NeurIPS 2018 Papers

We present group equivariant capsule networks, a framework to introduce guaranteed equivariance and invariance properties to the capsule network idea. Our work can be divided into two contributions. First, we present a generic routing by agreement algorithm defined on elements of a group and prove that equivariance of output pose vectors, as well as invariance of output activations, hold under certain conditions. Second, we connect the resulting equivariant capsule networks with work from the field of group convolutional networks. Through this connection, we provide intuitions of how both methods relate and are able to combine the strengths of both approaches in one deep neural network architecture. The resulting framework allows sparse evaluation of the group convolution operator, provides control over specific equivariance and invariance properties, and can use routing by agreement instead of pooling operations. In addition, it is able to provide interpretable and equivariant representation vectors as output capsules, which disentangle evidence of object existence from its pose.

To convert the input into binary code, hashing algorithm has been widely used for approximate nearest neighbor search on large-scale image sets due to its computation and storage efficiency. Deep hashing further improves the retrieval quality by combining the hash coding with deep neural network. However, a major difficulty in deep hashing lies in the discrete constraints imposed on the network output, which generally makes the optimization NP hard. In this work, we adopt the greedy principle to tackle this NP hard problem by iteratively updating the network toward the probable optimal discrete solution in each iteration. A hash coding layer is designed to implement our approach which strictly uses the sign function in forward propagation to maintain the discrete constraints, while in back propagation the gradients are transmitted intactly to the front layer to avoid the vanishing gradients. In addition to the theoretical derivation, we provide a new perspective to visualize and understand the effectiveness and efficiency of our algorithm. Experiments on benchmark datasets show that our scheme outperforms state-of-the-art hashing methods in both supervised and unsupervised tasks.

Approximate inference in probabilistic graphical models (PGMs) can be grouped into deterministic methods and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases that are hard to quantify. The latter enjoy asymptotic consistency, but can suffer from high computational costs. In this paper we present a way of bridging the gap between deterministic and stochastic inference. Specifically, we suggest an efficient sequential Monte Carlo (SMC) algorithm for PGMs which can leverage the output from deterministic inference methods. While generally applicable, we show explicitly how this can be done with loopy belief propagation, expectation propagation, and Laplace approximations. The resulting algorithm can be viewed as a post-correction of the biases associated with these methods and, indeed, numerical results show clear improvements over the baseline deterministic methods as well as over "plain" SMC.

We propose Graphical Generative Adversarial Networks (Graphical-GAN) to model structured data. Graphical-GAN conjoins the power of Bayesian networks on compactly representing the dependency structures among random variables and that of generative adversarial networks on learning expressive dependency functions. We introduce a structured recognition model to infer the posterior distribution of latent variables given observations. We generalize the Expectation Propagation (EP) algorithm to learn the generative model and recognition model jointly. Finally, we present two important instances of Graphical-GAN, i.e. Gaussian Mixture GAN (GMGAN) and State Space GAN (SSGAN), which can successfully learn the discrete and temporal structures on visual datasets, respectively.

We suggest a general oracle-based framework that captures parallel stochastic optimization in different parallelization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive lower bounds to study several specific parallel optimization settings, including delayed updates and parallel processing with intermittent communication. We highlight gaps between lower and upper bounds on the oracle complexity, and cases where the ``natural'' algorithms are not known to be optimal.

Generating novel graph structures that optimize given objectives while obeying some given underlying rules is fundamental for chemistry, biology and social science research. This is especially important in the task of molecular graph generation, whose goal is to discover novel molecules with desired properties such as drug-likeness and synthetic accessibility, while obeying physical laws such as chemical valency. However, designing models that finds molecules that optimize desired properties while incorporating highly complex and non-differentiable rules remains to be a challenging task. Here we propose Graph Convolutional Policy Network (GCPN), a general graph convolutional network based model for goal-directed graph generation through reinforcement learning. The model is trained to optimize domain-specific rewards and adversarial loss through policy gradient, and acts in an environment that incorporates domain-specific rules. Experimental results show that GCPN can achieve 61% improvement on chemical property optimization over state-of-the-art baselines while resembling known molecules, and achieve 184% improvement on the constrained property optimization task.

Modern large-scale machine learning applications require stochastic optimization algorithms to be implemented on distributed computational architectures. A key bottleneck is the communication overhead for exchanging information such as stochastic gradients among different workers. In this paper, to reduce the communication cost, we propose a convex optimization formulation to minimize the coding length of stochastic gradients. The key idea is to randomly drop out coordinates of the stochastic gradient vectors and amplify the remaining coordinates appropriately to ensure the sparsified gradient to be unbiased. To solve the optimal sparsification efficiently, several simple and fast algorithms are proposed for an approximate solution, with a theoretical guarantee for sparseness. Experiments on $\ell_2$ regularized logistic regression, support vector machines, and convolutional neural networks validate our sparsification approaches.

