An integer vector 𝑏 ∈ Z𝑑 is a degree sequence if there exists a hypergraph with vertices {1, … , 𝑑} such that each 𝑏𝑖 is the number of hyperedges containing 𝑖. The degree-sequence polytope 𝒵 𝑑 is the convex hull of all degree sequences. We show that all bu ...
Probing the architecture of neuronal circuits and the principles that underlie their functional organization remains an important challenge of modern neurosciences. This holds true, in particular, for the inference of neuronal connectivity from large-scale ...
In the past few years, Machine Learning (ML) techniques have ushered in a paradigm shift, allowing the harnessing of ever more abundant sources of data to automate complex tasks. The technical workhorse behind these important breakthroughs arguably lies in ...
Deep learning models are generally vulnerable to small perturbations, raising concerns about safety, security, and performance guarantees. Achieving robustness has been shown to be costly in terms of computational resources and quantity of data. This thesi ...
Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...
We consider the problem of learning implicit neural representations (INRs) for signals on non-Euclidean domains. In the Euclidean case, INRs are trained on a discrete sampling of a signal over a regular lattice. Here, we assume that the continuous signal e ...
Interacting particle systems play a key role in science and engineering. Access to the governing particle interaction law is fundamental for a complete understanding of such systems. However, the inherent system complexity keeps the particle interaction hi ...
