Related papers: Differentiating densities on smooth manifolds
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The stochastic density functional theory (sDFT) has exhibited advantages over the standard Kohn-Sham DFT method and has become an attractive approach for large-scale electronic structure calculations. The sDFT method avoids the expensive…
This essay explains an approach to the study of smooth manifolds which compares them to presheaves on a category of discs, also known as embedding calculus. We highlight recent work that shows this approach has many desirable properties, as…
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.…
Programs involving discontinuities introduced by control flow constructs such as conditional branches pose challenges to mathematical optimization methods that assume a degree of smoothness in the objective function's response surface.…
Tuning of measurement models is challenging in real-world applications of sequential Monte Carlo methods. Recent advances in differentiable particle filters have led to various efforts to learn measurement models through neural networks.…
For a real function, automatic differentiation is such a standard algorithm used to efficiently compute its gradient, that it is integrated in various neural network frameworks. However, despite the recent advances in using complex…
For a long time, people have been focusing on how to extract more information, such as off-diagonal observables, from the quantum Monte Carlo (QMC) simulation of the partition function, but there have been numerous difficulties, and many of…
Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…
The score function estimator is widely used for estimating gradients of stochastic objectives in stochastic computation graphs (SCG), eg, in reinforcement learning and meta-learning. While deriving the first-order gradient estimators by…
We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…
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…
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
Derivative of a function can be expressed in terms of integration over a small neighborhood of the point of differentiation, so-called differentiation by integration method. In this text a maximal generalization of existing results which…
Discrete gradient methods are geometric integration techniques that can preserve the dissipative structure of gradient flows. Due to the monotonic decay of the function values, they are well suited for general convex and nonconvex…
We prove a novel result wherein the density function of the gradients---corresponding to density function of the derivatives in one dimension---of a thrice differentiable function S (obtained via a random variable transformation of a…
We consider a hybrid Monte Carlo algorithm which is applicable to lattice theories defined on Lefschetz thimbles. In the algorithm, any point (field configuration) on a thimble is parametrized uniquely by the flow-direction and the…
Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…
We develop efficient numerical integration methods for computing an integral whose integrand is a product of a smooth function and the Gaussian function with a small standard deviation. Traditional numerical integration methods applied to…