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Related papers: A Hitchhiker's Guide to Automatic Differentiation

200 papers

Stencil loops are a common motif in computations including convolutional neural networks, structured-mesh solvers for partial differential equations, and image processing. Stencil loops are easy to parallelise, and their fast execution is…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-07-08 Jan Hückelheim , Navjot Kukreja , Sri Hari Krishna Narayanan , Fabio Luporini , Gerard Gorman , Paul Hovland

We introduce a general formulation for automatic differentiation through direct form filters, yielding a closed-form backpropagation that includes initial condition gradients. The result is a single expression that can represent both the…

Systems and Control · Electrical Eng. & Systems 2025-11-25 Chin-Yun Yu , György Fazekas

We show that, under certain circumstances, it is possible to automatically compute Jacobian-inverse-vector and Jacobian-inverse-transpose-vector products about as efficiently as Jacobian-vector and Jacobian-transpose-vector products. The…

Numerical Analysis · Mathematics 2026-03-18 Barak A. Pearlmutter , Jeffrey Mark Siskind

In a multi-agent network, we consider the problem of minimizing an objective function that is expressed as the sum of private convex and smooth functions, and a (possibly) non-differentiable convex regularizer. We propose a novel…

Optimization and Control · Mathematics 2021-09-30 Yichuan Li , Nikolaos M. Freris , Petros Voulgaris , Dusan Stipanovic

From implicit differentiation to probabilistic modeling, Jacobian and Hessian matrices have many potential use cases in Machine Learning (ML), but they are viewed as computationally prohibitive. Fortunately, these matrices often exhibit…

Machine Learning · Computer Science 2025-06-12 Adrian Hill , Guillaume Dalle

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…

Computational Physics · Physics 2023-08-28 Shi-Xin Zhang , Zhou-Quan Wan , Hong Yao

No single Automatic Differentiation (AD) system is the optimal choice for all problems. This means informed selection of an AD system and combinations can be a problem-specific variable that can greatly impact performance. In the Julia…

Mathematical Software · Computer Science 2022-02-08 Frank Schäfer , Mohamed Tarek , Lyndon White , Chris Rackauckas

Anomaly detection (AD) is the machine learning task of identifying highly discrepant abnormal samples by solely relying on the consistency of the normal training samples. Under the constraints of a distribution shift, the assumption that…

Machine Learning · Computer Science 2023-12-25 João B. S. Carvalho , Mengtao Zhang , Robin Geyer , Carlos Cotrini , Joachim M. Buhmann

We extend JAX with the capability to automatically differentiate higher-order functions (functionals and operators). By representing functions as a generalization of arrays, we seamlessly use JAX's existing primitive system to implement…

Programming Languages · Computer Science 2024-01-30 Min Lin

This paper presents an artificial intelligence algorithm that can be used to derive formulas from various scientific disciplines called automatic derivation machine. First, the formula is abstractly expressed as a multiway tree model, and…

Artificial Intelligence · Computer Science 2018-08-16 MinZhong Luo , Li Liu

Anomaly detection (AD) plays a vital role across a wide range of real-world domains by identifying data instances that deviate from expected patterns, potentially signaling critical events such as system failures, fraudulent activities, or…

Machine Learning · Computer Science 2025-07-11 Amirhossein Sadough , Mahyar Shahsavari , Mark Wijtvliet , Marcel van Gerven

Automatic generation of convex relaxations and subgradients is critical in global optimization, and is typically carried out using variants of automatic/algorithmic differentiation (AD). At previous AD conferences, variants of the forward…

Optimization and Control · Mathematics 2025-01-31 Yingkai Song , Kamil A. Khan

Differential machine learning combines automatic adjoint differentiation (AAD) with modern machine learning (ML) in the context of risk management of financial Derivatives. We introduce novel algorithms for training fast, accurate pricing…

Computational Finance · Quantitative Finance 2020-10-01 Brian Huge , Antoine Savine

The Dynamic Mode Decomposition (DMD) extracted dynamic modes are the non-orthogonal eigenvectors of the matrix that best approximates the one-step temporal evolution of the multivariate samples. In the context of dynamical system analysis,…

Statistics Theory · Mathematics 2020-03-09 Arvind Prasadan , Raj Rao Nadakuditi

We propose AD3, a new algorithm for approximate maximum a posteriori (MAP) inference on factor graphs based on the alternating directions method of multipliers. Like dual decomposition algorithms, AD3 uses worker nodes to iteratively solve…

Artificial Intelligence · Computer Science 2013-01-01 Andre F. T. Martins , Mario A. T. Figueiredo , Pedro M. Q. Aguiar , Noah A. Smith , Eric P. Xing

We derive the alternating-directions implicit (ADI) method based on a commuting operator split and apply the results in detail to the continuous time algebraic Lyapunov equation with low-rank constant term and approximate solution, giving…

Numerical Analysis · Mathematics 2025-01-24 Jonas Schulze , Jens Saak

Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE). Gradient-based optimization methods are considered…

Numerical Analysis · Mathematics 2019-12-17 Kailai Xu , Dongzhuo Li , Eric Darve , Jerry M. Harris

Trajectory prediction is central to the safe and seamless operation of autonomous vehicles (AVs). In deployment, however, prediction models inevitably face distribution shifts between training data and real-world conditions, where rare or…

Computer Vision and Pattern Recognition · Computer Science 2026-03-16 Tongfei Guo , Lili Su

Combinatory Homomorphic Automatic Differentiation (CHAD) was originally formulated as a semantics-driven source-to-source transformation for reverse-mode AD of total (terminating) functional programs. In this work, we extend CHAD to…

Programming Languages · Computer Science 2025-08-15 Fernando Lucatelli Nunes , Gordon Plotkin , Matthijs Vákár

The concept of a recently proposed Forward-Forward learning algorithm for fully connected artificial neural networks is applied to a single multi output perceptron for classification. The parameters of the system are trained with respect to…

Machine Learning · Computer Science 2023-04-07 K. Fredrik Karlsson