Most large-scale network models use neurons with static nonlinearities that produce analog output, despite the fact that information processing in the brain is predominantly carried out by dynamic neurons that produce discrete pulses called spikes. Research in spike-based computation has been impeded by the lack of efficient supervised learning algorithm for spiking neural networks. Here, we present a gradient descent method for optimizing spiking network models by introducing a differentiable formulation of spiking dynamics and deriving the exact gradient calculation. For demonstration, we trained recurrent spiking networks on two dynamic tasks: one that requires optimizing fast (~ millisecond) spike-based interactions for efficient encoding of information, and a delayed-memory task over extended duration (~ second). The results show that the gradient descent approach indeed optimizes networks dynamics on the time scale of individual spikes as well as on behavioral time scales. In conclusion, our method yields a general purpose supervised learning algorithm for spiking neural networks, which can facilitate further investigations on spike-based computations.

Shift-and-invert preconditioning, as a classic acceleration technique for the leading eigenvector computation, has received much attention again recently, owing to fast least-squares solvers for efficiently approximating matrix inversions in power iterations. In this work, we adopt an inexact Riemannian gradient descent perspective to investigate this technique on the effect of the step-size scheme. The shift-and-inverted power method is included as a special case with adaptive step-sizes. Particularly, two other step-size settings, i.e., constant step-sizes and Barzilai-Borwein (BB) step-sizes, are examined theoretically and/or empirically. We present a novel convergence analysis for the constant step-size setting that achieves a rate at $\tilde{O}(\sqrt{\frac{\lambda_{1}}{\lambda_{1}-\lambda_{p+1}}})$, where $\lambda_{i}$ represents the $i$-th largest eigenvalue of the given real symmetric matrix and $p$ is the multiplicity of $\lambda_{1}$. Our experimental studies show that the proposed algorithm can be significantly faster than the shift-and-inverted power method in practice.

Data parallelism can boost the training speed of convolutional neural networks (CNN), but could suffer from significant communication costs caused by gradient aggregation. To alleviate this problem, several scalar quantization techniques have been developed to compress the gradients. But these techniques could perform poorly when used together with decentralized aggregation protocols like ring all-reduce (RAR), mainly due to their inability to directly aggregate compressed gradients. In this paper, we empirically demonstrate the strong linear correlations between CNN gradients, and propose a gradient vector quantization technique, named GradiVeQ, to exploit these correlations through principal component analysis (PCA) for substantial gradient dimension reduction. GradiveQ enables direct aggregation of compressed gradients, hence allows us to build a distributed learning system that parallelizes GradiveQ gradient compression and RAR communications. Extensive experiments on popular CNNs demonstrate that applying GradiveQ slashes the wall-clock gradient aggregation time of the original RAR by more than 5x without noticeable accuracy loss, and reduce the end-to-end training time by almost 50%. The results also show that \GradiveQ is compatible with scalar quantization techniques such as QSGD (Quantized SGD), and achieves a much higher speed-up gain under the same compression ratio.

Flow-based generative models are conceptually attractive due to tractability of the exact log-likelihood, tractability of exact latent-variable inference, and parallelizability of both training and synthesis. In this paper we propose Glow, a simple type of generative flow using invertible 1x1 convolution. Using our method we demonstrate a significant improvement in log-likelihood and qualitative sample quality. Perhaps most strikingly, we demonstrate that a generative model optimized towards the plain log-likelihood objective is capable of efficient synthesis of large and subjectively realistic-looking images.

An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different diffusions are suitable for optimizing different classes of convex and non-convex functions. This allows us to design diffusions suitable for globally optimizing convex and non-convex functions not covered by the existing Langevin theory. Our non-asymptotic analysis delivers computable optimization and integration error bounds based on easily accessed properties of the objective and chosen diffusion. Central to our approach are new explicit Stein factor bounds on the solutions of Poisson equations. We complement these results with improved optimization guarantees for targets other than the standard Gibbs measure.

Multichannel blind deconvolution is the problem of recovering an unknown signal $f$ and multiple unknown channels $x_i$ from convolutional measurements $y_i=x_i \circledast f$ ($i=1,2,\dots,N$). We consider the case where the $x_i$'s are sparse, and convolution with $f$ is invertible. Our nonconvex optimization formulation solves for a filter $h$ on the unit sphere that produces sparse output $y_i\circledast h$. Under some technical assumptions, we show that all local minima of the objective function correspond to the inverse filter of $f$ up to an inherent sign and shift ambiguity, and all saddle points have strictly negative curvatures. This geometric structure allows successful recovery of $f$ and $x_i$ using a simple manifold gradient descent algorithm with random initialization. Our theoretical findings are complemented by numerical experiments, which demonstrate superior performance of the proposed approach over the previous methods.

