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The backpropagation of error algorithm (backprop) has been instrumental in the recent success of deep learning. However, a key question remains as to whether backprop can be formulated in a manner suitable for implementation in neural…

Neural and Evolutionary Computing · Computer Science 2020-10-13 Beren Millidge , Alexander Tschantz , Anil K Seth , Christopher L Buckley

Dual numbers are a well-established tool for computing derivatives and constitute the basis of forward-mode automatic differentiation. While the theoretical framework for computing derivatives of arbitrary order is well understood,…

Numerical Analysis · Mathematics 2026-02-06 F. Peñuñuri , K. B. Cantún-Avila , R. Peón-Escalante

Adaptive stochastic gradient methods such as AdaGrad have gained popularity in particular for training deep neural networks. The most commonly used and studied variant maintains a diagonal matrix approximation to second order information by…

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

Machine learning models often suffer from catastrophic forgetting of previously learned knowledge when learning new classes. Various methods have been proposed to mitigate this issue. However, rehearsal-based learning, which retains samples…

Machine Learning · Computer Science 2024-10-10 Hossein Rezaei , Mohammad Sabokrou

We propose Algorithm Distillation (AD), a method for distilling reinforcement learning (RL) algorithms into neural networks by modeling their training histories with a causal sequence model. Algorithm Distillation treats learning to…

Responding to the challenge of detecting unusual radar targets in a well identified environment, innovative anomaly and novelty detection methods keep emerging in the literature. This work aims at presenting a benchmark gathering common and…

Signal Processing · Electrical Eng. & Systems 2021-06-22 Martin Bauw , Santiago Velasco-Forero , Jesus Angulo , Claude Adnet , Olivier Airiau

This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…

History and Overview · Mathematics 2025-01-28 Paige Bright , Alan Edelman , Steven G. Johnson

Automatic diagnosis (AD), a critical application of AI in healthcare, employs machine learning techniques to assist doctors in gathering patient symptom information for precise disease diagnosis. The Transformer-based method utilizes an…

Computation and Language · Computer Science 2023-07-18 Huimin Wang , Wai-Chung Kwan , Kam-Fai Wong , Yefeng Zheng

We show how to apply forward and reverse mode Combinatory Homomorphic Automatic Differentiation (CHAD) to total functional programming languages with expressive type systems featuring the combination of - tuple types; - sum types; -…

Programming Languages · Computer Science 2023-11-13 Fernando Lucatelli Nunes , Matthijs Vákár

Tensor parallelism is an essential technique for distributed training of large neural networks. However, automatically determining an optimal tensor parallel strategy is challenging due to the gigantic search space, which grows…

Machine Learning · Computer Science 2025-08-06 Ziji Shi , Le Jiang , Ang Wang , Jie Zhang , Chencan Wu , Yong Li , Xiaokui Xiao , Wei Lin , Jialin Li

A novel approach is given to overcome the computational challenges of the full-matrix Adaptive Gradient algorithm (Full AdaGrad) in stochastic optimization. By developing a recursive method that estimates the inverse of the square root of…

Statistics Theory · Mathematics 2025-02-28 Antoine Godichon-Baggioni , Wei Lu , Bruno Portier

Inspired by the recent success of deep neural networks and the recent efforts to develop multi-layer dictionary models, we propose a Deep Analysis dictionary Model (DeepAM) which is optimized to address a specific regression task known as…

Machine Learning · Statistics 2021-02-03 Jun-Jie Huang , Pier Luigi Dragotti

Ptychography is a lensless imaging method that allows for wavefront sensing and phase-sensitive microscopy from a set of diffraction patterns. Recently, it has been shown that the optimization task in ptychography can be achieved via…

Image and Video Processing · Electrical Eng. & Systems 2021-01-13 Jacob Seifert , Dorian Bouchet , Lars Loetgering , Allard P. Mosk

In the realm of Adversarial Distillation (AD), strategic and precise knowledge transfer from an adversarially robust teacher model to a less robust student model is paramount. Our Dynamic Guidance Adversarial Distillation (DGAD) framework…

Computer Vision and Pattern Recognition · Computer Science 2024-09-04 Hyejin Park , Dongbo Min

The adaptive gradient online learning method known as AdaGrad has seen widespread use in the machine learning community in stochastic and adversarial online learning problems and more recently in deep learning methods. The method's…

Machine Learning · Computer Science 2016-10-05 Nishant A. Mehta , Alistair Rendell , Anish Varghese , Christfried Webers

Detecting out of distribution (OOD) samples is of paramount importance in all Machine Learning applications. Deep generative modeling has emerged as a dominant paradigm to model complex data distributions without labels. However, prior work…

Machine Learning · Computer Science 2021-01-05 Gowthami Somepalli , Yexin Wu , Yogesh Balaji , Bhanukiran Vinzamuri , Soheil Feizi

Stochastic gradient descent (SGD) has taken the stage as the primary workhorse for large-scale machine learning. It is often used with its adaptive variants such as AdaGrad, Adam, and AMSGrad. This paper proposes an adaptive stochastic…

Machine Learning · Computer Science 2021-01-01 Tianyi Chen , Ziye Guo , Yuejiao Sun , Wotao Yin

Deep learning has redefined the field of artificial intelligence (AI) thanks to the rise of artificial neural networks, which are architectures inspired by their neurological counterpart in the brain. Through the years, this dualism between…

Machine Learning · Computer Science 2023-02-21 Tommaso Salvatori , Yuhang Song , Thomas Lukasiewicz , Rafal Bogacz , Zhenghua Xu

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