Related papers: Computing Light Transport Gradients using the Adjo…
In this paper we give a way of equipping the derivation algebra of a group algebra with the structure of a graded algebra. The derived group is used as the grading group. For the proof, the identification of the derivation with the…
We provide a visual and intuitive introduction to effectively calculating in 2-groups along with explicit examples coming from non-abelian 1- and 2-form gauge theory. In particular, we utilize string diagrams, tools similar to tensor…
We propose a special computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes.…
In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…
Monotone gradient functions play a central role in solving the Monge formulation of the optimal transport (OT) problem, which arises in modern applications ranging from fluid dynamics to robot swarm control. When the transport cost is the…
We consider a scalar function depending on a numerical solution of an initial value problem, and its second-derivative (Hessian) matrix for the initial value. The need to extract the information of the Hessian or to solve a linear system…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic…
We present a new software system PETSc TSAdjoint for first-order and second-order adjoint sensitivity analysis of time-dependent nonlinear differential equations. The derivative calculation in PETSc TSAdjoint is essentially a high-level…
We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated…
The shape gradient is a local sensitivity function that provides the change in a figure of merit associated with a perturbation to the shape of the object. The shape gradient can be used for gradient-based optimization, sensitivity…
The calculation of transport profiles from experimental measurements belongs in the category of inverse problems which are known to come with issues of ill-conditioning or singularity. A reformulation of the calculation, the matricial…
We review the development of light-cone-ordered perturbation theory in coordinate space (C-LCOPT). Compared to light-cone-ordered perturbation theory in momentum space (LCOPT), the role of intermediate states in LCOPT is played in C-LCOPT…
Gradient descent is the method of choice for training large artificial intelligence systems. As these systems become larger, a better understanding of the mechanisms behind gradient training would allow us to alleviate compute costs and…
Decentralized methods to solve finite-sum minimization problems are important in many signal processing and machine learning tasks where the data is distributed over a network of nodes and raw data sharing is not permitted due to privacy…
Current differentiable renderers provide light transport gradients with respect to arbitrary scene parameters. However, the mere existence of these gradients does not guarantee useful update steps in an optimization. Instead, inverse…
We address the challenging problem of deep representation learning--the efficient adaption of a pre-trained deep network to different tasks. Specifically, we propose to explore gradient-based features. These features are gradients of the…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…
In the future, ab initio quantum simulations of heavy ion collisions may become possible with large-scale fault-tolerant quantum computers. We propose a quantum algorithm for studying these collisions by looking at a class of observables…