In most of existing deep convolutional neural networks (CNNs) for classification, global average (first-order) pooling (GAP) has become a standard module to summarize activations of the last convolution layer as final representation for prediction. Recent researches show integration of higher-order pooling (HOP) methods clearly improves performance of deep CNNs. However, both GAP and existing HOP methods assume unimodal distributions, which cannot fully capture statistics of convolutional activations, limiting representation ability of deep CNNs, especially for samples with complex contents. To overcome the above limitation, this paper proposes a global Gated Mixture of Second-order Pooling (GM-SOP) method to further improve representation ability of deep CNNs. To this end, we introduce a sparsity-constrained gating mechanism and propose a novel parametric SOP as component of mixture model. Given a bank of SOP candidates, our method can adaptively choose Top-K (K > 1) candidates for each input sample through the sparsity-constrained gating module, and performs weighted sum of outputs of K selected candidates as representation of the sample. The proposed GM-SOP can flexibly accommodate a large number of personalized SOP candidates in an efficient way, leading to richer representations. The deep networks with our GM-SOP can be end-to-end trained, having potential to characterize complex, multi-modal distributions. The proposed method is evaluated on two large scale image benchmarks (i.e., downsampled ImageNet-1K and Places365), and experimental results show our GM-SOP is superior to its counterparts and achieves very competitive performance. The source code will be available at http://www.peihuali.org/GM-SOP.

We present a unified framework to analyze the global convergence of Langevin dynamics based algorithms for nonconvex finite-sum optimization with $n$ component functions. At the core of our analysis is a direct analysis of the ergodicity of the numerical approximations to Langevin dynamics, which leads to faster convergence rates. Specifically, we show that gradient Langevin dynamics (GLD) and stochastic gradient Langevin dynamics (SGLD) converge to the \textit{almost minimizer}\footnote{Following \citet{raginsky2017non}, an almost minimizer is defined to be a point which is within the ball of the global minimizer with radius $O(d\log(\beta+1)/\beta)$, where $d$ is the problem dimension and $\beta$ is the inverse temperature parameter.} within $\tilde O\big(nd/(\lambda\epsilon) \big)$\footnote{$\tilde O(\cdot)$ notation hides polynomials of logarithmic terms and constants.} and $\tilde O\big(d^7/(\lambda^5\epsilon^5) \big)$ stochastic gradient evaluations respectively, where $d$ is the problem dimension, and $\lambda$ is the spectral gap of the Markov chain generated by GLD. Both results improve upon the best known gradient complexity\footnote{Gradient complexity is defined as the total number of stochastic gradient evaluations of an algorithm, which is the number of stochastic gradients calculated per iteration times the total number of iterations.} results \citep{raginsky2017non}. Furthermore, for the first time we prove the global convergence guarantee for variance reduced stochastic gradient Langevin dynamics (VR-SGLD) to the almost minimizer within $\tilde O\big(\sqrt{n}d^5/(\lambda^4\epsilon^{5/2})\big)$ stochastic gradient evaluations, which outperforms the gradient complexities of GLD and SGLD in a wide regime. Our theoretical analyses shed some light on using Langevin dynamics based algorithms for nonconvex optimization with provable guarantees.

We present recurrent geometry-aware neural networks that integrate visual in- formation across multiple views of a scene into 3D latent feature tensors, while maintaining an one-to-one mapping between 3D physical locations in the world scene and latent feature locations. Object detection, object segmentation, and 3D reconstruction is then carried out directly using the constructed 3D feature memory, as opposed to any of the input 2D images. The proposed models are equipped with differentiable egomotion-aware feature warping and (learned) depth-aware unprojection operations to achieve geometrically consistent mapping between the features in the input frame and the constructed latent model of the scene. We empirically show the proposed model generalizes much better than geometry- unaware LSTM/GRU networks, especially under the presence of multiple objects and cross-object occlusions. Combined with active view selection policies, our model learns to select informative viewpoints to integrate information from by “undoing" cross-object occlusions, seamlessly combining geometry with learning from experience.

We propose a new type of generative model for high-dimensional data that learns a manifold geometry of the data, rather than density, and can generate points evenly along this manifold. This is in contrast to existing generative models that represent data density, and are strongly affected by noise and other artifacts of data collection. We demonstrate how this approach corrects sampling biases and artifacts, thus improves several downstream data analysis tasks, such as clustering and classification. Finally, we demonstrate that this approach is especially useful in biology where, despite the advent of single-cell technologies, rare subpopulations and gene-interaction relationships are affected by biased sampling. We show that SUGAR can generate hypothetical populations, and it is able to reveal intrinsic patterns and mutual-information relationships between genes on a single-cell RNA sequencing dataset of hematopoiesis.

Monte Carlo sampling in high-dimensional, low-sample settings is important in many machine learning tasks. We improve current methods for sampling in Euclidean spaces by avoiding independence, and instead consider ways to couple samples. We show fundamental connections to optimal transport theory, leading to novel sampling algorithms, and providing new theoretical grounding for existing strategies. We compare our new strategies against prior methods for improving sample efficiency, including QMC, by studying discrepancy. We explore our findings empirically, and observe benefits of our sampling schemes for reinforcement learning and generative modelling.

We introduce the Genetic-Gated Networks (G2Ns), simple neural networks that combine a gate vector composed of binary genetic genes in the hidden layer(s) of networks. Our method can take both advantages of gradient-free optimization and gradient-based optimization methods, of which the former is effective for problems with multiple local minima, while the latter can quickly find local minima. In addition, multiple chromosomes can define different models, making it easy to construct multiple models and can be effectively applied to problems that require multiple models. We show that this G2N can be applied to typical reinforcement learning algorithms to achieve a large improvement in sample efficiency and performance.