We develop a mathematically rigorous framework for multilayer neural networks in the mean field regime. As the network's width increases, the network's learning trajectory is shown to be well captured by a meaningful and dynamically nonlinear limit (the \textit{mean field} limit), which is characterized by a system of ODEs. Our framework applies to a broad range of network architectures, learning dynamics and network initializations. Central to the framework is the new idea of a \textit{neuronal embedding}, which comprises of a non-evolving probability space that allows to embed neural networks of arbitrary widths. We demonstrate two applications of our framework. Firstly the framework gives a principled way to study the simplifying effects that independent and identically distributed initializations have on the mean field limit. Secondly we prove a global convergence guarantee for two-layer and three-layer networks. Unlike previous works that rely on convexity, our result requires a certain universal approximation property, which is a distinctive feature of infinite-width neural networks. To the best of our knowledge, this is the first time global convergence is established for neural networks of more than two layers in the mean field regime.

The transparent cornea is the window of the eye, facilitating the entry of light rays and controlling focusing the movement of the light within the eye. The cornea is critical, contributing to 75% of the refractive power of the eye. Keratoconus is a progressive and multifactorial corneal degenerative disease affecting 1 in 2000 individuals worldwide. Currently, there is no cure for keratoconus other than corneal transplantation for advanced stage keratoconus or corneal cross-linking, which can only halt KC progression. The ability to accurately identify subtle KC or KC progression is of vital clinical significance. To date, there has been little consensus on a useful model to classify KC patients, which therefore inhibits the ability to predict disease progression accurately. In this paper, we utilised machine learning to analyse data from 124 KC patients, including topographical and clinical variables. Both supervised multilayer perceptron and unsupervised variational autoencoder models were used to classify KC patients with reference to the existing Amsler-Krumeich (A-K) classification system. Both methods result in high accuracy, with the unsupervised method showing better performance. The result showed that the unsupervised method with a selection of 29 variables could be a powerful tool to provide an automatic classification tool for clinicians. These outcomes provide a platform for additional analysis for the progression and treatment of keratoconus.

Supervised deep learning has gained significant attention for speech enhancement recently. The state-of-the-art deep learning methods perform the task by learning a ratio/binary mask that is applied to the mixture in the time-frequency domain to produce the clean speech. Despite the great performance in the single-channel setting, these frameworks lag in performance in the multichannel setting as the majority of these methods a) fail to exploit the available spatial information fully, and b) still treat the deep architecture as a black box which may not be well-suited for multichannel audio processing. This paper addresses these drawbacks, a) by utilizing complex ratio masking instead of masking on the magnitude of the spectrogram, and more importantly, b) by introducing a channel-attention mechanism inside the deep architecture to mimic beamforming. We propose Channel-Attention Dense U-Net, in which we apply the channel-attention unit recursively on feature maps at every layer of the network, enabling the network to perform non-linear beamforming. We demonstrate the superior performance of the network against the state-of-the-art approaches on the CHiME-3 dataset.

For a robot to perform complex manipulation tasks, it is necessary for it to have a good grasping ability. However, vision based robotic grasp detection is hindered by the unavailability of sufficient labelled data. Furthermore, the application of semi-supervised learning techniques to grasp detection is under-explored. In this paper, a semi-supervised learning based grasp detection approach has been presented, which models a discrete latent space using a Vector Quantized Variational AutoEncoder (VQ-VAE). To the best of our knowledge, this is the first time a Variational AutoEncoder (VAE) has been applied in the domain of robotic grasp detection. The VAE helps the model in generalizing beyond the Cornell Grasping Dataset (CGD) despite having a limited amount of labelled data by also utilizing the unlabelled data. This claim has been validated by testing the model on images, which are not available in the CGD. Along with this, we augment the Generative Grasping Convolutional Neural Network (GGCNN) architecture with the decoder structure used in the VQ-VAE model with the intuition that it should help to regress in the vector-quantized latent space. Subsequently, the model performs significantly better than the existing approaches which do not make use of unlabelled images to improve the grasp.

Modern methods for data visualization via dimensionality reduction, such as t-SNE, usually have performance issues that prohibit their application to large amounts of high-dimensional data. In this work, we propose NCVis -- a high-performance dimensionality reduction method built on a sound statistical basis of noise contrastive estimation. We show that NCVis outperforms state-of-the-art techniques in terms of speed while preserving the representation quality of other methods. In particular, the proposed approach successfully proceeds a large dataset of more than 1 million news headlines in several minutes and presents the underlying structure in a human-readable way. Moreover, it provides results consistent with classical methods like t-SNE on more straightforward datasets like images of hand-written digits. We believe that the broader usage of such software can significantly simplify the large-scale data analysis and lower the entry barrier to this area.

