Deep learning models struggle with compositional generalization, i.e. the ability to recognize or generate novel combinations of observed elementary concepts. In hopes of enabling compositional generalization, various unsupervised learning algorithms …

We study the excess capacity of deep networks in the context of supervised classification. That is, given a capacity measure of the underlying hypothesis class – in our case, empirical Rademacher complexity – to what extent can we (a priori) …

This work investigates the use of robust optimal transport (OT) for shape matching. Specifically, we show that recent OT solvers improve both optimization-based and deep learning methods for point cloud registration, boosting accuracy at an …

Continuous-depth neural networks can be viewed as deep limits of discrete neural networks whose dynamics resemble a discretization of an ordinary differential equation (ODE). Although important steps have been taken to realize the advantages of such …

We introduce a region-specific diffeomorphic metric mapping (RDMM) registration approach. RDMM is non-parametric, estimating spatio-temporal velocity fields which parameterize the sought-for spatial transformation. Regularization of these velocity …

Inferring topological and geometrical information from data can offer an alternative perspective in machine learning problems. Methods from topological data analysis, eg, persistent homology, enable us to obtain such information, typically in the …

We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several …

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