This work suggests using sampling theory to analyze the function space represented by neural networks. First, it shows, under the assumption of a finite input domain, which is the common case in training neural networks, that the function space generated by multi-layer networks with non-expansive activation functions is smooth. This extends over previous works that show results for the case of infinite width ReLU networks. Then, under the assumption that the input is band-limited, we provide novel error bounds for univariate neural networks. We analyze both deterministic uniform and random sampling showing the advantage of the former.
Given a length $n$ sample from $\mathbb{R}^d$ and a neural network with a fixed architecture with $W$ weights, $k$ neurons, linear threshold activation functions, and binary outputs on each neuron, we study the problem of uniformly sampling from all possible labelings on the sample corresponding to different choices of weights. We provide an algorithm that runs in time polynomial both in $n$ and $W$ such that any labeling appears with probability at least $\left(\frac{W}{2ekn}\right)^W$ for $W<n$. For a single neuron, we also provide a random walk based algorithm that samples exactly uniformly…
Recently, neural architecture search (NAS) has been applied to automate the design of neural networks in real-world applications. A large number of algorithms have been developed to improve the search cost or the performance of the final selected architectures in NAS. Unfortunately, these NAS algorithms aim to select only one single well-performing architecture from their search spaces and thus have overlooked the capability of neural network ensemble (i.e., an ensemble of neural networks with diverse architectures) in achieving improved performance over a single final selected architecture. T…
The best neural architecture for a given machine learning problem depends on many factors: not only the complexity and structure of the dataset, but also on resource constraints including latency, compute, energy consumption, etc. Neural architecture search (NAS) for tabular datasets is an important but under-explored problem. Previous NAS algorithms designed for image search spaces incorporate resource constraints directly into the reinforcement learning (RL) rewards. However, for NAS on tabular datasets, this protocol often discovers suboptimal architectures. This paper develops TabNAS, a ne…
Sampling-based Motion Planners (SMPs) have become increasingly popular as they provide collision-free path solutions regardless of obstacle geometry in a given environment. However, their computational complexity increases significantly with the dimensionality of the motion planning problem. Adaptive sampling is one of the ways to speed up SMPs by sampling a particular region of a configuration space that is more likely to contain an optimal path solution. Although there are a wide variety of algorithms for adaptive sampling, they rely on hand-crafted heuristics; furthermore, their performance…
University of St.Gallen（圣加仑大学）；Samsung - SAIT AI Lab（三星SAIT人工智能实验室）；Institut de Robòtica i Informàtica Industrial（工业机器人与信息技术研究所）；Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）
Learning representations of neural network weights given a model zoo is an emerging and challenging area with many potential applications from model inspection, to neural architecture search or knowledge distillation. Recently, an autoencoder trained on a model zoo was able to learn a hyper-representation, which captures intrinsic and extrinsic properties of the models in the zoo. In this work, we extend hyper-representations for generative use to sample new model weights. We propose layer-wise loss normalization which we demonstrate is key to generate high-performing models and several sampli…
Princeton University（普林斯顿大学）；University of Washington（华盛顿大学）；Institute for Advanced Study（高等研究院）；Columbia University（哥伦比亚大学）
Leverage score sampling is a powerful technique that originates from theoretical computer science, which can be used to speed up a large number of fundamental questions, e.g. linear regression, linear programming, semi-definite programming, cutting plane method, graph sparsification, maximum matching and max-flow. Recently, it has been shown that leverage score sampling helps to accelerate kernel methods [Avron, Kapralov, Musco, Musco, Velingker and Zandieh 17]. In this work, we generalize the results in [Avron, Kapralov, Musco, Musco, Velingker and Zandieh 17] to a broader class of kernels. W…
University of California, Los Angeles（加州大学洛杉矶分校）；Google Research（谷歌研究院）
Thompson Sampling (TS) is one of the most effective algorithms for solving contextual multi-armed bandit problems. In this paper, we propose a new algorithm, called Neural Thompson Sampling, which adapts deep neural networks for both exploration and exploitation. At the core of our algorithm is a novel posterior distribution of the reward, where its mean is the neural network approximator, and its variance is built upon the neural tangent features of the corresponding neural network. We prove that, provided the underlying reward function is bounded, the proposed algorithm is guaranteed to achi…
