Dr Lindon Roberts will talk about: 'Optimization Algorithms for Bilevel Learning with Applications to Imaging'

Many imaging problems, such as denoising or inpainting, can be expressed as variational regularization problems. These are optimization problems for which many suitable algorithms exist. We consider the problem of learning suitable regularizers for imaging problems from example (training) data, which can be formulated as a large-scale bilevel optimization problem. 

In this talk, I will introduce new deterministic and stochastic algorithms for bilevel optimization, which require no or minimal hyperparameter tuning while retaining convergence guarantees. 

This is joint work with Mohammad Sadegh Salehi and Matthias Ehrhardt (University of Bath), and Subhadip Mukherjee (IIT Kharagpur).

In this seminar, I will explore how the sum over topologies in pure AdS_3​ quantum gravity furnishes a consistent statistical interpretation of the boundary CFT_2. By formulating a statistical version of the conformal bootstrap, which combines crossing symmetry with typicality at high energies, we will discover a large set of non-handlebody topologies in the bulk (of which I will give some examples) that are needed for consistency of the boundary description. Interestingly, this set contains only on-shell (i.e. hyperbolic) 3-manifolds, but not all of them. This suggests that the full sum over all on-shell saddles in 3d gravity may be a highly non-minimal solution of the statistical bootstrap. Based on the recent work 2601.07906 with Belin, Collier, Eberhardt and Liska.