We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that arediscrete tokens corresponding to positions in an input sequence.Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines,because the number of target classes in eachstep of the output depends on the length of the input, which is variable.Problems such as sorting variable sized sequences, and various combinatorialoptimization problems belong to this class. Our model solvesthe problem of variable size output dictionaries using a recently proposedmechanism of neural attention. It differs from the previous attentionattempts in that, instead of using attention to blend hidden units of anencoder to a context vector at each decoder step, it uses attention asa pointer to select a member of the input sequence as the output. We call this architecture a Pointer Net (Ptr-Net).We show Ptr-Nets can be used to learn approximate solutions to threechallenging geometric problems -- finding planar convex hulls, computingDelaunay triangulations, and the planar Travelling Salesman Problem-- using training examples alone. Ptr-Nets not only improve oversequence-to-sequence with input attention, butalso allow us to generalize to variable size output dictionaries.We show that the learnt models generalize beyond the maximum lengthsthey were trained on. We hope our results on these taskswill encourage a broader exploration of neural learning for discreteproblems.

In recent years, approaches based on machine learning have achieved state-of-the-art performance on image restoration problems. Successful approaches include both generative models of natural images as well as discriminative training of deep neural networks. Discriminative training of feed forward architectures allows explicit control over the computational cost of performing restoration and therefore often leads to better performance at the same cost at run time. In contrast, generative models have the advantage that they can be trained once and then adapted to any image restoration task by a simple use of Bayes' rule. In this paper we show how to combine the strengths of both approaches by training a discriminative, feed-forward architecture to predict the state of latent variables in a generative model of natural images. We apply this idea to the very successful Gaussian Mixture Model (GMM) of natural images. We show that it is possible to achieve comparable performance as the original GMM but with two orders of magnitude improvement in run time while maintaining the advantage of generative models.

Sequential Monte Carlo (SMC), or particle filtering, is a popular class of methods for sampling from an intractable target distribution using a sequence of simpler intermediate distributions. Like other importance sampling-based methods, performance is critically dependent on the proposal distribution: a bad proposal can lead to arbitrarily inaccurate estimates of the target distribution. This paper presents a new method for automatically adapting the proposal using an approximation of the Kullback-Leibler divergence between the true posterior and the proposal distribution. The method is very flexible, applicable to any parameterized proposal distribution and it supports online and batch variants. We use the new framework to adapt powerful proposal distributions with rich parameterizations based upon neural networks leading to Neural Adaptive Sequential Monte Carlo (NASMC). Experiments indicate that NASMC significantly improves inference in a non-linear state space model outperforming adaptive proposal methods including the Extended Kalman and Unscented Particle Filters. Experiments also indicate that improved inference translates into improved parameter learning when NASMC is used as a subroutine of Particle Marginal Metropolis Hastings. Finally we show that NASMC is able to train a latent variable recurrent neural network (LV-RNN) achieving results that compete with the state-of-the-art for polymorphic music modelling. NASMC can be seen as bridging the gap between adaptive SMC methods and the recent work in scalable, black-box variational inference.

Despite their success, convolutional neural networks are computationally expensive because they must examine all image locations. Stochastic attention-based models have been shown to improve computational efficiency at test time, but they remain difficult to train because of intractable posterior inference and high variance in the stochastic gradient estimates. Borrowing techniques from the literature on training deep generative models, we present the Wake-Sleep Recurrent Attention Model, a method for training stochastic attention networks which improves posterior inference and which reduces the variability in the stochastic gradients. We show that our method can greatly speed up the training time for stochastic attention networks in the domains of image classification and caption generation.

We explore an as yet unexploited opportunity for drastically improving the efficiency of stochastic gradient variational Bayes (SGVB) with global model parameters. Regular SGVB estimators rely on sampling of parameters once per minibatch of data, and have variance that is constant w.r.t. the minibatch size. The efficiency of such estimators can be drastically improved upon by translating uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such reparameterizations with local noise can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence.We find an important connection with regularization by dropout: the original Gaussian dropout objective corresponds to SGVB with local noise, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose \emph{variational dropout}, a generalization of Gaussian dropout, but with a more flexibly parameterized posterior, often leading to better generalization. The method is demonstrated through several experiments.

This paper presents the Deep Convolution Inverse Graphics Network (DC-IGN), a model that aims to learn an interpretable representation of images, disentangled with respect to three-dimensional scene structure and viewing transformations such as depth rotations and lighting variations. The DC-IGN model is composed of multiple layers of convolution and de-convolution operators and is trained using the Stochastic Gradient Variational Bayes (SGVB) algorithm. We propose a training procedure to encourage neurons in the graphics code layer to represent a specific transformation (e.g. pose or light). Given a single input image, our model can generate new images of the same object with variations in pose and lighting. We present qualitative and quantitative tests of the model's efficacy at learning a 3D rendering engine for varied object classes including faces and chairs.

Deep dynamic generative models are developed to learn sequential dependencies in time-series data. The multi-layered model is designed by constructing a hierarchy of temporal sigmoid belief networks (TSBNs), defined as a sequential stack of sigmoid belief networks (SBNs). Each SBN has a contextual hidden state, inherited from the previous SBNs in the sequence, and is used to regulate its hidden bias. Scalable learning and inference algorithms are derived by introducing a recognition model that yields fast sampling from the variational posterior. This recognition model is trained jointly with the generative model, by maximizing its variational lower bound on the log-likelihood. Experimental results on bouncing balls, polyphonic music, motion capture, and text streams show that the proposed approach achieves state-of-the-art predictive performance, and has the capacity to synthesize various sequences.

Discrete Fourier transforms provide a significant speedup in the computation of convolutions in deep learning. In this work, we demonstrate that, beyond its advantages for efficient computation, the spectral domain also provides a powerful representation in which to model and train convolutional neural networks (CNNs).We employ spectral representations to introduce a number of innovations to CNN design. First, we propose spectral pooling, which performs dimensionality reduction by truncating the representation in the frequency domain. This approach preserves considerably more information per parameter than other pooling strategies and enables flexibility in the choice of pooling output dimensionality. This representation also enables a new form of stochastic regularization by randomized modification of resolution. We show that these methods achieve competitive results on classification and approximation tasks, without using any dropout or max-pooling. Finally, we demonstrate the effectiveness of complex-coefficient spectral parameterization of convolutional filters. While this leaves the underlying model unchanged, it results in a representation that greatly facilitates optimization. We observe on a variety of popular CNN configurations that this leads to significantly faster convergence during training.

We introduce a neural network with a recurrent attention model over a possibly large external memory. The architecture is a form of Memory Network (Weston et al., 2015) but unlike the model in that work, it is trained end-to-end, and hence requires significantly less supervision during training, making it more generally applicable in realistic settings. It can also be seen as an extension of RNNsearch to the case where multiple computational steps (hops) are performed per output symbol. The flexibility of the model allows us to apply it to tasks as diverse as (synthetic) question answering and to language modeling. For the former our approach is competitive with Memory Networks, but with less supervision. For the latter, on the Penn TreeBank and Text8 datasets our approach demonstrates comparable performance to RNNs and LSTMs. In both cases we show that the key concept of multiple computational hops yields improved results.

We revisit the choice of SGD for training deep neural networks by reconsidering the appropriate geometry in which to optimize the weights. We argue for a geometry invariant to rescaling of weights that does not affect the output of the network, and suggest Path-SGD, which is an approximate steepest descent method with respect to a path-wise regularizer related to max-norm regularization. Path-SGD is easy and efficient to implement and leads to empirical gains over SGD and AdaGrad.