Stochastic gradient descent samples uniformly the training set to build an unbiased gradient estimate with a limited number of samples. However, at a given step of the training process, some data are more helpful than others to continue learning. Importance sampling for training deep neural networks has been widely studied to propose sampling schemes yielding better performance than the uniform sampling scheme. After recalling the theory of importance sampling for deep learning, this paper reviews the challenges inherent to this research area. In particular, we propose a metric allowing the as…
Canadian University Dubai（迪拜加拿大大学）；University of Sharjah（沙迦大学）
Imbalanced data occurs in a wide range of scenarios. The skewed distribution of the target variable elicits bias in machine learning algorithms. One of the popular methods to combat imbalanced data is to artificially balance the data through resampling. In this paper, we compare the efficacy of a recently proposed kernel density estimation (KDE) sampling technique in the context of artificial neural networks. We benchmark the KDE sampling method against two base sampling techniques and perform comparative experiments using 8 datasets and 3 neural networks architectures. The results show that K…
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；IBM Research（IBM研究院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；Goldman Sachs（高盛）；OPKO Diagnostics（OPKO诊断公司）
Sampling is an established technique to scale graph neural networks to large graphs. Current approaches however assume the graphs to be homogeneous in terms of relations and ignore relation types, critically important in biomedical graphs. Multi-relational graphs contain various types of relations that usually come with variable frequency and have different importance for the problem at hand. We propose an approach to modeling the importance of relation types for neighborhood sampling in graph neural networks and show that we can learn the right balance: relation-type probabilities that reflec…
Texas A&M University（德克萨斯A&M大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
We propose a unified framework for adaptive connection sampling in graph neural networks (GNNs) that generalizes existing stochastic regularization methods for training GNNs. The proposed framework not only alleviates over-smoothing and over-fitting tendencies of deep GNNs, but also enables learning with uncertainty in graph analytic tasks with GNNs. Instead of using fixed sampling rates or hand-tuning them as model hyperparameters in existing stochastic regularization methods, our adaptive connection sampling can be trained jointly with GNN model parameters in both global and local fashions. …
Mitsubishi Electric Research Laboratories (MERL)（三菱电机研究实验室（MERL））；Shanghai Jiao Tong University（上海交通大学）
We propose interpretable graph neural networks for sampling and recovery of graph signals, respectively. To take informative measurements, we propose a new graph neural sampling module, which aims to select those vertices that maximally express their corresponding neighborhoods. Such expressiveness can be quantified by the mutual information between vertices' features and neighborhoods' features, which are estimated via a graph neural network. To reconstruct an original graph signal from the sampled measurements, we propose a graph neural recovery module based on the algorithm-unrolling techni…
Heidelberg University（海德堡大学）；Özyeğin University（厄兹耶因大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
We propose a new Bayesian Neural Net formulation that affords variational inference for which the evidence lower bound is analytically tractable subject to a tight approximation. We achieve this tractability by (i) decomposing ReLU nonlinearities into the product of an identity and a Heaviside step function, (ii) introducing a separate path that decomposes the neural net expectation from its variance. We demonstrate formally that introducing separate latent binary variables to the activations allows representing the neural network likelihood as a chain of linear operations. Performing variatio…
Efi Arazi School of Computer Science（埃菲·阿拉齐计算机学院）；The Interdisciplinary Center（跨学科中心）
We present a selective sampling method designed to accelerate the training of deep neural networks. To this end, we introduce a novel measurement, the minimal margin score (MMS), which measures the minimal amount of displacement an input should take until its predicted classification is switched. For multi-class linear classification, the MMS measure is a natural generalization of the margin-based selection criterion, which was thoroughly studied in the binary classification setting. In addition, the MMS measure provides an interesting insight into the progress of the training process and can …
Recurrent neural networks are nowadays successfully used in an abundance of applications, going from text, speech and image processing to recommender systems. Backpropagation through time is the algorithm that is commonly used to train these networks on specific tasks. Many deep learning frameworks have their own implementation of training and sampling procedures for recurrent neural networks, while there are in fact multiple other possibilities to choose from and other parameters to tune. In existing literature this is very often overlooked or ignored. In this paper we therefore give an overv…
This paper introduces scalable, sampling-based algorithms that optimize trained neural networks with ReLU activations. We first propose an iterative algorithm that takes advantage of the piecewise linear structure of ReLU neural networks and reduces the initial mixed-integer optimization problem (MIP) into multiple easy-to-solve linear optimization problems (LPs) through sampling. Subsequently, we extend this approach by searching around the neighborhood of the LP solution computed at each iteration. This scheme allows us to devise a second, enhanced algorithm that reduces the initial MIP prob…