Anna Sergeevna Bosman Department of Computer Science University of Pretoria Pretoria, South Africa anna.bosman@up.ac.za Abstract --Saliency maps are often used in computer vision to provide intuitive interpretations of what input regions a model has used to produce a specific prediction. A number of approaches to saliency map generation are available, but most require access to model parameters. This work proposes an approach for saliency map generation for black-box models, where no access to model parameters is available, using a Bayesian optimisation sampling method. The approach aims to find the global salient image region responsible for a particular (black-box) model's prediction. This is achieved by a sampling-based approach to model perturbations that seeks to localise salient regions of an image to the black-box model. Results show that the proposed approach to saliency map generation outperforms grid-based perturbation approaches, and performs similarly to gradient-based approaches which require access to model parameters. I NTRODUCTION Deep learning (DL) techniques have become a standard approach in computer vision. Specifically, the convolutional neural network (CNN) architecture has shown exceptional performance, achieving results comparable to human performance on image recognition tasks [1]-[3]. As a result, the CNN models are often deployed in real life as efficient black-box tools.

Commonly researchers need to run deep learning models repeatedlyto understand the variation in performance. The reruns will commonly be done using new seeds for the creation o f minibatches and for initialisation. We show here that for ResNets in TensorFlow Keras running on GPU s the variation caused by these sources of noise is dominated by that coming from the intrinsic non-d eterminism of GPUs themselves. While the existence of GPU non-determinism is well-known, the scale of its e ffect is perhaps less well understood - especially in the context of contemporary machine learning algorithm s. First we explain the source of this GPU-induced variability, across pa ckages and operating systems. Then we study the effects of GPU non-determinism on standard ResNet a rchitectures. To isolate the effect of GPU non-determinism we held constant the sources of randomness tha t effect the training of a ResNet other than GPU non-determinism: initial parameter weights and the ordering of training minibatches.

Predicting stochastic cellular dynamics as emerging from the mechanistic models of molecular interactions is a long-standing challenge in systems biology: low-level chemical reaction network (CRN) models give raise to a highly-dimensional continuous-time Markov chain (CTMC) which is computationally demanding and often prohibitive to analyse in practice. A recently proposed abstraction method uses deep learning to replace this CTMC with a discrete-time continuous-space process, by training a mixture density deep neural network with traces sampled at regular time intervals (which can obtained either by simulating a given CRN or as time-series data from experiment). The major advantage of such abstraction is that it produces a computational model that is dramatically cheaper to execute, while preserving the statistical features of the training data. In general, the abstraction accuracy improves with the amount of training data. However, depending on a CRN, the overall quality of the method -- the efficiency gain and abstraction accuracy -- will also depend on the choice of neural network architecture given by hyper-parameters such as the layer types and connections between them. As a consequence, in practice, the modeller would have to take care of finding the suitable architecture manually, for each given CRN, through a tedious and time-consuming trial-and-error cycle. In this paper, we propose to further automatise deep abstractions for stochastic CRNs, through learning the optimal neural network architecture along with learning the transition kernel of the abstract process. Automated search of the architecture makes the method applicable directly to any given CRN, which is time-saving for deep learning experts and crucial for non-specialists. We implement the method and demonstrate its performance on a number of representative CRNs with multi-modal emergent phenotypes.

With the recent success and popularity of pre-trained language models (LMs) in natural language processing, there has been a rise in efforts to understand their inner workings. In line with such interest, we propose a novel method that assists us in investigating the extent to which pre-trained LMs capture the syntactic notion of constituency. Our method provides an effective way of extracting constituency trees from the pre-trained LMs without training. In addition, we report intriguing findings in the induced trees, including the fact that some pre-trained LMs outperform other approaches in correctly demarcating adverb phrases in sentences.

Emotion plays an essential role in human-to-human communication, enabling us to convey feelings such as happiness, frustration, and sincerity. While modern speech technologies rely heavily on speech recognition and natural language understanding for speech content understanding, the investigation of vocal expression is increasingly gaining attention. Key considerations for building robust emotion models include characterizing and improving the extent to which a model, given its training data distribution, is able to generalize to unseen data conditions. This work investigated a long-shot-term memory (LSTM) network and a time convolution - LSTM (TC-LSTM) to detect primitive emotion attributes such as valence, arousal, and dominance, from speech. It was observed that training with multiple datasets and using robust features improved the concordance correlation coefficient (CCC) for valence, by 30\% with respect to the baseline system. Additionally, this work investigated how emotion primitives can be used to detect categorical emotions such as happiness, disgust, contempt, anger, and surprise from neutral speech, and results indicated that arousal, followed by dominance was a better detector of such emotions.