Generative adversarial networks (GANs) use neural networks as generative models, creating realistic samples that mimic real-life reference samples (for instance, images of faces, bedrooms, and more). These networks require an adaptive critic function while training, to teach the networks how to move improve their samples to better match the reference data. I will describe a kernel divergence measure, the maximum mean discrepancy, which represents one such critic function. With gradient regularisation, the MMD is used to obtain current state-of-the art performance on challenging image generation tasks, including 160 × 160 CelebA and 64 × 64 ImageNet. In addition to adversarial network training, I'll discuss issues of gradient bias for GANs based on integral probability metrics, and mechanisms for benchmarking GAN performance.

Data science has become a topic of great interest lately and has triggered new widescale research activities around efficientl first order methods for optimisation and Bayesian sampling. The National Physical Laboratory is addressing some of these challenges with particular focus on  robustness and confidence in the solution.  In this talk, I will present some problems and recent results concerning i. robust learning in the presence of outliers based on the Median of Means (MoM) principle and ii. stability of the solution in super-resolution (joint work with A. Thompson and B. Toader).

In this talk we will show how the floating point errors in the simulation of SDEs (stochastic differential equations) can be modelled as stochastic. Furthermore, we will show how these errors can be corrected within a multilevel Monte Carlo approach which performs most calculations with low precision, but a few calculations with higher precision. The same procedure can also be used to correct for errors in converting from uniform random numbers to approximate Normal random numbers. Numerical results will be generated on both CPUs (using single/double precision) and GPUs (using half/single precision).

We propose a novel class of network models for temporal dyadic interaction data. Our objective is to capture important features often observed in social interactions: sparsity, degree heterogeneity, community structure and reciprocity. We use mutually-exciting Hawkes processes to model the interactions between each (directed) pair of individuals. The intensity of each process allows interactions to arise as responses to opposite interactions (reciprocity), or due to shared interests between individuals (community structure). For sparsity and degree heterogeneity, we build the non time dependent part of the intensity function on compound random measures following (Todeschini et al., 2016). We conduct experiments on real- world temporal interaction data and show that the proposed model outperforms competing approaches for link prediction, and leads to interpretable parameters.

Link to paper: https://papers.nips.cc/paper/7502-modelling-sparsity-heterogeneity-reci…

The Grothendieck ring of varieties over a field is a simple idea that formalizes various cut-and-paste arguments in algebraic geometry. We will explain how this intuitive construction leads to nontrivial results, such as computing Euler characteristics, counting points of varieties over finite fields, and determining Hodge numbers. As an example, we will investigate cubic hypersurfaces, especially the varieties parametrizing lines on them. If time permits, we will discuss some of the stranger properties of the Grothendieck ring.

In a joint work with Matt Tointon, we study the fine structure of approximate groups. We deduce various applications on growth, isoperimetry and quantitative estimates for the the simple random walk on finite vertex transitive graphs.