A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement, system combination and expectations as linear algebra operations. This paper explores how density matrices can be used as a building block to build machine learning models exploiting their ability to straightforwardly combine linear algebra and probability. One of the main results of the paper is to show that density matrices coupled with random Fourier features could approximate arbitrary probability distributions over $\mathbb{R}^n$. Based on this finding the paper builds different models for density estimation, classification and regression. These models are differentiable, so it is possible to integrate them with other differentiable components, such as deep learning architectures and to learn their parameters using gradient-based optimization. In addition, the paper presents optimization-less training strategies based on estimation and model averaging. The models are evaluated in benchmark tasks and the results are reported and discussed.

We perform scalable approximate inference in a recently-proposed family of continuous-depth Bayesian neural networks. In this model class, uncertainty about separate weights in each layer produces dynamics that follow a stochastic differential equation (SDE). We demonstrate gradient-based stochastic variational inference in this infinite-parameter setting, producing arbitrarily-flexible approximate posteriors. We also derive a novel gradient estimator that approaches zero variance as the approximate posterior approaches the true posterior. This approach further inherits the memory-efficient training and tunable precision of neural ODEs.

Rockfall detection is a crucial procedure in the field of geology, which helps to reduce the associated risks. Currently, geologists identify rockfall events almost manually utilizing point cloud and imagery data obtained from different caption devices such as Terrestrial Laser Scanner or digital cameras. Multi-temporal comparison of the point clouds obtained with these techniques requires a tedious visual inspection to identify rockfall events which implies inaccuracies that depend on several factors such as human expertise and the sensibility of the sensors. This paper addresses this issue and provides an intelligent framework for rockfall event detection for any individual working in the intersection of the geology domain and decision support systems. The development of such an analysis framework poses significant research challenges and justifies intensive experimental analysis. In particular, we propose an intelligent system that utilizes multiple machine learning algorithms to detect rockfall clusters of point cloud data. Due to the extremely imbalanced nature of the problem, a plethora of state-of-the-art resampling techniques accompanied by multiple models and feature selection procedures are being investigated. Various machine learning pipeline combinations have been benchmarked and compared applying well-known metrics to be incorporated into our system. Specifically, we developed statistical and machine learning techniques and applied them to analyze point cloud data extracted from Terrestrial Laser Scanner in two distinct case studies, involving different geological contexts: the basaltic cliff of Castellfollit de la Roca and the conglomerate Montserrat Massif, both located in Spain. Our experimental data suggest that some of the above-mentioned machine learning pipelines can be utilized to detect rockfall incidents on mountain walls, with experimentally proven accuracy.

Second-order methods have the capability of accelerating optimization by using much richer curvature information than first-order methods. However, most are impractical in a deep learning setting where the number of training parameters is huge. In this paper, we propose KF-QN-CNN, a new Kronecker-factored quasi-Newton method for training convolutional neural networks (CNNs), where the Hessian is approximated by a layer-wise block diagonal matrix and each layer's diagonal block is further approximated by a Kronecker product corresponding to the structure of the Hessian restricted to that layer. New damping and Hessian-action techniques for BFGS are designed to deal with the non-convexity and the particularly large size of Kronecker matrices in CNN models and convergence results are proved for a variant of KF-QN-CNN under relatively mild conditions. KF-QN-CNN has memory requirements comparable to first-order methods and much less per-iteration time complexity than traditional second-order methods. Compared with state-of-the-art first- and second-order methods on several CNN models, KF-QN-CNN consistently exhibited superior performance in all of our tests.

Automatic speech recognition (ASR) is widely used in consumer electronics. ASR greatly improves the utility and accessibility of technology, but usually the output is only word sequences without punctuation. This can result in ambiguity in inferring user-intent. We first present a transformer-based approach for punctuation prediction that achieves 8% improvement on the IWSLT 2012 TED Task, beating the previous state of the art [1]. We next describe our multimodal model that learns from both text and audio, which achieves 8% improvement over the text-only algorithm on an internal dataset for which we have both the audio and transcriptions. Finally, we present an approach to learning a model using contextual dropout that allows us to handle variable amounts of future context at test time.

