines performance. These results suggest that many previous results comparing RNN architectures are driven primarily by differences in training effectiveness, rather than differences in capacity. Supporting this observation, we compare training difficulty for several architectures, and show that vanilla RNNs are far more difficult to train, yet have slightly higher capacity. Finally, we propose two novel RNN architectures, one of which is easier to train than the LSTM or GRU for deeply stacked architectures.

Topic models are one of the most popular methods for learning representations of text, but a major challenge is that any change to the topic model requires mathematically deriving a new inference algorithm. A promising approach to address this problem is autoencoding variational Bayes (AEVB), but it has proven diffi- cult to apply to topic models in practice. We present what is to our knowledge the first effective AEVB based inference method for latent Dirichlet allocation (LDA), which we call Autoencoded Variational Inference For Topic Model (AVITM). This model tackles the problems caused for AEVB by the Dirichlet prior and by component collapsing. We find that AVITM matches traditional methods in accuracy with much better inference time. Indeed, because of the inference network, we find that it is unnecessary to pay the computational cost of running variational optimization on test data. Because AVITM is black box, it is readily applied to new topic models. As a dramatic illustration of this, we present a new topic model called ProdLDA, that replaces the mixture model in LDA with a product of experts. By changing only one line of code from LDA, we find that ProdLDA yields much more interpretable topics, even if LDA is trained via collapsed Gibbs sampling.

Regularization is key for deep learning since it allows training more complex models while keeping lower levels of overfitting. However, the most prevalent regularizations do not leverage all the capacity of the models since they rely on reducing the effective number of parameters. Feature decorrelation is an alternative for using the full capacity of the models but the overfitting reduction margins are too narrow given the overhead it introduces. In this paper, we show that regularizing negatively correlated features is an obstacle for effective decorrelation and present OrthoReg, a novel regularization technique that locally enforces feature orthogonality. As a result, imposing locality constraints in feature decorrelation removes interferences between negatively correlated feature weights, allowing the regularizer to reach higher decorrelation bounds, and reducing the overfitting more effectively. In particular, we show that the models regularized with OrthoReg have higher accuracy bounds even when batch normalization and dropout are present. Moreover, since our regularization is directly performed on the weights, it is especially suitable for fully convolutional neural networks, where the weight space is constant compared to the feature map space. As a result, we are able to reduce the overfitting of state-of-the-art CNNs on CIFAR-10, CIFAR-100, and SVHN.

Current language modeling architectures often use recurrent neural networks. Recently, various methods for incorporating differentiable memory into these architectures have been proposed. When predicting the next token, these models query information from a memory of the recent history and thus can facilitate learning mid- and long-range dependencies. However, conventional attention models produce a single output vector per time step that is used for predicting the next token as well as the key and value of a differentiable memory of the history of tokens. In this paper, we propose a key-value attention mechanism that produces separate representations for the key and value of a memory, and for a representation that encodes the next-word distribution. This usage of past memories outperforms existing memory-augmented neural language models on two corpora. Yet, we found that it mainly utilizes past memory only of the previous five representations. This led to the unexpected main finding that a much simpler model which simply uses a concatenation of output representations from the previous three-time steps is on par with more sophisticated memory-augmented neural language models.

We present a novel layerwise optimization algorithm for the learning objective of Piecewise-Linear Convolutional Neural Networks (PL-CNNs), a large class of convolutional neural networks. Specifically, PL-CNNs employ piecewise linear non-linearities such as the commonly used ReLU and max-pool, and an SVM classifier as the final layer. The key observation of our approach is that the prob- lem corresponding to the parameter estimation of a layer can be formulated as a difference-of-convex (DC) program, which happens to be a latent structured SVM. We optimize the DC program using the concave-convex procedure, which requires us to iteratively solve a structured SVM problem. This allows to design an opti- mization algorithm with an optimal learning rate that does not require any tuning. Using the MNIST, CIFAR and ImageNet data sets, we show that our approach always improves over the state of the art variants of backpropagation and scales to large data and large network settings.

In recent years, Deep Learning (DL) has found great success in domains such as multimedia understanding. However, the complex nature of multimedia data makes it difficult to develop DL-based software. The state-of-the-art tools, such as Caffe, TensorFlow, Torch7, and CNTK, while are successful in their applicable domains, are programming libraries with fixed user interface, internal representation, and execution environment. This makes it difficult to implement portable and customized DL applications. In this paper, we present DeepDSL, a domain specific language (DSL) embedded in Scala, that compiles deep networks written in DeepDSL to Java source code. Deep DSL provides (1) intuitive constructs to support compact encoding of deep networks; (2) symbolic gradient derivation of the networks; (3) static analysis for memory consumption and error detection; and (4) DSL-level optimization to improve memory and runtime efficiency. DeepDSL programs are compiled into compact, efficient, customizable, and portable Java source code, which operates the CUDA and CUDNN interfaces running on NVIDIA GPU via a Java Native Interface (JNI) library. We evaluated DeepDSL with a number of popular DL networks. Our experiments show that the compiled programs have very competitive runtime performance and memory efficiency compared to the existing libraries.