To adopt neural networks in safety critical domains, knowing whether we can trust their predictions is crucial. Bayesian neural networks (BNNs) provide uncertainty estimates by averaging predictions with respect to the posterior weight distribution. Variational inference methods for BNNs approximate the intractable weight posterior with a tractable distribution, yet mostly rely on sampling from the variational distribution during training and inference. Recent sampling-free approaches offer an alternative, but incur a significant parameter overhead. We here propose a more efficient parameteriz…
University of Cambridge（剑桥大学）；Google Research（谷歌研究院）
We introduce repriorisation, a data-dependent reparameterisation which transforms a Bayesian neural network (BNN) posterior to a distribution whose KL divergence to the BNN prior vanishes as layer widths grow. The repriorisation map acts directly on parameters, and its analytic simplicity complements the known neural network Gaussian process (NNGP) behaviour of wide BNNs in function space. Exploiting the repriorisation, we develop a Markov chain Monte Carlo (MCMC) posterior sampling algorithm which mixes faster the wider the BNN. This contrasts with the typically poor performance of MCMC in hi…
Indian Institute of Technology, Varanasi（印度理工学院（瓦拉纳西））；Harvard University（哈佛大学）
Neural network-based methods for solving differential equations have been gaining traction. They work by improving the differential equation residuals of a neural network on a sample of points in each iteration. However, most of them employ standard sampling schemes like uniform or perturbing equally spaced points. We present a novel sampling scheme which samples points adversarially to maximize the loss of the current solution estimate. A sampler architecture is described along with the loss terms used for training. Finally, we demonstrate that this scheme outperforms pre-existing schemes by …
School of Computing Science（计算科学学院）；University of Glasgow（格拉斯哥大学）；OxBrdgRbtx Ltd（OxBrdgRbtx有限公司）
We demonstrate the feasibility of framing a classically learned deep neural network as an energy based model that can be processed on a one-step quantum annealer in order to exploit fast sampling times. We propose approaches to overcome two hurdles for high resolution image classification on a quantum processing unit (QPU): the required number and binary nature of the model states. With this novel method we successfully transfer a convolutional neural network to the QPU and show the potential for classification speedup of at least one order of magnitude.
Institute of Computer Science & Technology, Peking University（北京大学计算机科学技术研究所）；IBM China Research Lab（IBM中国研究院）
Syntactic features play an essential role in identifying relationship in a sentence. Previous neural network models often suffer from irrelevant information introduced when subjects and objects are in a long distance. In this paper, we propose to learn more robust relation representations from the shortest dependency path through a convolution neural network. We further propose a straightforward negative sampling strategy to improve the assignment of subjects and objects. Experimental results show that our method outperforms the state-of-the-art methods on the SemEval-2010 Task 8 dataset.
Computational results demonstrate that posterior sampling for reinforcement learning (PSRL) dramatically outperforms algorithms driven by optimism, such as UCRL2. We provide insight into the extent of this performance boost and the phenomenon that drives it. We leverage this insight to establish an $\tilde{O}(H\sqrt{SAT})$ Bayesian expected regret bound for PSRL in finite-horizon episodic Markov decision processes, where $H$ is the horizon, $S$ is the number of states, $A$ is the number of actions and $T$ is the time elapsed. This improves upon the best previous bound of $\tilde{O}(H S \sqrt{A…
The Pennsylvania State University（宾夕法尼亚州立大学）；Microsoft Bing（微软必应）
Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the compo…
Recent work on mode connectivity in the loss landscape of deep neural networks has demonstrated that the locus of (sub-)optimal weight vectors lies on continuous paths. In this work, we train a neural network that serves as a hypernetwork, mapping a latent vector into high-performance (low-loss) weight vectors, generalizing recent findings of mode connectivity to higher dimensional manifolds. We formulate the training objective as a compromise between accuracy and diversity, where the diversity takes into account trivial symmetry transformations of the target network. We demonstrate how to red…
Deep neural networks (DNN) are the state of the art on many engineering problems such as computer vision and audition. A key factor in the success of the DNN is scalability - bigger networks work better. However, the reason for this scalability is not yet well understood. Here, we interpret the DNN as a discrete system, of linear filters followed by nonlinear activations, that is subject to the laws of sampling theory. In this context, we demonstrate that over-sampled networks are more selective, learn faster and learn more robustly. Our findings may ultimately generalize to the human brain.
