Related papers: ACORNS: An Easy-To-Use Code Generator for Gradient…
We derive and implement a second-order adjoint method to compute exact gradients and Hessians for a prototypical quantum optimal control problem, that of solving for the minimal energy applied electric field that drives a molecule from a…
Studies in thermodynamics often require the reduction of some first or second order partial derivatives in terms of a smaller basic set. A simple algorithm to perform such a reduction is presented here, together with a review of earlier…
ADF95 is a tool to automatically calculate numerical first derivatives for any mathematical expression as a function of user defined independent variables. Accuracy of derivatives is achieved within machine precision. ADF95 may be applied…
Differentiation is a cornerstone of computing and data analysis in every discipline of science and engineering. Indeed, most fundamental physics laws are expressed as relationships between derivatives in space and time. However, derivatives…
Optimization of beamlines and lattices is a common problem in accelerator physics, which is usually solved with semi-analytical methods and numerical optimization routines. However, these are usually of the gradient-free or…
A computational procedure is developed for the efficient calculation of derivatives of integrals over non-separable Gaussian-type basis functions, used for the evaluation of gradients of the total energy in quantum-mechanical simulations.…
While most work on the quantum simulation of chemistry has focused on computing energy surfaces, a similarly important application requiring subtly different algorithms is the computation of energy derivatives. Almost all molecular…
Coded distributed computation has become common practice for performing gradient descent on large datasets to mitigate stragglers and other faults. This paper proposes a novel algorithm that encodes the partial derivatives themselves and…
We propose to apply several gradient estimation techniques to enable the differentiation of programs with discrete randomness in High Energy Physics. Such programs are common in High Energy Physics due to the presence of branching processes…
Automatic differentiation is a tool for numerically calculating derivatives of a given function up to machine precision. This tool is useful for quantum chemistry methods, which require the calculation of gradients either for the…
Finite-sum optimization problems are ubiquitous in machine learning, and are commonly solved using first-order methods which rely on gradient computations. Recently, there has been growing interest in \emph{second-order} methods, which rely…
Backpropagation is a classic automatic differentiation algorithm computing the gradient of functions specified by a certain class of simple, first-order programs, called computational graphs. It is a fundamental tool in several fields, most…
Automatic differentiation (AD) is an essential primitive for machine learning programming systems. Tangent is a new library that performs AD using source code transformation (SCT) in Python. It takes numeric functions written in a syntactic…
This paper develops coding techniques to reduce the running time of distributed learning tasks. It characterizes the fundamental tradeoff to compute gradients (and more generally vector summations) in terms of three parameters: computation…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
Linear optical circuits with single-photon sources offer a promising platform for quantum chemistry and machine learning. However, current applications are all based on support vector machines or gradient-free optimization methods. This…
Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…
In industry, shape optimization problems are of utter importance when designing structures such as aircraft, automobiles and turbines. For many of these applications, the structure changes over time, with a prescribed or non-prescribed…
Automatic differentiation (AD) is a technique for computing the derivative of a function represented by a program. This technique is considered as the de-facto standard for computing the differentiation in many machine learning and…
In Computational Science, Engineering and Finance (CSEF) scripts typically serve as the "glue" between potentially highly complex and computationally expensive external subprograms. Differentiability of the resulting programs turns out to…