相关论文: Is Witsenhausen's counterexample a relevant toy?
The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…
We study the problem of list-decodable linear regression, where an adversary can corrupt a majority of the examples. Specifically, we are given a set $T$ of labeled examples $(x, y) \in \mathbb{R}^d \times \mathbb{R}$ and a parameter $0<…
We study the stochastic nonlinear Schroedinger equations with linear multiplicative noise, particularly in the defocusing mass-critical and energy-critical cases. For general initial data, we prove the global existence and uniqueness of…
Gaussian quantum channels are well understood and have many applications, e.g., in Quantum Information Theory and in Quantum Optics. For more general quantum channels one can in general use semiclassical approximations or perturbation…
We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the…
Motivated by recent efforts to analyze corrections to Weinberg's relations for the scattering length and effective range in the presence of a near-threshold bound state, we play around with an instructive toy model for non-relativistic…
In this paper we present two different results in the context of nonlinear analysis. The first one is essentially a nonlinear technique that, in view of its strong generality, may be useful in different practical problems. The second…
Dephasing is a prominent noise mechanism that afflicts quantum information carriers, and it is one of the main challenges towards realizing useful quantum computation, communication, and sensing. Here we consider discrimination and…
Lattice gauge theories (LGTs) form an intriguing class of theories highly relevant to both high-energy particle physics and low-energy condensed matter physics with the rapid development of engineered quantum devices providing new tools to…
We consider the classical obstacle problem on bounded, connected Lipschitz domains $D \subset \mathbb{R}^n$. We derive quantitative bounds on the changes to contact sets under general perturbations to both the right hand side and the…
The solution of large systems of nonlinear differential equations is needed for many applications in science and engineering. In this study, we present three main improvements to existing quantum algorithms based on the Carleman…
We analyze Stackelberg Gaussian signaling games where the encoder and decoder have a linear sensitivity mismatch. Unlike the standard additive-bias model, a sensitivity mismatch means the encoder prefers the decoder to track a linear…
We show that quantum oracles provide an advantage over classical oracles for answering classical counterfactual questions in causal models, or equivalently, for identifying unknown causal parameters such as distributions over functional…
Recently, contrastive learning has found impressive success in advancing the state of the art in solving various machine learning tasks. However, the existing generalization analysis is very limited or even not meaningful. In particular,…
Learning methods are increasingly used to synthesize controllers from data, yet existing sample-complexity characterizations for continuous control are sharp only in the fully observed setting. This paper studies the partially observed case…
In this paper we present a linear quadratic Gaussian (LQG) feedback control strategy for a class of linear non-Markovian quantum systems. The feedback control law is designed based on the estimated states of a whitening quantum filter for…
Microscopic current fluctuations are inseparable from conductance. We give an integral account of both quantized conductance and nonequilibrium thermal noise in one-dimensional ballistic wires. Our high-current noise theory opens a very…
This paper is concerned with a linear-quadratic partially observed Stackelberg stochastic differential game with correlated state and observation noises, where the diffusion coefficient does not contain the control variable and the control…
Counterfactual analysis is intuitively performed by humans on a daily basis eg. "What should I have done differently to get the loan approved?". Such counterfactual questions also steer the formulation of scientific hypotheses. More…
Katznelson's Question is a long-standing open question concerning recurrence in topological dynamics with strong historical and mathematical ties to open problems in combinatorics and harmonic analysis. In this article, we give a positive…