Anastasis Kratsios talk at DataSig Seminar

DataSig

'An Approximation Theory for Metric Space-Valued Functions With A View Towards Deep Learning'

<p>We build universal approximators of continuous maps between arbitrary Polish metric spaces X and Y using universal approximators between Euclidean spaces as building blocks. Earlier results assume that the output space Y is a topological vector space. We overcome this limitation by "randomization": our approximators output discrete probability measures over Y. When X and Y are Polish without additional structure, we prove very general qualitative guarantees; when they have suitable combinatorial structure, we prove quantitative guarantees for Hölder-like maps, including maps between finite graphs, solution operators to rough differential equations between certain Carnot groups, and continuous non-linear operators between Banach spaces arising in inverse problems. In particular, we show that the required number of Dirac measures is determined by the combinatorial structure of X and Y. For barycentric Y, including Banach spaces, R-trees, Hadamard manifolds, or Wasserstein spaces on Polish metric spaces, our approximators reduce to Y-valued functions. When the Euclidean approximators are neural networks, our constructions generalize transformer networks, providing a new probabilistic viewpoint of geometric deep learning.<br><br></p>

Our {communityGuidelinesLink} describe the sort of content we prohibit on Eventbrite. If you suspect an event may be in violation, you can report it to us so we can investigate.

To report other categories of prohibited or illegal content, submit {link}

Anastasis Kratsios talk at DataSig Seminar

More events from DataSig

Discover more events from DataSig, from Science & Tech to other experiences you might love.

Still looking for the right event?

Explore all online events to browse and filter by date, category, and more.

Anastasis Kratsios talk at DataSig Seminar

More events from DataSig

Discover more events from DataSig, from Science & Tech to other experiences you might love.

More Science & Tech events

Browse more Science & Tech events with different dates, prices, and formats to find your next great experience.

Still looking for the right event?

Explore all online events to browse and filter by date, category, and more.