Homophily modulates double descent generalization in graph convolution networks.

Graph neural networks (GNNs) excel in modeling relational data such as biological, social, and transportation networks, but the underpinnings of their success are not well understood. Traditional complexity measures from statistical learning theory fail to account for observed phenomena like the double descent or the impact of relational semantics on generalization error. Motivated by experimental observations of "transductive" double descent in key networks and datasets, we use analytical tools from statistical physics and random matrix theory to precisely characterize generalization in simple graph convolution networks on the contextual stochastic block model.

The Fastest l Prox in the West.

Proximal operators are of particular interest in optimization problems dealing with non-smooth objectives because in many practical cases they lead to optimization algorithms whose updates can be computed in closed form or very efficiently. A well-known example is the proximal operator of the vector l norm, which is given by the soft-thresholding operator. In this paper we study the proximal operator of the mixed l matrix norm and show that it can be computed in closed form by applying the well-known soft-thresholding operator to each column of the matrix.

Acoustic echoes reveal room shape.

Imagine that you are blindfolded inside an unknown room. You snap your fingers and listen to the room's response. Can you hear the shape of the room? Some people can do it naturally, but can we design computer algorithms that hear rooms? We show how to compute the shape of a convex polyhedral room from its response to a known sound, recorded by a few microphones.

Metals in proteins: correlation between the metal-ion type, coordination number and the amino-acid residues involved in the coordination.

Metal ions are constituents of many metalloproteins, in which they have either catalytic (metalloenzymes) or structural functions. In this work, the characteristics of various metals were studied (Cu, Zn, Mg, Mn, Fe, Co, Ni, Cd and Ca in proteins with known crystal structure) as well as the specificity of their environments. The analysis was performed on two data sets: the set of protein structures in the Protein Data Bank (PDB) determined with resolution <1.