The problem of vanishing and exploding gradients has been a long-standing obstacle that hinders the effective training of neural networks. Despite various tricks and techniques that have been employed to alleviate the problem in practice, there still lacks satisfactory theories or provable solutions. In this paper, we address the problem from the perspective of high-dimensional probability theory. We provide a rigorous result that shows, under mild conditions, how the vanishing/exploding gradients problem disappears with high probability if the neural networks have sufficient width. Our main idea is to constrain both forward and backward signal propagation in a nonlinear neural network through a new class of activation functions, namely Gaussian-Poincar\'e normalized functions, and orthogonal weight matrices. Experiments on both synthetic and real-world data validate our theory and confirm its effectiveness on very deep neural networks when applied in practice.

Adaptive gradient methods such as RMSProp and Adam use exponential moving estimate of the squared gradient to compute coordinate-wise adaptive step sizes, achieving better convergence than SGD in face of noisy objectives. However, Adam can have undesirable convergence behavior due to unstable or extreme adaptive learning rates. Methods such as AMSGrad and AdaBound have been proposed to stabilize the adaptive learning rates of Adam in the later stage of training, but they do not outperform Adam in some practical tasks such as training Transformers. In this paper, we propose an adaptive learning rate principle, in which the running mean of squared gradient is replaced by a weighted mean, with weights chosen to maximize the estimated variance of each coordinate. This gives a worst-case estimate for the local gradient variance, taking smaller steps when large curvatures or noisy gradients are present, which leads to more desirable convergence behavior than Adam. We prove the proposed algorithm converges under mild assumptions for nonconvex stochastic optimization problems, and demonstrate the improved efficacy of our adaptive averaging approach on image classification, machine translation and natural language understanding tasks. Moreover, our method overcomes the non-convergence issue of Adam in BERT pretraining at large batch sizes, while achieving better test performance than LAMB in the same setting. The code is available at https://github.com/zhuchen03/MaxVA.

Ad hoc teamwork is the challenging problem of designing an autonomous agent which can adapt quickly to collaborate with previously unknown teammates. Prior work in this area has focused on closed teams in which the number of agents is fixed. In this work, we consider open teams by allowing agents of varying types to enter and leave the team without prior notification. Our solution builds on graph neural networks to learn agent models and joint action-value decompositions under varying team sizes, which can be trained with reinforcement learning using a discounted returns objective. We demonstrate empirically that our approach effectively models the impact of other agents actions on the controlled agent's returns to produce policies which can robustly adapt to dynamic team composition and is able to effectively generalize to larger teams than were seen during training.

Conventional Neural Networks can approximate simple arithmetic operations, but fail to generalize beyond the range of numbers that were seen during training. Neural Arithmetic Units aim to overcome this difficulty, but current arithmetic units are either limited to operate on positive numbers or can only represent a subset of arithmetic operations. We introduce the Neural Power Unit (NPU) that operates on the full domain of real numbers and is capable of learning arbitrary power functions in a single layer. The NPU thus fixes the shortcomings of existing arithmetic units and extends their expressivity. We achieve this by using complex arithmetic without requiring a conversion of the network to complex numbers. A simplification of the unit to the RealNPU yields a highly transparent model. We show that the NPUs outperform their competitors in terms of accuracy and sparsity on artificial arithmetic datasets, and that the RealNPU can discover the governing equations of a dynamical system only from data.

Mean aortic pressure (MAP) is a major determinant of perfusion in all organs systems. The ability to forecast MAP would enhance the ability of physicians to estimate prognosis of the patient and assist in early detection of hemodynamic instability. However, forecasting MAP is challenging because the blood pressure (BP) time series is noisy and can be highly non-stationary. The aim of this study was to forecast the mean aortic pressure five minutes in advance, using the 25 Hz time series data of previous five minutes as input. We provide a benchmark study of different deep learning models for BP forecasting. We investigate a left ventricular dwelling transvalvular micro-axial device, the Impella, in patients undergoing high-risk percutaneous intervention. The Impella provides hemodynamic support, thus aiding in native heart function recovery. It is also equipped with pressure sensors to capture high frequency MAP measurements at origin, instead of peripherally. Our dataset and the clinical application is novel in the BP forecasting field. We performed a comprehensive study on time series with increasing, decreasing, and stationary trends. The experiments show that recurrent neural networks with Legendre Memory Unit achieve the best performance with an overall forecasting error of 1.8 mmHg.

