There has recently been much work on the "wide limit" of neural networks, where Bayesian neural networks (BNNs) are shown to converge to a Gaussian process (GP) as all hidden layers are sent to infinite width. However, these results do not apply to architectures that require one or more of the hidden layers to remain narrow. In this paper, we consider the wide limit of BNNs where some hidden layers, called "bottlenecks", are held at finite width. The result is a composition of GPs that we term a "bottleneck neural network Gaussian process" (bottleneck NNGP). Although intuitive, the subtlety of the proof is in showing that the wide limit of a composition of networks is in fact the composition of the limiting GPs. We also analyze theoretically a single-bottleneck NNGP, finding that the bottleneck induces dependence between the outputs of a multi-output network that persists through extreme post-bottleneck depths, and prevents the kernel of the network from losing discriminative power at extreme post-bottleneck depths.

LAS VEGAS – A connected world means paying for gas with your voice and sensing when a plant needs water. The annual CES technology conference in Las Vegas runs through Friday and offers a forum for big companies and startups to unveil their products and services for the coming year. If swiping a credit card is too much of a chore, you'll soon be able to pay for gas by voice. Later this year, those who have Amazon's voice assistant Alexa in their cars will be able to drive into Exxon and Mobil stations and say, "Alexa, pay for gas." Alexa will then ask you to confirm what station you're at and which pump you're using.

Samsung has shown off an 8K QKED bezel-less TV that is 99 per cent screen and ultra-thin – only 15mm. Fellow South Korean rival LG has its own set of OLED TVs that double as'a piece of art' thanks to an outer edge that mimics a picture frame and the ability to display HD art pieces when not in use. Sony unveiled a concept connected car loaded with sensors and technology from its audio/visual business as part of its own push into mobility. Panasonic had as part of its CES showcase a miniature, battery-powered prototype fire engine that can transport the same level of equipment as a full-sized fire engine but at a fraction of the cost and energy. Lenovo has showcased its foldable PC with a 13.3-inch screen that it says is more durable than Samsung's Galaxy Fold.

It is organized in a tensor of the shape (M,J,N), where M 10, 000 is the total ensemble size, J 32 is the spatial discretization size, and N 50 is the sampled time instants with the time step Δt 0.01. Thus the initial data for training are given as the tKdV solutions in the time window 0,0.5.

For a country that holds 12 percent of the planet's water supply, Brazil faces significant water management issues. In addition to its commonly known sanitation problems, the country's infrastructure lends itself to distribution issues, including fraudulent use. Fraudulent water use can be particularly hard to track and identify, and often goes unaddressed for significant periods of time – especially in highly populated areas where physically checking people's homes and water meters isn't an option. Instead, companies need to find ways to swiftly identify and eliminate fraudulent water activity which impacts an already scarce supply and costs communities money. To address this challenge, a utilities company from Mato Grosso, Brazil recently worked with a group of data engineers at ScientificCloud. The goal was to develop a solution that could better locate fraudulent water usage by tracking data patterns based on home location and property attributes. As a Sao Paolo-based data science company that develops and deploys machine learning (ML) and artificial intelligence (AI)-powered applications, ScientificCloud understood these problems first hand.

People like to call millennials "lazy" when in fact we're just a bunch of tech-savvy innovators who increasingly show that you don't have to do everything the same way your parents or grandparents did. Case in point: You don't have to have cable. You don't actually have to call people on the phone, ever. And splitting monthly bills with strangers can actually be normal. Adults born in the 1980s and early 1990s have practically become experts at finding alternatives to everyday tasks so they can get more done with less physical exertion.

Market intelligence firm Tractica has released a new report which explores the global market for artificial intelligence (AI) software between 2018 and 2025. According to the study, the annual global AI software revenue will grow from $10.1 billion to $126.0 billion during the forecast period. More than 330 AI software use cases will contribute to market growth across 28 Industries. The strongest enterprise AI opportunities are in the automotive, consumer, financial services, telecommunications and retail industries. The top five sectors dominating the AI software market have clear business cases for incorporating AI unlike other industries with pie-in-the-sky use cases that may not generate a return on investment for many years.

It is the first boat to be showcased at CES in Las Vegas, but the state-of-the-art Sea Ray SLX-R 400e is far from a traditional water vessel. The 40-foot yacht is equip with auto-docking capabilities and allows passengers to communicate with it using gestures and voice commands through a new'Future Helm'. It seats 22 people and comes with a lithium battery pack that can power the craft's high-performance engines in order to save energy. Steve Langlais, Sea Ray president, said: 'CES presents a unique opportunity to debut the new SLX-R 400e in front of an audience that will truly appreciate its beauty, capabilities and incredible suite of new technologies.' 'This pioneering new model, which will be available in 2020, showcases the kind of unique, advanced technologies that are worthy of the world's largest consumer electronics show.'

Carbon capture and storage (CCS) can aid decarbonization of the atmosphere to limit further global temperature increases. A framework utilizing unsupervised learning is used to generate a range of subsurface geologic volumes to investigate potential sites for long-term storage of carbon dioxide. Generative adversarial networks are used to create geologic volumes, with a further neural network used to sample the posterior distribution of a trained Generator conditional to sparsely sampled physical measurements. These generative models are further conditioned to historic dynamic fluid flow data through Bayesian inversion to improve the resolution of the forecast of the storage capacity of injected carbon dioxide.

X, MONTH YEAR 1 Coupled Tensor Completion via Low-rank Tensor Ring Huyan Huang, Yipeng Liu, Senior Member, IEEE, Ce Zhu, Fellow, IEEE Abstract --The coupled tensor decomposition aims to reveal the latent data structure which may share common factors. Using the recently proposed tensor ring decomposition, in this paper we propose a non-convex method by alternately optimizing the latent factors. We provide an excess risk bound for the proposed alternating minimization model, which shows the improvement in completion performance. The proposed algorithm is validated on synthetic data. Index T erms--tensor ring, coupled tensor completion, alternating least squares, excess risk bound, permutational Rademacher complexity I. I NTRODUCTION Tensor is a multidimensional array and able to model the interaction between different modes in high-dimensional data.