We present the Neural Physics Engine (NPE), a framework for learning simulators of intuitive physics that naturally generalize across variable object count and different scene configurations. We propose a factorization of a physical scene into composable object-based representations and a neural network architecture whose compositional structure factorizes object dynamics into pairwise interactions. Like a symbolic physics engine, the NPE is endowed with generic notions of objects and their interactions; realized as a neural network, it can be trained via stochastic gradient descent to adapt to specific object properties and dynamics of different worlds. We evaluate the efficacy of our approach on simple rigid body dynamics in two-dimensional worlds. By comparing to less structured architectures, we show that the NPE's compositional representation of the structure in physical interactions improves its ability to predict movement, generalize across variable object count and different scene configurations, and infer latent properties of objects such as mass.

Our formal understanding of the inductive bias that drives the success of convolutional networks on computer vision tasks is limited. In particular, it is unclear what makes hypotheses spaces born from convolution and pooling operations so suitable for natural images. In this paper we study the ability of convolutional networks to model correlations among regions of their input. We theoretically analyze convolutional arithmetic circuits, and empirically validate our findings on other types of convolutional networks as well. Correlations are formalized through the notion of separation rank, which for a given partition of the input, measures how far a function is from being separable. We show that a polynomially sized deep network supports exponentially high separation ranks for certain input partitions, while being limited to polynomial separation ranks for others. The network's pooling geometry effectively determines which input partitions are favored, thus serves as a means for controlling the inductive bias. Contiguous pooling windows as commonly employed in practice favor interleaved partitions over coarse ones, orienting the inductive bias towards the statistics of natural images. Other pooling schemes lead to different preferences, and this allows tailoring the network to data that departs from the usual domain of natural imagery. In addition to analyzing deep networks, we show that shallow ones support only linear separation ranks, and by this gain insight into the benefit of functions brought forth by depth - they are able to efficiently model strong correlation under favored partitions of the input.

We propose a framework for detecting action patterns from motion sequences and modeling the sensory-motor relationship of animals, using a generative recurrent neural network. The network has a discriminative part (classifying actions) and a generative part (predicting motion), whose recurrent cells are laterally connected, allowing higher levels of the network to represent high level behavioral phenomena. We test our framework on two types of tracking data, fruit fly behavior and online handwriting. Our results show that 1) taking advantage of unlabeled sequences, by predicting future motion, significantly improves action detection performance when training labels are scarce, 2) the network learns to represent high level phenomena such as writer identity and fly gender, without supervision, and 3) simulated motion trajectories, generated by treating motion prediction as input to the network, look realistic and may be used to qualitatively evaluate whether the model has learnt generative control rules.

Many machine learning systems are built to solve the hardest examples of a particular task, which often makes them large and expensive to run---especially with respect to the easier examples, which might require much less computation. For an agent with a limited computational budget, this "one-size-fits-all" approach may result in the agent wasting valuable computation on easy examples, while not spending enough on hard examples. Rather than learning a single, fixed policy for solving all instances of a task, we introduce a metacontroller which learns to optimize a sequence of "imagined" internal simulations over predictive models of the world in order to construct a more informed, and more economical, solution. The metacontroller component is a model-free reinforcement learning agent, which decides both how many iterations of the optimization procedure to run, as well as which model to consult on each iteration. The models (which we call "experts") can be state transition models, action-value functions, or any other mechanism that provides information useful for solving the task, and can be learned on-policy or off-policy in parallel with the metacontroller. When the metacontroller, controller, and experts were trained with "interaction networks" (Battaglia et al., 2016) as expert models, our approach was able to solve a challenging decision-making problem under complex non-linear dynamics. The metacontroller learned to adapt the amount of computation it performed to the difficulty of the task, and learned how to choose which experts to consult by factoring in both their reliability and individual computational resource costs. This allowed the metacontroller to achieve a lower overall cost (task loss plus computational cost) than more traditional fixed policy approaches. These results demonstrate that our approach is a powerful framework for using rich forward models for efficient model-based reinforcement learning.

The loss surface of deep neural networks has recently attracted interest in the optimization and machine learning communities as a prime example of high-dimensional non-convex problem. Some insights were recently gained using spin glass models and mean-field approximations, but at the expense of strongly simplifying the nonlinear nature of the model. In this work, we do not make any such approximation and study conditions on the data distribution and model architecture that prevent the existence of bad local minima. Our theoretical work quantifies and formalizes two important folklore facts: (i) the landscape of deep linear networks has a radically different topology from that of deep half-rectified ones, and (ii) that the energy landscape in the non-linear case is fundamentally controlled by the interplay between the smoothness of the data distribution and model over-parametrization. Our main theoretical contribution is to prove that half-rectified single layer networks are asymptotically connected, and we provide explicit bounds that reveal the aforementioned interplay. The conditioning of gradient descent is the next challenge we address. We study this question through the geometry of the level sets, and we introduce an algorithm to efficiently estimate the regularity of such sets on large-scale networks. Our empirical results show that these level sets remain connected throughout all the learning phase, suggesting a near convex behavior, but they become exponentially more curvy as the energy level decays, in accordance to what is observed in practice with very low curvature attractors.

