相关论文: Alternating minimization for computing doubly mini…

In this paper we consider the problem of minimizing composite objective functions consisting of a convex differentiable loss function plus a non-smooth regularization term, such as $L_1$ norm or nuclear norm, under R\'enyi differential…

The measured relative entropy and measured R\'enyi relative entropy are quantifiers of the distinguishability of two quantum states $\rho$ and $\sigma$. They are defined as the maximum classical relative entropy or R\'enyi relative entropy…

We study statistical properties of the random variables $X_{\sigma}(\pi)$, the number of occurrences of the pattern $\sigma$ in the permutation $\pi$. We present two contrasting approaches to this problem: traditional probability theory and…

In this paper, we study distributionally robust offline reinforcement learning (robust offline RL), which seeks to find an optimal policy purely from an offline dataset that can perform well in perturbed environments. In specific, we…

This article investigates the approximation quality achievable for biobjective minimization problems with respect to the Pareto cone by solutions that are (approximately) optimal with respect to larger ordering cones. When simultaneously…

The average bipartite quantum mutual information $\langle I(A{:}B)\rangle$ of Haar-random pure states can be expressed exactly through Page's formula in terms of digamma functions. We show that this quantity admits a single non-perturbative…

Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex…

This work proposes a general learned proximal alternating minimization algorithm, LPAM, for solving learnable two-block nonsmooth and nonconvex optimization problems. We tackle the nonsmoothness by an appropriate smoothing technique with…

We derive a new bound on the effectiveness of the Petz map as a universal recovery channel in approximate quantum error correction using the second sandwiched R\'{e}nyi relative entropy $\tilde{D}_{2}$. For large Hilbert spaces, our bound…

We study the quantum umlaut information, a correlation measure defined for bipartite quantum states $\rho_{AB}$ as a reversed variant of the quantum mutual information: $U(A;B)_\rho = \min_{\sigma_B} D(\rho_A\otimes \sigma_B\|\rho_{AB})$ in…

We derive a strengthened monotonicity inequality for quantum relative entropy by employing properties of $\alpha$-R\'{e}nyi relative entropy. We develop a unifying treatment towards the improvement of some quantum entropy inequalities. In…

Allreduce is one of the most frequently used MPI collective operations, and thus its performance attracts much attention in the past decades. Many algorithms were developed with different properties and purposes. We present a novel approach…

This paper proposes a geometric estimator of dependency between a pair of multivariate samples. The proposed estimator of dependency is based on a randomly permuted geometric graph (the minimal spanning tree) over the two multivariate…

We study alternating minimization for matrix completion in the simplest possible setting: completing a rank-one matrix from a revealed subset of the entries. We bound the asymptotic convergence rate by the variational characterization of…

Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related to its solution. This can be seen as a constrained minimization problem where one wishes to minimize the…

It is a well-established fact in quantum information theory, that uniform averaging over the collective action of a unitary group on a multipartite quantum state projects the state to a form equivalent to a permutation operator of the…

Performativity, the phenomenon where outcomes are influenced by predictions, is particularly prevalent in social contexts where individuals strategically respond to a deployed model. In order to preserve the high accuracy of machine…

A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two…

In standard optical tomographic methods, the off-diagonal elements of a density matrix $\rho$ are measured indirectly. Thus, the reconstruction of $\rho$, even if it is based on linear inversion, typically magnifies small errors in the…

Machine unlearning aims to efficiently eliminate the influence of specific training data, known as the forget set, from the model. However, existing unlearning methods for Large Language Models (LLMs) face a critical challenge: they rely…