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Video analysis is a challenging task due to its high dimensionality and the complex, entangled spatio-temporal context. Applying this understanding to healthcare applications requires AI to align with humans’ expectations and values, i.e., making them responsible. In this seminar, I will introduce high-level geometric features, such as bounding boxes and human skeletal representations, for video analysis and explain how they reduce computational complexity, improve model generalizability, and facilitate the extraction of clinically relevant motion patterns. Furthermore, I will explore how incorporating geometric concepts enhances the interpretability, privacy, and fairness of deep learning models, fostering responsible AI. This is demonstrated through predicting Parkinson’s disease and cerebral palsy, as well as analyzing surgery videos.

Consider the following computational problem: Given a real function g on a space X, a compactly generated semi-group S acting on X, and a point x in X, is g positive on every point of the orbit of x under S?

This generalises a large number of widely studied problems, such as safety and liveness verification for discrete-time dynamical systems (corresponding to semi-groups with a single generator), threshold problems for stochastic (corresponding stochastic matrices acting on probability distributions) or quantum automata (corresponding to unitary operators acting on Hilbert spaces) and more.

When the objects above are presented via rational or algebraic data, the associated problems quickly become undecidable or very sensitive to the problem formulation. For example, threshold problems for stochastic automata are undecidable in general, and threshold problems for quantum automata are decidable if and only if they are formulated using strict inequality.

I will consider the above problem in its general form from the computable analysis perspective, replacing decidability with maximal partial decidability. I will give a sound algorithm that partially decides the problem over effectively locally compact spaces. I will show that the algorithm is complete when the space is zero-dimensional or locally contractible, and give some examples of spaces where the algorithm is not complete but the problem is maximally partially decidable and spaces where the problem is not maximally partially decidable at all.