We prove universal approximation theorems of neural networks in $L^{p}(\mathbb{R} \times [0, 1]^n)$, under the conditions that $p \in [2, \infty)$ and that the activiation function belongs to among others a monotone sigmoid, relu, elu, softplus or leaky relu. Our results partially generalize classical universal approximation theorems on $[0,1]^n.$

ABSTRACT In this paper, we present a machine learning approach for estimating the number of incident wavefronts in a direction of arrival scenario. In contrast to previous works, a multilayer neural network with a cross-entropy objective is trained. Furthermore, we investigate an online training procedure that allows an adaption of the neural network to imperfections of an antenna array without explicitly calibrating the array manifold. We show via simulations that the proposed method outperforms classical model order selection schemes based on information criteria in terms of accuracy, especially for a small number of snapshots and at low signal-to-noise-ratios. Also, the online training procedure enables the neural network to adapt with only a few online training samples, if initialized by offline training on artificial data.

Deep neural networks with convolutional layers usually process the entire spectrogram of an audio signal with the same time-frequency resolutions, number of filters, and dimensionality reduction scale. According to the constant-Q transform, good features can be extracted from audio signals if the low frequency bands are processed with high frequency resolution filters and the high frequency bands with high time resolution filters. In the spectrogram of a mixture of singing voices and music signals, there is usually more information about the voice in the low frequency bands than the high frequency bands. These raise the need for processing each part of the spectrogram differently. In this paper, we propose a multi-band multi-resolution fully convolutional neural network (MBR-FCN) for singing voice separation. The MBR-FCN processes the frequency bands that have more information about the target signals with more filters and smaller dimentionality reduction scale than the bands with less information. Furthermore, the MBR-FCN processes the low frequency bands with high frequency resolution filters and the high frequency bands with high time resolution filters. Our experimental results show that the proposed MBR-FCN with very few parameters achieves better singing voice separation performance than other deep neural networks.

Bayesian optimization is a powerful tool for expensive stochastic black-box optimization problems such as simulation-based optimization or machine learning hyperparameter tuning. Many stochastic objective functions implicitly require a random number seed as input. By explicitly reusing a seed a user can exploit common random numbers, comparing two or more inputs under the same randomly generated scenario, such as a common customer stream in a job shop problem, or the same random partition of training data into training and validation set for a machine learning algorithm. With the aim of finding an input with the best average performance over infinitely many seeds, we propose a novel Gaussian process model that jointly models both the output for each seed and the average. We then introduce the Knowledge gradient for Common Random Numbers that iteratively determines a combination of input and random seed to evaluate the objective and automatically trades off reusing old seeds and querying new seeds, thus overcoming the need to evaluate inputs in batches or measuring differences of pairs as suggested in previous methods. We investigate the Knowledge Gradient for Common Random Numbers both theoretically and empirically, finding it achieves significant performance improvements with only moderate added computational cost.

Deep convolutional neural networks have achieved great successes over recent years, particularly in the domain of computer vision. They are fast, convenient, and -- thanks to mature frameworks -- relatively easy to implement and deploy. However, their reasoning is hidden inside a black box, in spite of a number of proposed approaches that try to provide human-understandable explanations for the predictions of neural networks. It is still a matter of debate which of these explainers are best suited for which situations, and how to quantitatively evaluate and compare them. In this contribution, we focus on the capabilities of explainers for convolutional deep neural networks in an extreme situation: a setting in which humans and networks fundamentally disagree. Deep neural networks are susceptible to adversarial attacks that deliberately modify input samples to mislead a neural network's classification, without affecting how a human observer interprets the input. Our goal with this contribution is to evaluate explainers by investigating whether they can identify adversarially attacked regions of an image. In particular, we quantitatively and qualitatively investigate the capability of three popular explainers of classifications -- classic salience, guided backpropagation, and LIME -- with respect to their ability to identify regions of attack as the explanatory regions for the (incorrect) prediction in representative examples from image classification. We find that LIME outperforms the other explainers.

In this paper, we explore a general Aggregated Gradient Langevin Dynamics framework (AGLD) for the Markov Chain Monte Carlo (MCMC) sampling. We investigate the nonasymptotic convergence of AGLD with a unified analysis for different data accessing (e.g. random access, cyclic access and random reshuffle) and snapshot updating strategies, under convex and nonconvex settings respectively. It is the first time that bounds for I/O friendly strategies such as cyclic access and random reshuffle have been established in the MCMC literature. The theoretic results also indicate that methods in AGLD possess the merits of both the low per-iteration computational complexity and the short mixture time. Empirical studies demonstrate that our framework allows to derive novel schemes to generate high-quality samples for large-scale Bayesian posterior learning tasks.

Conditional generative adversarial networks (cGANs) have gained a considerable attention in recent years due to its class-wise controllability and superior quality for complex generation tasks. We introduce a simple yet effective approach to improving cGANs by measuring the discrepancy between the data distribution and the model distribution on given samples. The proposed measure, coined the gap of log-densities (GOLD), provides an effective self-diagnosis for cGANs while being efficienty computed from the discriminator. We propose three applications of the GOLD: example re-weighting, rejection sampling, and active learning, which improve the training, inference, and data selection of cGANs, respectively. Our experimental results demonstrate that the proposed methods outperform corresponding baselines for all three applications on different image datasets.

Spatio-temporal event data are becoming increasingly available in a wide variety of applications, such as electronic transaction records, social network data, and crime data. How to efficiently detect anomalies in these dynamic systems using these streaming event data? We propose a novel anomaly detection framework for such event data combining the Long short-term memory (LSTM) and marked spatio-temporal point processes. The detection procedure can be computed in an online and distributed fashion via feeding the streaming data through an LSTM and a neural network-based discriminator. We study the false-alarm-rate and detection delay using theory and simulation and show that it can achieve weak signal detection by aggregating local statistics over time and networks. Finally, we demonstrate the good performance using real-world datasets.

The Nesterov's Accelerated Quasi-Newton (NAQ) method has shown to drastically improve the convergence speed compared to the conventional quasi-Newton method. This paper implements NAQ for non-convex optimization on T ensorflow. Two modifications have been proposed to the original NAQ algorithm to ensure global convergence and eliminate linesearch. The performance of the proposed algorithm - mNAQ is evaluated on standard non-convex function approximation benchmark problems and microwave circuit modelling problems. The results show that the improved algorithm converges better and faster compared to first order optimizers such as AdaGrad, RMSProp, Adam, and the second order methods such as the quasi-Newton method. Index T erms --Neural networks, training algorithm, quasi-Newton method, Nesterov's accelerated gradient, Global convergence, T ensorflow, highly-nonlinear function modeling.

Deep reinforcement learning (DRL) is a booming area of artificial intelligence. Many practical applications of DRL naturally involve more than one collaborative learners, making it important to study DRL in a multi-agent context. Previous research showed that effective learning in complex multi-agent systems demands for highly coordinated environment exploration among all the participating agents. Many researchers attempted to cope with this challenge through learning centralized value functions. However, the common strategy for every agent to learn their local policies directly often fail to nurture strong inter-agent collaboration and can be sample inefficient whenever agents alter their communication channels. To address these issues, we propose a new framework known as centralized training and exploration with decentralized execution via policy distillation. Guided by this framework and the maximum-entropy learning technique, we will first train agents' policies with shared global component to foster coordinated and effective learning. Locally executable policies will be derived subsequently from the trained global policies via policy distillation. Experiments show that our new framework and algorithm can achieve significantly better performance and higher sample efficiency than a cutting-edge baseline on several multi-agent DRL benchmarks.