Related papers: A Bifurcation Lemma for Invariant Subspaces
Learning the structure of Bayesian networks (BNs) from data is challenging, especially for datasets involving a large number of variables. The recently proposed divide-and-conquer (D\&D) strategies present a promising approach for learning…
Classifiers are biased when trained on biased datasets. As a remedy, we propose Learning to Split (ls), an algorithm for automatic bias detection. Given a dataset with input-label pairs, ls learns to split this dataset so that predictors…
We consider two areas of research that have been developing in parallel over the last decade: blind source separation (BSS) and electromagnetic source estimation (ESE). BSS deals with the recovery of source signals when only mixtures of…
Self-supervised learning (SSL) has emerged as a promising paradigm for learning flexible speech representations from unlabeled data. By designing pretext tasks that exploit statistical regularities, SSL models can capture useful…
A new construction of BPS monodromies for 4d ${\mathcal N}=2$ theories of class S is introduced. A novel feature of this construction is its manifest invariance under Kontsevich-Soibelman wall crossing, in the sense that no information on…
Symplectic geometry plays an increasingly important role in mathematics, physics and applications, and naturally gives rise to interesting matrix families and properties. One of these is the notion of symplectic eigenvalues, whose existence…
We consider the linear regression problem under semi-supervised settings wherein the available data typically consists of: (i) a small or moderate sized 'labeled' data, and (ii) a much larger sized 'unlabeled' data. Such data arises…
The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple…
The key distinguishing property of a Bayesian approach is marginalization instead of optimization, not the prior, or Bayes rule. Bayesian inference is especially compelling for deep neural networks. (1) Neural networks are typically…
In this paper, we rigorously derive Central Limit Theorems (CLT) for Bayesian two-layerneural networks in the infinite-width limit and trained by variational inference on a regression task. The different networks are trained via different…
The extension of the classical Bayesian penalized spline method to inference on vector-valued functions is considered, with an emphasis on characterizing the suitability of the method for general application.We show that the standard…
In this paper we propose a new sampling-free approach to solve Bayesian model inversion problems that is an extension of the previously proposed spectral likelihood expansions (SLE) method. Our approach, called stochastic spectral…
The likelihood-informed subspace (LIS) method offers a viable route to reducing the dimensionality of high-dimensional probability distributions arising in Bayesian inference. LIS identifies an intrinsic low-dimensional linear subspace…
We consider the bifurcation problem $u'' + \lambda u = N(u)$ with two point boundary conditions where $N(u)$ is a general nonlinear term which may also depend on the eigenvalue $\lambda$. We give a variational characterization of the…
In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix when the population covariance matrices are not uniformly bounded, which is a nontrivial…
Vision-language models (VLMs) align images and text with remarkable success, yet the geometry of their shared embedding space remains poorly understood. To probe this geometry, we begin from the Iso-Energy Assumption, which exploits…
A large class of N=2 quantum field theories admits a BPS quiver description and the study of their BPS spectra is then reduced to a representation theory problem. In such theories the coupling to a line defect can be modelled by framed…
We investigate dynamics and bifurcations in a mathematical model that captures electrochemical experiments on arrays of microelectrodes. In isolation, each individual microelectrode is described by a one-dimensional unit with a bistable…
The omega-regular separability problem for B\"uchi VASS coverability languages has recently been shown to be decidable, but with an EXPSPACE lower and a non-primitive recursive upper bound -- the exact complexity remained open. We close…
We unify and extend previous bijections on plane quadrangulations to bipartite and quasibipartite plane maps. Starting from a bipartite plane map with a distinguished edge and two distinguished corners (in the same face or in two different…