Related papers: Universality in polytope phase transitions and mes…
Topological phase transition is accompanied with a change of topological numbers. It has been believed that the gap closing and the breakdown of the adiabaticity at the transition point is necessary in general. However, the gap closing is…
We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in…
Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…
Numerically efficient transfer matrix technique for studying statistics of coherent adsorbates on small nanotubes has been developed. In the framework of a realistic microscopic model fitted to the data of ab initio calculations taken from…
We identify a new universality class of phase transitions that emerges in non-normal systems, extending the classical framework beyond eigenvalue instabilities. Unlike traditional critical phenomena, where transitions occur when eigenvalues…
We investigate the random dynamics of rational maps on the Riemann sphere and the dynamics of semigroups of rational maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, in most cases, the chaos of the…
For approximate inference in the generalized quadratic equations model, many state-of-the-art algorithms lack any prior knowledge of the target signal structure, exhibits slow convergence, and can not handle any analytic prior knowledge of…
The classical universal approximation (UA) theorem for neural networks establishes mild conditions under which a feedforward neural network can approximate a continuous function $f$ with arbitrary accuracy. A recent result shows that neural…
We propose a testable universality hypothesis, asserting that seemingly disparate neural network solutions observed in the simple task of modular addition are unified under a common abstract algorithm. While prior work interpreted…
We study the geometry of infinite random Boltzmann planar maps with vertices of high degree. These correspond to the duals of the Boltzmann maps associated to a critical weight sequence $(q_{k})_{ k \geq 0}$ for the faces with polynomial…
In this paper we investigate how common is the phenomenon of Finite Time Disentanglement (FTD) with respect to the set of quantum dynamics of bipartite quantum states with finite dimensional Hilbert spaces. Considering a quantum dynamics…
Message passing on factor graphs is a powerful framework for probabilistic inference, which finds important applications in various scientific domains. The most wide-spread message passing scheme is the sum-product algorithm (SPA) which…
Here several perfect simulation algorithms are brought under a single framework, and shown to derive from the same probabilistic result, called here the Fundamental Theorem of Perfect Simulation (FTPS). An exact simulation algorithm has…
Considering the worst-case scenario, junction tree algorithm remains the most general solution for exact MAP inference with polynomial run-time guarantees. Unfortunately, its main tractability assumption requires the treewidth of a…
The study of universal approximation of arbitrary functions $f: \mathcal{X} \to \mathcal{Y}$ by neural networks has a rich and thorough history dating back to Kolmogorov (1957). In the case of learning finite dimensional maps, many authors…
We consider the problem of the determination of the isotropy classes of the orbit spaces of all the real linear groups, with three independent basic invariants satisfying only one independent relation. The results are obtained in the $\hat…
We consider single-particle quantum transport on parametrized complex networks. Based on general arguments regarding the spectrum of the corresponding Hamiltonian, we derive bounds for a measure of the global transport efficiency defined by…
The matrix scaling problem, particularly the Sinkhorn-Knopp algorithm, has been studied for over 60 years. In practice, the algorithm often yields high-quality approximations within just a few iterations. Theoretically, however, the…
We introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to…
A basic problem in machine learning is to find a mapping $f$ from a low dimensional latent space $\mathcal{Y}$ to a high dimensional observation space $\mathcal{X}$. Modern tools such as deep neural networks are capable to represent general…