Related papers: O1NumHess: a fast and accurate seminumerical Hessi…

Wasserstein gradient and Hamiltonian flows have emerged as essential tools for modeling complex dynamics in the natural sciences, with applications ranging from partial differential equations (PDEs) and optimal transport to quantum…

We consider low-space algorithms for the classic Element Distinctness problem: given an array of $n$ input integers with $O(\log n)$ bit-length, decide whether or not all elements are pairwise distinct. Beame, Clifford, and Machmouchi [FOCS…

We develop and analyze a fault-tolerant quantum algorithm for computing $n$-th order response properties necessary for analysis of non-linear spectroscopies of molecular and condensed phase systems. We use a semi-classical description in…

Grover's algorithm is a fundamental quantum algorithm that achieves a quadratic speedup for unstructured search problems of size $N$. Recent studies have reformulated this task as a maximization problem on the unitary manifold and solved it…

A large class of machine learning techniques requires the solution of optimization problems involving spectral functions of parametric matrices, e.g. log-determinant and nuclear norm. Unfortunately, computing the gradient of a spectral…

This paper establishes the theoretical foundations of the online scaled gradient methods (OSGM), a framework that utilizes online learning to adapt stepsizes and provably accelerate first-order methods. OSGM quantifies the effectiveness of…

We discuss the problem of numerically backpropagating Hessians through ordinary differential equations (ODEs) in various contexts and elucidate how different approaches may be favourable in specific situations. We discuss both theoretical…

In recent years, variational quantum algorithms have garnered significant attention as a candidate approach for near-term quantum advantage using noisy intermediate-scale quantum (NISQ) devices. In this article we introduce kernel descent,…

Choosing a basis set is the first step of a quantum chemistry calculation and it sets its maximum accuracy. This choice of orbitals is limited by strong technical constraints as one must be able to compute a large number of six dimensional…

Computational studies of chemical reactions in complex environments such as proteins, nanostructures, or on surfaces require accurate and efficient atomistic models applicable to the nanometer scale. In general, an accurate parametrization…

As is well known, both sampling from the posterior and computing the mean of the posterior in Gaussian process regression reduces to solving a large linear system of equations. We study the use of stochastic gradient descent for solving…

We present singly-exponential quantum algorithms for the One-Sided Crossing Minimization (OSCM) problem. Given an $n$-vertex bipartite graph $G=(U,V,E\subseteq U \times V)$, a $2$-level drawing $(\pi_U,\pi_V)$ of $G$ is described by a…

We provide an exact analysis of a class of randomized algorithms for solving overdetermined least-squares problems. We consider first-order methods, where the gradients are pre-conditioned by an approximation of the Hessian, based on a…

Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…

In distributed training of deep neural networks, people usually run Stochastic Gradient Descent (SGD) or its variants on each machine and communicate with other machines periodically. However, SGD might converge slowly in training some deep…

Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…

We derive methods to compute higher order differentials (Hessians and Hessian-vector products) of the rendering operator. Our approach is based on importance sampling of a convolution that represents the differentials of rendering…

Gradient-based algorithms are one of the methods of choice for the optimisation of Markov Decision Processes. In this article we will present a novel approximate Newton algorithm for the optimisation of such models. The algorithm has…

Neutron stars (NSs) probe the high-density regime of the nuclear equation of state (EOS). However, inferring the EOS from observations of NSs is a computationally challenging task. In this work, we efficiently solve this inverse problem by…

We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant…