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Reliable uncertainty estimation is crucial for machine learning models, especially in safety-critical domains. While exact Bayesian inference offers a principled approach, it is often computationally infeasible for deep neural networks.…

Machine Learning · Computer Science 2025-12-18 Aslak Djupskås , Alexander Johannes Stasik , Signe Riemer-Sørensen

Derivatives of differential equation solutions are commonly for parameter estimation, fitting neural differential equations, and as model diagnostics. However, with a litany of choices and a Cartesian product of potential methods, it can be…

Numerical Analysis · Computer Science 2021-07-21 Yingbo Ma , Vaibhav Dixit , Mike Innes , Xingjian Guo , Christopher Rackauckas

Modern neural network training relies on piece-wise (sub-)differentiable functions in order to use backpropagation to update model parameters. In this work, we introduce a novel method to allow simple non-differentiable functions at…

Machine Learning · Computer Science 2019-10-29 Jason Ramapuram , Russ Webb

We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher-order language with algebraic data types and we characterise it as the unique structure-preserving macro given a…

Programming Languages · Computer Science 2026-05-07 Mathieu Huot , Sam Staton , Matthijs Vákár

Lax-Wendroff methods combined with discontinuous Galerkin/flux reconstruction spatial discretization provide a high-order, single-stage, quadrature-free method for solving hyperbolic conservation laws. In this work, we introduce automatic…

Numerical Analysis · Mathematics 2026-02-06 Arpit Babbar , Valentin Churavy , Michael Schlottke-Lakemper , Hendrik Ranocha

This paper derives new inexact variants of the Douglas-Rachford splitting method for maximal monotone operators and the alternating direction method of multipliers (ADMM) for convex optimization. The analysis is based on a new inexact…

Optimization and Control · Mathematics 2019-04-25 M. Marques Alves , Jonathan Eckstein , Marina Geremia , Jefferson Melo

AutoAugment has been a powerful algorithm that improves the accuracy of many vision tasks, yet it is sensitive to the operator space as well as hyper-parameters, and an improper setting may degenerate network optimization. This paper delves…

Computer Vision and Pattern Recognition · Computer Science 2020-03-26 Longhui Wei , An Xiao , Lingxi Xie , Xin Chen , Xiaopeng Zhang , Qi Tian

The existence of completely aligned and paired multi-modal neuroimaging data has proved its effectiveness in the diagnosis of brain diseases. However, collecting the full set of well-aligned and paired data is impractical, since the…

Image and Video Processing · Electrical Eng. & Systems 2022-07-19 Jinbao Wang , Guoyang Xie , Yawen Huang , Yefeng Zheng , Yaochu Jin , Feng Zheng

Automatic differentiation (AD) has been a topic of interest for researchers in many disciplines, with increased popularity since its application to machine learning and neural networks. Although many researchers appreciate and know how to…

Programming Languages · Computer Science 2023-08-10 Birthe van den Berg , Tom Schrijvers , James McKinna , Alexander Vandenbroucke

We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich history spanning statistics, machine learning…

Data Structures and Algorithms · Computer Science 2019-03-18 Ilias Diakonikolas , Gautam Kamath , Daniel Kane , Jerry Li , Ankur Moitra , Alistair Stewart

In this paper we introduce DiffSharp, an automatic differentiation (AD) library designed with machine learning in mind. AD is a family of techniques that evaluate derivatives at machine precision with only a small constant factor of…

Mathematical Software · Computer Science 2015-11-30 Atilim Gunes Baydin , Barak A. Pearlmutter , Jeffrey Mark Siskind

The commitment to single-precision floating-point arithmetic is widespread in the deep learning community. To evaluate whether this commitment is justified, the influence of computing precision (single and double precision) on the…

Machine Learning · Computer Science 2022-11-01 Tomas Hrycej , Bernhard Bermeitinger , Siegfried Handschuh

Reducing hardware overhead of neural networks for faster or lower power inference and training is an active area of research. Uniform quantization using integer multiply-add has been thoroughly investigated, which requires learning many…

Numerical Analysis · Computer Science 2018-11-06 Jeff Johnson

Due to massive amounts of data distributed across multiple locations, distributed machine learning has attracted a lot of research interests. Alternating Direction Method of Multipliers (ADMM) is a powerful method of designing distributed…

Machine Learning · Computer Science 2020-12-10 Jiahao Ding , Xiaoqi Qin , Wenjun Xu , Yanmin Gong , Chi Zhang , Miao Pan

Fractional-order differentiation has many characteristics different from integer-order differentiation. These characteristics can be applied to the optimization algorithms of artificial neural networks to obtain better results. However, due…

Machine Learning · Computer Science 2025-06-10 Xiaojun zhou , Chunna Zhao , Yaqun Huang , Chengli Zhou , Junjie Ye , Kemeng Xiang

We develop nested automatic differentiation (AD) algorithms for exact inference and learning in integer latent variable models. Recently, Winner, Sujono, and Sheldon showed how to reduce marginalization in a class of integer latent variable…

Machine Learning · Statistics 2018-06-11 Daniel Sheldon , Kevin Winner , Debora Sujono

We show how forward-mode automatic differentiation (AD) can be employed within larger reverse-mode computations to dynamically differentiate broadcast operations in a GPU-friendly manner. Our technique fully exploits the broadcast…

Mathematical Software · Computer Science 2018-10-26 Jarrett Revels , Tim Besard , Valentin Churavy , Bjorn De Sutter , Juan Pablo Vielma

Deep artificial neural networks famously struggle to learn from non-stationary streams of data. Without dedicated mitigation strategies, continual learning is associated with continuous forgetting of previous tasks and a progressive loss of…

Neurons and Cognition · Quantitative Biology 2025-12-29 Suzanne van der Veldt , Gido M. van de Ven , Sanne Moorman , Guillaume Etter

When training deep neural networks, keeping all tensors in high precision (e.g., 32-bit or even 16-bit floats) is often wasteful. However, keeping all tensors in low precision (e.g., 8-bit floats) can lead to unacceptable accuracy loss.…

Machine Learning · Computer Science 2023-06-26 Wonyeol Lee , Rahul Sharma , Alex Aiken

Automatic differentiation (autodiff) has revolutionized machine learning. It allows to express complex computations by composing elementary ones in creative ways and removes the burden of computing their derivatives by hand. More recently,…