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Complex-valued neural networks (CVNNs) have recently been successful in various pioneering areas which involve wave-typed information and frequency-domain processing. This work addresses different structures and classification of CVNNs. The…

Machine Learning · Computer Science 2023-12-12 Rayyan Abdalla

We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal $\pm$ rank-$r$ symmetric positive definite matrices. This special type of metric allows for a…

Optimization and Control · Mathematics 2018-11-27 Stephen Becker , Jalal Fadili , Peter Ochs

We introduce new multilevel methods for solving large-scale unconstrained optimization problems. Specifically, the philosophy of multilevel methods is applied to Newton-type methods that regularize the Newton sub-problem using second order…

Optimization and Control · Mathematics 2024-07-16 Nick Tsipinakis , Panos Parpas

Gradients have been exploited in proposal distributions to accelerate the convergence of Markov chain Monte Carlo algorithms on discrete distributions. However, these methods require a natural differentiable extension of the target discrete…

Machine Learning · Computer Science 2023-02-28 Yue Xiang , Dongyao Zhu , Bowen Lei , Dongkuan Xu , Ruqi Zhang

Perforated Backpropagation is a neural network optimization technique based on modern understanding of the computational importance of dendrites within biological neurons. This paper explores further experiments from the original…

Machine Learning · Computer Science 2025-06-03 Rorry Brenner , Evan Davis , Rushi Chaudhari , Rowan Morse , Jingyao Chen , Xirui Liu , Zhaoyi You , Laurent Itti

Despite being the cornerstone of deep learning, backpropagation is criticized for its inherent sequentiality, which can limit the scalability of very deep models. Such models faced convergence issues due to vanishing gradient, later…

Machine Learning · Computer Science 2025-04-01 Erwan Fagnou , Paul Caillon , Blaise Delattre , Alexandre Allauzen

The choice of activation function can significantly influence the performance of neural networks. The lack of guiding principles for the selection of activation function is lamentable. We try to address this issue by introducing our…

Machine Learning · Computer Science 2018-10-16 Yiwei Li , Enzhi Li

Memory footprint is one of the main limiting factors for large neural network training. In backpropagation, one needs to store the input to each operation in the computational graph. Every modern neural network model has quite a few…

Machine Learning · Computer Science 2022-02-04 Georgii Novikov , Daniel Bershatsky , Julia Gusak , Alex Shonenkov , Denis Dimitrov , Ivan Oseledets

A technique for accelerating global convergence of pseudo-transient continuation Newton methods is proposed based on residual smoothing. The technique is motivated by the effectiveness of local nonlinear smoothers at overcoming strong…

Numerical Analysis · Mathematics 2018-05-11 Dimitri Mavriplis

Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modeled as the solution to an optimization problem. Here the exact gradient with respect to the hyperparameters…

Optimization and Control · Mathematics 2023-11-16 Matthias J. Ehrhardt , Lindon Roberts

The back-propagation (BP) algorithm has been considered the de-facto method for training deep neural networks. It back-propagates errors from the output layer to the hidden layers in an exact manner using the transpose of the feedforward…

Neural and Evolutionary Computing · Computer Science 2018-05-01 Hongyin Luo , Jie Fu , James Glass

Deep learning has shown promising results in many machine learning applications. The hierarchical feature representation built by deep networks enable compact and precise encoding of the data. A kernel analysis of the trained deep networks…

Machine Learning · Computer Science 2017-03-22 Mandar Kulkarni , Shirish Karande

Ability of deep networks to extract high level features and of recurrent networks to perform time-series inference have been studied. In view of universality of one hidden layer network at approximating functions under weak constraints, the…

Neural and Evolutionary Computing · Computer Science 2014-12-19 Sharat C. Prasad , Piyush Prasad

We describe, implement and test a novel method for training neural networks to estimate the Jacobian matrix $J$ of an unknown multivariate function $F$. The training set is constructed from finitely many pairs $(x,F(x))$ and it contains no…

Machine Learning · Computer Science 2022-04-04 Frédéric Latrémolière , Sadananda Narayanappa , Petr Vojtěchovský

Working with any gradient-based machine learning algorithm involves the tedious task of tuning the optimizer's hyperparameters, such as its step size. Recent work has shown how the step size can itself be optimized alongside the model…

Machine Learning · Computer Science 2022-10-18 Kartik Chandra , Audrey Xie , Jonathan Ragan-Kelley , Erik Meijer

We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably…

Machine Learning · Computer Science 2014-05-15 Ohad Shamir , Nathan Srebro , Tong Zhang

Neural network learning is usually time-consuming since backpropagation needs to compute full gradients and backpropagate them across multiple layers. Despite its success of existing works in accelerating propagation through sparseness, the…

Machine Learning · Computer Science 2020-10-28 Zhiyuan Zhang , Pengcheng Yang , Xuancheng Ren , Qi Su , Xu Sun

Homomorphic encryption (HE) is a promising technique used for privacy-preserving computation. Since HE schemes only support primitive polynomial operations, homomorphic evaluation of polynomial approximations for non-polynomial functions…

Cryptography and Security · Computer Science 2024-05-27 John Chiang

Bilevel optimization has been recently revisited for designing and analyzing algorithms in hyperparameter tuning and meta learning tasks. However, due to its nested structure, evaluating exact gradients for high-dimensional problems is…

Machine Learning · Computer Science 2019-04-09 Amirreza Shaban , Ching-An Cheng , Nathan Hatch , Byron Boots

This work proposes an algorithm for taking advantage of backpropagation gradients to determine feature importance at different stages of training. Additionally, we propose a way to represent the learning process qualitatively. Experiments…

Machine Learning · Computer Science 2020-12-08 Roberto Reyes-Ochoa , Servando Lopez-Aguayo