MINDsLab Inc.（MINDsLab公司）；Seoul National University（首尔国立大学）
Conventionally, audio super-resolution models fixed the initial and the target sampling rates, which necessitate the model to be trained for each pair of sampling rates. We introduce NU-Wave 2, a diffusion model for neural audio upsampling that enables the generation of 48 kHz audio signals from inputs of various sampling rates with a single model. Based on the architecture of NU-Wave, NU-Wave 2 uses short-time Fourier convolution (STFC) to generate harmonics to resolve the main failure modes of NU-Wave, and incorporates bandwidth spectral feature transform (BSFT) to condition the bandwidths o…
Tampere University（坦佩雷大学）；Aarhus University（奥胡斯大学）
Progressive Neural Network Learning is a class of algorithms that incrementally construct the network's topology and optimize its parameters based on the training data. While this approach exempts the users from the manual task of designing and validating multiple network topologies, it often requires an enormous number of computations. In this paper, we propose to speed up this process by exploiting subsets of training data at each incremental training step. Three different sampling strategies for selecting the training samples according to different criteria are proposed and evaluated. We al…
University of Science and Technology of China（中国科学技术大学）
Sampling is an important process in many GNN structures in order to train larger datasets with a smaller computational complexity. However, compared to other processes in GNN (such as aggregate, backward propagation), the sampling process still costs tremendous time, which limits the speed of training. To reduce the time of sampling, hardware acceleration is an ideal choice. However, state of the art GNN acceleration proposal did not specify how to accelerate the sampling process. What's more, directly accelerating traditional sampling algorithms will make the structure of the accelerator very…
Evaluating Negative Sampling Approaches for Neural Topic Models
School of Mathematical and Computational Sciences, Indian Association for the Cultivation of Science（印度科学促进会数学与计算科学学院）；Ashoka University（阿育王大学）；Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校）
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Yahoo! Research（雅虎研究院）；Etsy Inc.（Etsy公司）
Recent advances in neural networks have inspired people to design hybrid recommendation algorithms that can incorporate both (1) user-item interaction information and (2) content information including image, audio, and text. Despite their promising results, neural network-based recommendation algorithms pose extensive computational costs, making it challenging to scale and improve upon. In this paper, we propose a general neural network-based recommendation framework, which subsumes several existing state-of-the-art recommendation algorithms, and address the efficiency issue by investigating s…
Though neural network models demonstrate impressive performance, we do not understand exactly how these black-box models make individual predictions. This drawback has led to substantial research devoted to understand these models in areas such as robustness, interpretability, and generalization ability. In this paper, we consider the problem of exploring the prediction level sets of a classifier using probabilistic programming. We define a prediction level set to be the set of examples for which the predictor has the same specified prediction confidence with respect to some arbitrary data dis…
Aplicaciones en Informática Avanzada (AIA)（高级信息应用公司）；University of Geneva（日内瓦大学）
The generation of accurate neutrino-nucleus cross-section models needed for neutrino oscillation experiments require simultaneously the description of many degrees of freedom and precise calculations to model nuclear responses. The detailed calculation of complete models makes the Monte Carlo generators slow and impractical. We present Exhaustive Neural Importance Sampling (ENIS), a method based on normalizing flows to find a suitable proposal density for rejection sampling automatically and efficiently, and discuss how this technique solves common issues of the rejection algorithm.
