The expressiveness of deep neural networks of bounded width has recently been investigated in a series of articles. The understanding about the minimum width needed to ensure universal approximation for different kind of activation functions has progressively been extended (Park et al., 2020). In particular, it turned out that, with respect to approximation on general compact sets in the input space, a network width less than or equal to the input dimension excludes universal approximation. In this work, we focus on network functions of width less than or equal to the latter critical bound. We prove that in this regime the exact fit of partially constant functions on disjoint compact sets is still possible for ReLU network functions under some conditions on the mutual location of these components. Conversely, we conclude from a maximum principle that for all continuous and monotonic activation functions, universal approximation of arbitrary continuous functions is impossible on sets that coincide with the boundary of an open set plus an inner point of that set. We also show that some network functions of maximum width two, respectively one, allow universal approximation on finite sets.

The increasing amount of available data and more affordable hardware solutions have opened a gate to the realm of Deep Learning (DL). Due to the rapid advancements and ever-growing popularity of DL, it has begun to invade almost every field, where machine learning is applicable, by altering the traditional state-of-the-art methods. While many researchers in the speaker recognition area have also started to replace the former state-of-the-art methods with DL techniques, some of the traditional i-vector-based methods are still state-of-the-art in the context of text-independent speaker verification (TI-SV). In this paper, we discuss the most recent generalized end-to-end (GE2E) DL technique based on Long Short-term Memory (LSTM) units for TI-SV by Google and compare different scenarios and aspects including utterance duration, training time, and accuracy to prove that our method outperforms the traditional methods.

Reinforcement learning was carried out in a simulated environment to learn continuous velocity control over multiple motor axes. This was then applied to a real-world optical tweezers experiment with the objective of moving a laser-trapped microsphere to a target location whilst avoiding collisions with other free-moving microspheres. The concept of training a neural network in a virtual environment has significant potential in the application of machine learning for experimental optimization and control, as the neural network can discover optimal methods for problem solving without the risk of damage to equipment, and at a speed not limited by movement in the physical environment. As the neural network treats both virtual and physical environments equivalently, we show that the network can also be applied to an augmented environment, where a virtual environment is combined with the physical environment. This technique may have the potential to unlock capabilities associated with mixed and augmented reality, such as enforcing safety limits for machine motion or as a method of inputting observations from additional sensors.

In astronomy, neural networks are often trained on simulated data with the prospect of being applied to real observations. Unfortunately, simply training a deep neural network on images from one domain does not guarantee satisfactory performance on new images from a different domain. The ability to share cross-domain knowledge is the main advantage of modern deep domain adaptation techniques. Here we demonstrate the use of two techniques -- Maximum Mean Discrepancy (MMD) and adversarial training with Domain Adversarial Neural Networks (DANN) -- for the classification of distant galaxy mergers from the Illustris-1 simulation, where the two domains presented differ only due to inclusion of observational noise. We show how the addition of either MMD or adversarial training greatly improves the performance of the classifier on the target domain when compared to conventional machine learning algorithms, thereby demonstrating great promise for their use in astronomy.

Activity recognition using built-in sensors in smart and wearable devices provides great opportunities to understand and detect human behavior in the wild and gives a more holistic view of individuals' health and well being. Numerous computational methods have been applied to sensor streams to recognize different daily activities. However, most methods are unable to capture different layers of activities concealed in human behavior. Also, the performance of the models starts to decrease with increasing the number of activities. This research aims at building a hierarchical classification with Neural Networks to recognize human activities based on different levels of abstraction. We evaluate our model on the Extrasensory dataset; a dataset collected in the wild and containing data from smartphones and smartwatches. We use a two-level hierarchy with a total of six mutually exclusive labels namely, "lying down", "sitting", "standing in place", "walking", "running", and "bicycling" divided into "stationary" and "non-stationary". The results show that our model can recognize low-level activities (stationary/non-stationary) with 95.8% accuracy and overall accuracy of 92.8% over six labels. This is 3% above our best performing baseline.

