This paper presents a new family of backpropagation-free neural architectures, Gated Linear Networks (GLNs). What distinguishes GLNs from contemporary neural networks is the distributed and local nature of their credit assignment mechanism; each neuron directly predicts the target, forgoing the ability to learn feature representations in favor of rapid online learning. Individual neurons are able to model nonlinear functions via the use of data-dependent gating in conjunction with online convex optimization. We show that this architecture gives rise to universal learning capabilities in the limit, with effective model capacity increasing as a function of network size in a manner comparable with deep ReLU networks. Furthermore, we demonstrate that the GLN learning mechanism possesses extraordinary resilience to catastrophic forgetting, performing almost on par to an MLP with dropout and Elastic Weight Consolidation on standard benchmarks.

information about population flows to model potential transmissions across local areas. A simple approach to posterior simulation quickly becomes computationally infeasible, which is problematic if the system is required to provide timely predictions. We describe how to make posterior simulation for the model efficient, so that we are able to provide daily updates on epidemic developments.The results can be found at our web site https://localcovid.info, which is updated daily to display estimated instantaneous reproduction numbers and predicted case counts for the next weeks, across local authorities in Great Britain. The codebase updating the web site can be found at https://github.com/oxcsml/Rmap. We hope that our methodology and web site will be of interest to researchers, policy-makers and the public alike, to help identify upcoming local outbreaks and to aid in the containment of Covid-19 through both public health measures and personal decisions taken by the general public. DATAOur model is applied to publicly available daily counts of positive test results reported under the combined Pillars 1 (NHS and PHE) and 2 (commercial partners) of the UK's Covid-19 testing strategy. 1 The data are available for 312 lower-tier local authorities (LTLAs) in England, 14 NHS Health Boards in Scotland (each covering multiple local authorities) and 22 unitary local authorities in Wales, for a total of n = 348 local areas. The data are daily counts of lab-confirmed (PCR swab) cases presented by specimen date, starting from 30 January 2020. The original data are from the respective national public health authorities of England 2 , Scotland 3 and Wales 4 and we access them through the DELVE Global Covid-19 Dataset 5 (Bhoopchand et al., 2020). Due to delays in processing tests, we ignore the last 7 days of case counts. METHODOur method is based on an approach to infectious disease modelling using discrete renewal processes. These have a long history, and have served as the basis for a number of recent studies estimating instantaneous reproduction numbers, (Cori et al., 2013;Flaxman et al., 2020;Fraser, 2007; Wallinga & Teunis, 2004). See Bhatt et al. ( 2020) and references therein for historical and mathematical background, as well as Gostic et al. ( 2020) for important practical considerations.Following Flaxman et al. (2020), we model latent time series of incidence rates via renewal processes, and separate observations of reported cases using negative binomial distributions, to account for uncertainties in case reporting, outliers in case counts, and delays between infection and testing. We introduce a number of extensions and differences addressing issues that arise for applications to modelling epidemics at local authority level rather than regional 1 https://www.gov.uk/government/publications/coronavirus-covid-19-scaling-up-testing-programmes 2 https://coronavirus.data.gov.uk 3 https://publichealthscotland.scot/our-areas-of-work/sharing-our-data-and-intelligence/coronavirus-covid-19-dataand-guidance/ 4 https://phw.nhs.wal...

The Game Theory & Multi-Agent team at DeepMind studies several aspects of multi-agent learning ranging from computing approximations to fundamental concepts in game theory to simulating social dilemmas in rich spatial environments and training 3-d humanoids in difficult team coordination tasks. A signature aim of our group is to use the resources and expertise made available to us at DeepMind in deep reinforcement learning to explore multi-agent systems in complex environments and use these benchmarks to advance our understanding. Here, we summarise the recent work of our team and present a taxonomy that we feel highlights many important open challenges in multi-agent research.