Edge computing was introduced as a technical enabler for the demanding requirements of new network technologies like 5G. It aims to overcome challenges related to centralized cloud computing environments by distributing computational resources to the edge of the network towards the customers. The complexity of the emerging infrastructures increases significantly, together with the ramifications of outages on critical use cases such as self-driving cars or health care. Artificial Intelligence for IT Operations (AIOps) aims to support human operators in managing complex infrastructures by using machine learning methods. This paper describes the system design of an AIOps platform which is applicable in heterogeneous, distributed environments. The overhead of a high-frequency monitoring solution on edge devices is evaluated and performance experiments regarding the applicability of three anomaly detection algorithms on edge devices are conducted. The results show, that it is feasible to collect metrics with a high frequency and simultaneously run specific anomaly detection algorithms directly on edge devices with a reasonable overhead on the resource utilization.

We investigate the local spectral statistics of the loss surface Hessians of artificial neural networks, where we discover excellent agreement with Gaussian Orthogonal Ensemble statistics across several network architectures and datasets. These results shed new light on the applicability of Random Matrix Theory to modelling neural networks and suggest a previously unrecognised role for it in the study of loss surfaces in deep learning. Inspired by these observations, we propose a novel model for the true loss surfaces of neural networks, consistent with our observations, which allows for Hessian spectral densities with rank degeneracy and outliers, extensively observed in practice, and predicts a growing independence of loss gradients as a function of distance in weight-space. We further investigate the importance of the true loss surface in neural networks and find, in contrast to previous work, that the exponential hardness of locating the global minimum has practical consequences for achieving state of the art performance.

Corrupted supervision is a common issue in real-world learning tasks, where the learning targets are potentially noisy due to errors in the data collection or labeling process. Such corruptions can have severe consequences especially in deep learning models, whose large degree-of-freedom makes them easier to memorize the corrupted examples, and thus, susceptible to overfitting (Zhang et al., 2016). There have been extensive efforts to achieve robustness against corrupted supervision. A natural approach to deal with corrupted supervision in deep neural networks (DNNs) is to reduce the model exposure to corrupted data points during training. By detecting and filtering (or re-weighting) the possible corrupted samples, the learning is expected to deliver a model that is similar to the one trained on clean data (without corruption) (Kumar et al., 2010; Han et al., 2018; Zheng et al., 2020). There are various criteria designed to identify the corrupted data points in training. For example, Kumar et al. (2010); Han et al. (2018); Jiang et al. (2018) leveraged the loss function values of the data points; Zheng et al. (2020) considered prediction uncertainty for filtering data; Malach and Shalev-Shwartz (2017) used the disagreement between two deep networks; while Reed et al. (2014) utilized the prediction consistency of neighboring iterations. The success of these methods highly depends on the effectiveness of the detection criteria in correctly identifying the corrupted data points. Since the true corrupted points remain unknown throughout the learning process, such "unsupervised" methods may not be effective, either lacking in theoretical guarantees of robustness (Han et al., 2018; Reed et al., 2014; Malach and Shalev-Shwartz, 2017; Li et al., 2017) or providing guarantees only

The test loss of well-trained neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains and connects these scaling laws. We identify variance-limited and resolution-limited scaling behavior for both dataset and model size, for a total of four scaling regimes. The variance-limited scaling follows simply from the existence of a well-behaved infinite data or infinite width limit, while the resolution-limited regime can be explained by positing that models are effectively resolving a smooth data manifold. In the large width limit, this can be equivalently obtained from the spectrum of certain kernels, and we present evidence that large width and large dataset resolution-limited scaling exponents are related by a duality. We exhibit all four scaling regimes in the controlled setting of large random feature and pretrained models and test the predictions empirically on a range of standard architectures and datasets. We also observe several empirical relationships between datasets and scaling exponents: super-classing image tasks does not change exponents, while changing input distribution (via changing datasets or adding noise) has a strong effect. We further explore the effect of architecture aspect ratio on scaling exponents.

When engineers train deep learning models, they are very much "flying blind". Commonly used approaches for real-time training diagnostics, such as monitoring the train/test loss, are limited. Assessing a network's training process solely through these performance indicators is akin to debugging software without access to internal states through a debugger. To address this, we present Cockpit, a collection of instruments that enable a closer look into the inner workings of a learning machine, and a more informative and meaningful status report for practitioners. It facilitates the identification of learning phases and failure modes, like ill-chosen hyperparameters. These instruments leverage novel higher-order information about the gradient distribution and curvature, which has only recently become efficiently accessible. We believe that such a debugging tool, which we open-source for PyTorch, represents an important step to improve troubleshooting the training process, reveal new insights, and help develop novel methods and heuristics.