The ability of the Generative Adversarial Networks (GANs) framework to learn generative models mapping from simple latent distributions to arbitrarily complex data distributions has been demonstrated empirically, with compelling results showing generators learn to "linearize semantics" in the latent space of such models. Intuitively, such latent spaces may serve as useful feature representations for auxiliary problems where semantics are relevant. However, in their existing form, GANs have no means of learning the inverse mapping -- projecting data back into the latent space. We propose Bidirectional Generative Adversarial Networks (BiGANs) as a means of learning this inverse mapping, and demonstrate that the resulting learned feature representation is useful for auxiliary supervised discrimination tasks, competitive with contemporary approaches to unsupervised and self-supervised feature learning.

PixelCNNs are a recently proposed class of powerful generative models with tractable likelihood. Here we discuss our implementation of PixelCNNs which we make available at https://github.com/openai/pixel-cnn. Our implementation contains a number of modifications to the original model that both simplify its structure and improve its performance. 1) We use a discretized logistic mixture likelihood on the pixels, rather than a 256-way softmax, which we find to speed up training. 2) We condition on whole pixels, rather than R/G/B sub-pixels, simplifying the model structure. 3) We use downsampling to efficiently capture structure at multiple resolutions. 4) We introduce additional short-cut connections to further speed up optimization. 5) We regularize the model using dropout. Finally, we present state-of-the-art log likelihood results on CIFAR-10 to demonstrate the usefulness of these modifications.

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.

Natural image generation is currently one of the most actively explored fields in Deep Learning. Many approaches, e.g. for state-of-the-art artistic style transfer or natural texture synthesis, rely on the statistics of hierarchical representations in supervisedly trained deep neural networks. It is, however, unclear what aspects of this feature representation are crucial for natural image generation: is it the depth, the pooling or the training of the features on natural images? We here address this question for the task of natural texture synthesis and show that none of the above aspects are indispensable. Instead, we demonstrate that natural textures of high perceptual quality can be generated from networks with only a single layer, no pooling and random filters.

There is a lot of research interest in encoding variable length sentences into fixed length vectors, in a way that preserves the sentence meanings. Two common methods include representations based on averaging word vectors, and representations based on the hidden states of recurrent neural networks such as LSTMs. The sentence vectors are used as features for subsequent machine learning tasks or for pre-training in the context of deep learning. However, not much is known about the properties that are encoded in these sentence representations and about the language information they capture. We propose a framework that facilitates better understanding of the encoded representations. We define prediction tasks around isolated aspects of sentence structure (namely sentence length, word content, and word order), and score representations by the ability to train a classifier to solve each prediction task when using the representation as input. We demonstrate the potential contribution of the approach by analyzing different sentence representation mechanisms. The analysis sheds light on the relative strengths of different sentence embedding methods with respect to these low level prediction tasks, and on the effect of the encoded vector’s dimensionality on the resulting representations.

Ensembles of neural networks are known to be much more robust and accurate than individual networks. However, training multiple deep networks for model averaging is computationally expensive. In this paper, we propose a method to obtain the seemingly contradictory goal of ensembling multiple neural networks at no additional training cost. We achieve this goal by training a single neural network, converging to several local minima along its optimization path and saving the model parameters. To obtain repeated rapid convergence, we leverage recent work on cyclic learning rate schedules. The resulting technique, which we refer to as Snapshot Ensembling, is simple, yet surprisingly effective. We show in a series of experiments that our approach is compatible with diverse network architectures and learning tasks. It consistently yields lower error rates than state-of-the-art single models at no additional training cost, and compares favorably with traditional network ensembles. On CIFAR-10 and CIFAR-100 our DenseNet Snapshot Ensembles obtain error rates of 3.4% and 17.4% respectively.

The diversity of painting styles represents a rich visual vocabulary for the construction of an image. The degree to which one may learn and parsimoniously capture this visual vocabulary measures our understanding of the higher level features of paintings, if not images in general. In this work we investigate the construction of a single, scalable deep network that can parsimoniously capture the artistic style of a diversity of paintings. We demonstrate that such a network generalizes across a diversity of artistic styles by reducing a painting to a point in an embedding space. Importantly, this model permits a user to explore new painting styles by arbitrarily combining the styles learned from individual paintings. We hope that this work provides a useful step towards building rich models of paintings and offers a window on to the structure of the learned representation of artistic style.