Code retrieval is a key task aiming to match natural and programming languages. In this work, we propose adversarial learning for code retrieval, that is regularized by question-description relevance. First, we adapt a simple adversarial learning technique to generate difficult code snippets given the input question, which can help the learning of code retrieval that faces bi-modal and data-scarce challenges. Second, we propose to leverage question-description relevance to regularize adversarial learning, such that a generated code snippet should contribute more to the code retrieval training loss, only if its paired natural language description is predicted to be less relevant to the user given question. Experiments on large-scale code retrieval datasets of two programming languages show that our adversarial learning method is able to improve the performance of state-of-the-art models. Moreover, using an additional duplicate question prediction model to regularize adversarial learning further improves the performance, and this is more effective than using the duplicated questions in strong multi-task learning baselines

Determining whether inputs are out-of-distribution (OOD) is an essential building block for safely deploying machine learning models in the open world. However, previous methods relying on the softmax confidence score suffer from overconfident posterior distributions for OOD data. We propose a unified framework for OOD detection that uses an energy score. We show that energy scores better distinguish in- and out-of-distribution samples than the traditional approach using the softmax scores. Unlike softmax confidence scores, energy scores are theoretically aligned with the probability density of the inputs and are less susceptible to the overconfidence issue. Within this framework, energy can be flexibly used as a scoring function for any pre-trained neural classifier as well as a trainable cost function to shape the energy surface explicitly for OOD detection. On a CIFAR-10 pre-trained WideResNet, using the energy score reduces the average FPR (at TPR 95%) by 18.03% compared to the softmax confidence score. With energy-based training, our method outperforms the state-of-the-art on common benchmarks.

We propose a novel theoretical framework to understand self-supervised learning methods that employ dual pairs of deep ReLU networks (e.g., SimCLR, BYOL). First, we prove that in each SGD update of SimCLR with various loss functions (simple contrastive loss, soft Triplet loss and InfoNCE loss), the weights at each layer are updated by a covariance operator that specifically amplifies initial random selectivities that vary across data samples but survive averages over data augmentations. We show this leads to the emergence of hierarchical features, if the input data are generated from a hierarchical latent tree model. With the same framework, we also show analytically that in BYOL, the combination of Batch-Norm and a predictor network creates an implicit contrastive term, acting as an approximate covariance operator. Additionally, for linear architectures we derive exact solutions for BYOL that provide conceptual insights into how BYOL can learn useful non-collapsed representations without any contrastive terms that separate negative pairs. Extensive ablation studies justify our theoretical findings. Unlike supervised learning (SL) that deals with labeled data, SSL learns meaningful structures from randomly initialized networks without human-provided labels. In this paper, we propose a systematic theoretical analysis of SSL with deep ReLU networks. Our analysis imposes no parametric assumptions on the input data distribution and is applicable to stateof-the-art SSL methods that typically involve two parallel (or dual) deep ReLU networks during training (e.g., SimCLR (Chen et al., 2020a), BYOL (Grill et al., 2020), etc). We do so by developing an analogy between SSL and a theoretical framework for analyzing supervised learning, namely the student-teacher setting (Tian, 2020; Allen-Zhu and Li, 2020; Lampinen and Ganguli, 2018; Saad and Solla, 1996), which also employs a pair of dual networks.

This course concerns the latest techniques in deep learning and representation learning, focusing on supervised and unsupervised deep learning, embedding methods, metric learning, convolutional and recurrent nets, with applications to computer vision, natural language understanding, and speech recognition. The prerequisites include: DS-GA 1001 Intro to Data Science or a graduate-level machine learning course.

We are near the end of the hype cycle for artificial intelligence (AI). The human champion of the game of Go decided to retire, saying AI cannot be beaten after AlphaGo defeated him. Domain-specific chatbots are engaging with customers and providing them with the answers they need. AI is about to revolutionize our broken health-care system. Is your company ready for AI? Anyone with deep data claims to be using AI.