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An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…

Optimization and Control · Mathematics 2026-05-11 Yunlang Zhu , Lingjun Guo , Zahra Khatti , Xiaoyi Qu , Chia-Yuan Wu , Lara Zebiane , Frank E. Curtis

The fragility of deep neural networks to adversarially-chosen inputs has motivated the need to revisit deep learning algorithms. Including adversarial examples during training is a popular defense mechanism against adversarial attacks. This…

Optimization and Control · Mathematics 2020-05-05 Jacob H. Seidman , Mahyar Fazlyab , Victor M. Preciado , George J. Pappas

Loss function learning is a new meta-learning paradigm that aims to automate the essential task of designing a loss function for a machine learning model. Existing techniques for loss function learning have shown promising results, often…

Machine Learning · Computer Science 2025-10-14 Christian Raymond , Qi Chen , Bing Xue , Mengjie Zhang

This work formulates the machine learning mechanism as a bi-level optimization problem. The inner level optimization loop entails minimizing a properly chosen loss function evaluated on the training data. This is nothing but the…

Machine Learning · Computer Science 2023-01-27 Maziar Raissi

Cross-entropy is a widely used loss function in applications. It coincides with the logistic loss applied to the outputs of a neural network, when the softmax is used. But, what guarantees can we rely on when using cross-entropy as a…

Machine Learning · Computer Science 2023-06-21 Anqi Mao , Mehryar Mohri , Yutao Zhong

Learning from label proportions (LLP) aims at learning an instance-level classifier with label proportions in grouped training data. Existing deep learning based LLP methods utilize end-to-end pipelines to obtain the proportional loss with…

Machine Learning · Computer Science 2021-05-25 Jiabin Liu , Bo Wang , Xin Shen , Zhiquan Qi , Yingjie Tian

Training of neural networks amounts to nonconvex optimization problems that are typically solved by using backpropagation and (variants of) stochastic gradient descent. In this work we propose an alternative approach by viewing the training…

Optimization and Control · Mathematics 2022-04-14 Brecht Evens , Puya Latafat , Andreas Themelis , Johan Suykens , Panagiotis Patrinos

We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply…

Statistical Mechanics · Physics 2026-02-05 Lorenzo Buffa , Dario Mazzilli , Riccardo Piombo , Fabio Saracco , Giulio Cimini , Aurelio Patelli

We introduce two-scale loss functions for use in various gradient descent algorithms applied to classification problems via deep neural networks. This new method is generic in the sense that it can be applied to a wide range of machine…

Numerical Analysis · Mathematics 2021-09-03 Leonid Berlyand , Robert Creese , Pierre-Emmanuel Jabin

This paper presents an implementation of multilayer feed forward neural networks (NN) to optimize CMOS analog circuits. For modeling and design recently neural network computational modules have got acceptance as an unorthodox and useful…

Neural and Evolutionary Computing · Computer Science 2012-12-13 Mriganka Chakraborty

Multi-task learning (MTL) is an active field in deep learning in which we train a model to jointly learn multiple tasks by exploiting relationships between the tasks. It has been shown that MTL helps the model share the learned features…

Computer Vision and Pattern Recognition · Computer Science 2021-11-30 Akihiro Nakano , Shi Chen , Kazuyuki Demachi

The weights of a deep neural network model are optimized in conjunction with the governing flow equations to provide a model for sub-grid-scale stresses in a temporally developing plane turbulent jet at Reynolds number $Re_0=6\,000$. The…

Fluid Dynamics · Physics 2023-03-23 Jonathan F. MacArt , Justin Sirignano , Jonathan B. Freund

In sequence prediction tasks like neural machine translation, training with cross-entropy loss often leads to models that overgeneralize and plunge into local optima. In this paper, we propose an extended loss function called \emph{dual…

Computation and Language · Computer Science 2021-04-20 Zuchao Li , Hai Zhao , Yingting Wu , Fengshun Xiao , Shu Jiang

We propose a training formulation for ResNets reflecting an optimal control problem that is applicable for standard architectures and general loss functions. We suggest bridging both worlds via penalizing intermediate outputs of hidden…

Machine Learning · Computer Science 2025-06-27 Jens Püttschneider , Simon Heilig , Asja Fischer , Timm Faulwasser

The cross-entropy (CE) method is simple and versatile technique for optimization, based on Kullback-Leibler (or cross-entropy) minimization. The method can be applied to a wide range of optimization tasks, including continuous, discrete,…

Computation · Statistics 2015-03-09 Tim Benham , Qibin Duan , Dirk P. Kroese , Benoit Liquet

This paper aims to overcome a fundamental problem in the theory and application of deep neural networks (DNNs). We propose a method to solve the local minimum problem in training DNNs directly. Our method is based on the cross-entropy loss…

Machine Learning · Computer Science 2020-12-29 Huachuan Wang , James Ting-Ho Lo

A method is provided for designing and training noise-driven recurrent neural networks as models of stochastic processes. The method unifies and generalizes two known separate modeling approaches, Echo State Networks (ESN) and Linear…

Adaptation and Self-Organizing Systems · Physics 2014-04-14 Mathieu N. Galtier , Camille Marini , Gilles Wainrib , Herbert Jaeger

Although deep learning performs really well in a wide variety of tasks, it still suffers from catastrophic forgetting -- the tendency of neural networks to forget previously learned information upon learning new tasks where previous data is…

Computer Vision and Pattern Recognition · Computer Science 2020-02-04 Ankur Singh

The traditional approach to distributed machine learning is to adapt learning algorithms to the network, e.g., reducing updates to curb overhead. Networks based on intelligent edge, instead, make it possible to follow the opposite approach,…

Networking and Internet Architecture · Computer Science 2022-07-07 Francesco Malandrino , Carla Fabiana Chiasserini , Nuria Molner , Antonio De La Oliva

In this work, we propose a novel cross Q-learning algorithm, aim at alleviating the well-known overestimation problem in value-based reinforcement learning methods, particularly in the deep Q-networks where the overestimation is exaggerated…

Artificial Intelligence · Computer Science 2020-09-30 Xing Wang , Alexander Vinel
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