Constrained motion planning is a challenging field of research, aiming for computationally efficient methods that can find a collision-free path connecting a given start and goal by transversing zero-volume constraint manifolds for a given planning problem. These planning problems come up surprisingly frequently, such as in robot manipulation for performing daily life assistive tasks. However, few solutions to constrained motion planning are available, and those that exist struggle with high computational time complexity in finding a path solution on the manifolds. To address this challenge, we present Constrained Motion Planning Networks X (CoMPNetX). It is a neural planning approach, comprising a conditional deep neural generator and discriminator with neural gradients-based fast projections to the constraint manifolds. We also introduce neural task and scene representations conditioned on which the CoMPNetX generates implicit manifold configurations to turbo-charge any underlying classical planner such as Sampling-based Motion Planning methods for quickly solving complex constrained planning tasks. We show that our method, equipped with any constrained-adherence technique, finds path solutions with high success rates and lower computation times than state-of-the-art traditional path-finding tools on various challenging scenarios.

Relation extraction (RE) is one of the most important tasks in information extraction, as it provides essential information for many NLP applications. In this paper, we propose a cross-lingual RE approach that does not require any human annotation in a target language or any cross-lingual resources. Building upon unsupervised cross-lingual representation learning frameworks, we develop several deep Transformer based RE models with a novel encoding scheme that can effectively encode both entity location and entity type information. Our RE models, when trained with English data, outperform several deep neural network based English RE models. More importantly, our models can be applied to perform zero-shot cross-lingual RE, achieving the state-of-the-art cross-lingual RE performance on two datasets (68-89% of the accuracy of the supervised target-language RE model). The high cross-lingual transfer efficiency without requiring additional training data or cross-lingual resources shows that our RE models are especially useful for low-resource languages.

The Intent in Android plays an important role in inter-process and intra-process communications. The implicit Intent that an application could accept are declared in its manifest and are amongst the easiest feature to extract from an apk. Implicit Intents could even be extracted online and in real-time. So far neither the feasibility of developing an Intrusion Detection System solely on implicit Intent has been explored, nor are any benchmarks available of a malware classifier that is based on implicit Intent alone. We demonstrate that despite Intent is implicit and well declared, it can provide very intuitive insights to distinguish malicious from non-malicious applications. We conducted exhaustive experiments with over 40 different end-to-end Deep Learning configurations of Auto-Encoders and Multi-Layer-Perceptron to create a benchmark for a malware classifier that works exclusively on implicit Intent. Using the results from the experiments we create an intrusion detection system using only the implicit Intents and end-to-end Deep Learning architecture. We obtained an area-under-curve statistic of 0.81, and accuracy of 77.2% along with false-positive-rate of 0.11 on Drebin dataset.

Advanced Generative Adversarial Networks (GANs) are remarkable in generating intelligible audio from a random latent vector. In this paper, we examine the task of recovering the latent vector of both synthesized and real audio. Previous works recovered latent vectors of given audio through an auto-encoder inspired technique that trains an encoder network either in parallel with the GAN or after the generator is trained. With our approach, we train a deep residual neural network architecture to project audio synthesized by WaveGAN into the corresponding latent space with near identical reconstruction performance. To accommodate for the lack of an original latent vector for real audio, we optimize the residual network on the perceptual loss between the real audio samples and the reconstructed audio of the predicted latent vectors. In the case of synthesized audio, the Mean Squared Error (MSE) between the ground truth and recovered latent vector is minimized as well. We further investigated the audio reconstruction performance when several gradient optimization steps are applied to the predicted latent vector. Through our deep neural network based method of training on real and synthesized audio, we are able to predict a latent vector that corresponds to a reasonable reconstruction of real audio. Even though we evaluated our method on WaveGAN, our proposed method is universal and can be applied to any other GANs.

Fine-tuning deep neural networks pre-trained on large scale datasets is one of the most practical transfer learning paradigm given limited quantity of training samples. To obtain better generalization, using the starting point as the reference, either through weights or features, has been successfully applied to transfer learning as a regularizer. However, due to the domain discrepancy between the source and target tasks, there exists obvious risk of negative transfer. In this paper, we propose a novel transfer learning algorithm, introducing the idea of Target-awareness REpresentation Disentanglement (TRED), where the relevant knowledge with respect to the target task is disentangled from the original source model and used as a regularizer during fine-tuning the target model. Experiments on various real world datasets show that our method stably improves the standard fine-tuning by more than 2% in average. TRED also outperforms other state-of-the-art transfer learning regularizers such as L2-SP, AT, DELTA and BSS.