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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…

Symbolic Computation · Computer Science 2014-05-20 Juan Luis Valerdi , Fernando Raul Rodriguez

An activation function is an element-wise mathematical function and plays a crucial role in deep neural networks (DNN). Many novel and sophisticated activation functions have been proposed to improve the DNN accuracy but also consume…

Machine Learning · Computer Science 2022-09-23 Cong Guo , Yuxian Qiu , Jingwen Leng , Chen Zhang , Ying Cao , Quanlu Zhang , Yunxin Liu , Fan Yang , Minyi Guo

Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…

Programming Languages · Computer Science 2020-02-04 Martin Abadi , Gordon D. Plotkin

Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had…

Machine Learning · Computer Science 2024-05-07 Christina Runkel , Ander Biguri , Carola-Bibiane Schönlieb

Optimizing neural networks with loss that contain high-dimensional and high-order differential operators is expensive to evaluate with back-propagation due to $\mathcal{O}(d^{k})$ scaling of the derivative tensor size and the…

Machine Learning · Computer Science 2025-01-14 Zekun Shi , Zheyuan Hu , Min Lin , Kenji Kawaguchi

Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…

Machine Learning · Computer Science 2025-05-29 Zhonglin Xie , Yiman Fong , Haoran Yuan , Zaiwen Wen

In the past few years, Differentiable Neural Architecture Search (DNAS) rapidly imposed itself as the trending approach to automate the discovery of deep neural network architectures. This rise is mainly due to the popularity of DARTS, one…

Machine Learning · Computer Science 2023-05-02 Alexandre Heuillet , Ahmad Nasser , Hichem Arioui , Hedi Tabia

This document presents a new C++ Automatic Differentiation (AD) tool, AD-HOC (Automatic Differentiation for High-Order Calculations). This tool aims to have the following features: -Calculation of user specified derivatives of arbitrary…

Mathematical Software · Computer Science 2024-12-13 Juan Lucas Rey

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

Automatic differentiation---the mechanical transformation of numeric computer programs to calculate derivatives efficiently and accurately---dates to the origin of the computer age. Reverse mode automatic differentiation both antedates and…

Machine Learning · Computer Science 2014-04-30 Atilim Gunes Baydin , Barak A. Pearlmutter

Neural differential equation models have garnered significant attention in recent years for their effectiveness in machine learning applications.Among these, fractional differential equations (FDEs) have emerged as a promising tool due to…

Machine Learning · Computer Science 2025-03-21 Wenjun Cui , Qiyu Kang , Xuhao Li , Kai Zhao , Wee Peng Tay , Weihua Deng , Yidong Li

Knowledge distillation has been widely used to produce portable and efficient neural networks which can be well applied on edge devices for computer vision tasks. However, almost all top-performing knowledge distillation methods need to…

Computer Vision and Pattern Recognition · Computer Science 2021-10-06 Haoran Zhao , Xin Sun , Junyu Dong , Hui Yu , Huiyu Zhou

Model-based design of experiments (MBDOE) is essential for efficient parameter estimation in nonlinear dynamical systems. However, conventional adaptive MBDOE requires costly posterior inference and design optimization between each…

Machine Learning · Statistics 2026-03-25 Arno Strouwen , Sebastian Micluţa-Câmpeanu

Although distributed machine learning has opened up many new and exciting research frontiers, fragmentation of models and data across different machines, nodes, and sites still results in considerable communication overhead, impeding…

Machine Learning · Computer Science 2022-02-04 Bradley T. Baker , Aashis Khanal , Vince D. Calhoun , Barak Pearlmutter , Sergey M. Plis

In this paper, we illustrate a novel method for solving optimization problems when derivatives are not explicitly available. We show that combining implicit filtering (IF), an existing derivative free optimization (DFO) method, with a deep…

Optimization and Control · Mathematics 2021-05-20 Brian Irwin , Eldad Haber , Raviv Gal , Avi Ziv

We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…

Numerical Analysis · Mathematics 2025-08-29 Zhenyu Zhao , Yanfei Wang , Xinran Liu

Anomaly detection techniques enable effective anomaly detection and diagnosis in multi-variate time series data, which are of major significance for today's industrial applications. However, establishing an anomaly detection system that can…

Machine Learning · Computer Science 2024-05-02 Lingrui Yu

The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or…

Machine Learning · Computer Science 2022-12-01 Zhilu Lai , Wei Liu , Xudong Jian , Kiran Bacsa , Limin Sun , Eleni Chatzi

NeurAlly-Decomposed Oracle (NADO) is a powerful approach for controllable generation with large language models. It is designed to avoid catastrophic forgetting while achieving guaranteed convergence to an entropy-maximized closed-form…

Computation and Language · Computer Science 2024-06-10 Sidi Lu , Wenbo Zhao , Chenyang Tao , Arpit Gupta , Shanchan Wu , Tagyoung Chung , Nanyun Peng

Algorithmic differentiation (AD) has become increasingly capable and straightforward to use. However, AD is inefficient when applied directly to solvers, a feature of most engineering analyses. We can leverage implicit differentiation to…

Optimization and Control · Mathematics 2023-06-28 Andrew Ning , Taylor McDonnell