University of Maryland, College Park（马里兰大学帕克分校）；Amazon Web Services（亚马逊云科技）；Amazon.com, Inc.（亚马逊公司）
Bayesian learning of model parameters in neural networks is important in scenarios where estimates with well-calibrated uncertainty are important. In this paper, we propose Bayesian quantized networks (BQNs), quantized neural networks (QNNs) for which we learn a posterior distribution over their discrete parameters. We provide a set of efficient algorithms for learning and prediction in BQNs without the need to sample from their parameters or activations, which not only allows for differentiable learning in QNNs, but also reduces the variance in gradients. We evaluate BQNs on MNIST, Fashion-MN…
University of Vienna（维也纳大学）；Johann Radon Institute（约翰·拉东研究所）
We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently stochastic gradient descent and its variants) are used extensively in the field of deep learning. One of the most important problems in this field concerns the question of whether it is possible to realize theoretically provable neural network approximation rates by such algorithms. We answer this question in the negative by proving hardness results for the problems…
Ulsan National Institute of Science and Technology（蔚山国立科学技术研究院）；Korea Advanced Institute of Science and Technology（韩国高等科学技术研究院）
Deep generative neural networks (DGNNs) have achieved realistic and high-quality data generation. In particular, the adversarial training scheme has been applied to many DGNNs and has exhibited powerful performance. Despite of recent advances in generative networks, identifying the image generation mechanism still remains challenging. In this paper, we present an explorative sampling algorithm to analyze generation mechanism of DGNNs. Our method efficiently obtains samples with identical attributes from a query image in a perspective of the trained model. We define generative boundaries which …
We consider the closely related problems of sampling from a distribution known up to a normalizing constant, and estimating said normalizing constant. We show how variational autoencoders (VAEs) can be applied to this task. In their standard applications, VAEs are trained to fit data drawn from an intractable distribution. We invert the logic and train the VAE to fit a simple and tractable distribution, on the assumption of a complex and intractable latent distribution, specified up to normalization. This procedure constructs approximations without the use of training data or Markov chain Mont…
Generative moment matching networks (GMMNs) are suggested for modeling the cross-sectional dependence between stochastic processes. The stochastic processes considered are geometric Brownian motions and ARMA-GARCH models. Geometric Brownian motions lead to an application of pricing American basket call options under dependence and ARMA-GARCH models lead to an application of simulating predictive distributions. In both types of applications the benefit of using GMMNs in comparison to parametric dependence models is highlighted and the fact that GMMNs can produce dependent quasi-random samples w…
The development of neural vocoders (NVs) has resulted in the high-quality and fast generation of waveforms. However, conventional NVs target a single sampling rate and require re-training when applied to different sampling rates. A suitable sampling rate varies from application to application due to the trade-off between speech quality and generation speed. In this study, we propose a method to handle multiple sampling rates in a single NV, called the MSR-NV. By generating waveforms step-by-step starting from a low sampling rate, MSR-NV can efficiently learn the characteristics of each frequen…
This paper considers the subject of information losses arising from the finite datasets used in the training of neural classifiers. It proves a relationship between such losses as the product of the expected total variation of the estimated neural model with the information about the feature space contained in the hidden representation of that model. It then bounds this expected total variation as a function of the size of randomly sampled datasets in a fairly general setting, and without bringing in any additional dependence on model complexity. It ultimately obtains bounds on information los…
Physics-Informed Neural Networks (PINNs) have become a kind of attractive machine learning method for obtaining solutions of partial differential equations (PDEs). Training PINNs can be seen as a semi-supervised learning task, in which only exact values of initial and boundary points can be obtained in solving forward problems, and in the whole spatio-temporal domain collocation points are sampled without exact labels, which brings training difficulties. Thus the selection of collocation points and sampling methods are quite crucial in training PINNs. Existing sampling methods include fixed an…
What target labels are most effective for graph neural network (GNN) training? In some applications where GNNs excel-like drug design or fraud detection, labeling new instances is expensive. We develop a data-efficient active sampling framework, ScatterSample, to train GNNs under an active learning setting. ScatterSample employs a sampling module termed DiverseUncertainty to collect instances with large uncertainty from different regions of the sample space for labeling. To ensure diversification of the selected nodes, DiverseUncertainty clusters the high uncertainty nodes and selects the repr…
