Related papers: Automated differential computation in the Adams sp…

We present an intensity speckle simulation algorithm based on stochastic differential equations. Intensity speckles are generated with a negative exponential distribution and an exponential auto-correlation decay. The mean of the…

En este trabajo se presenta una propuesta para realizar Diferenciaci\'on Autom\'atica Anidada utilizando cualquier biblioteca de Diferenciaci\'on Autom\'atica que permita sobrecarga de operadores. Para calcular las derivadas anidadas en una…

We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

We investigate the automatic differentiation of hybrid models, viz. models that may contain delays, logical tests and discontinuities or loops. We consider differentiation with respect to parameters, initial conditions or the time. We…

We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has…

Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…

Distance metric learning is successful in discovering intrinsic relations in data. However, most algorithms are computationally demanding when the problem size becomes large. In this paper, we propose a discriminative metric learning…

We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be…

Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…

Denoising Diffusion Probabilistic Models (DDPMs) have emerged as powerful tools for generative modeling. However, their sequential computation requirements lead to significant inference-time bottlenecks. In this work, we utilize the…

We propose an algorithm for schema-based determinization of finite automata on words and of step-wise hedge automata on nested words. The idea is to integrate schema-based cleaning directly into automata determinization. We prove the…

The technique of abstracting abstract machines (AAM) provides a systematic approach for deriving computable approximations of evaluators that are easily proved sound. This article contributes a complementary step-by-step process for…

Simulation-based optimization using agent-based models is typically carried out under the assumption that the gradient describing the sensitivity of the simulation output to the input cannot be evaluated directly. To still apply…

This article provides an overview of some of the mathematical principles of Automatic Differentiation (AD). In particular, we summarise different descriptions of the Forward Mode of AD, like the matrix-vector product based approach, the…

Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…

Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…

We provide a general product formula for the solution of nonautonomous abstract delay equations. After having shown the convergence we obtain estimates on the order of convergence for differentiable history functions. Finally, the…

Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the…

Differentiation along algorithms, i.e., piggyback propagation of derivatives, is now routinely used to differentiate iterative solvers in differentiable programming. Asymptotics is well understood for many smooth problems but the…

Deep-learning algorithms enable precise image recognition based on high-dimensional hierarchical image features. Here, we report the development and implementation of a deep-learning-based image segmentation algorithm in an autonomous…