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Differential equations are used in a wide variety of disciplines, describing the complex behavior of the physical world. Analytic solutions to these equations are often difficult to solve for, limiting our current ability to solve complex…

机器学习 · 计算机科学 2022-08-09 Ethan Mills , Alexey Pozdnyakov

A method is presented that allows to reduce a problem described by differential equations with initial and boundary conditions to the problem described only by differential equations. The advantage of using the modified problem for…

Supervised training of deep neural nets typically relies on minimizing cross-entropy. However, in many domains, we are interested in performing well on metrics specific to the application. In this paper we propose a direct loss minimization…

机器学习 · 计算机科学 2016-06-03 Yang Song , Alexander G. Schwing , Richard S. Zemel , Raquel Urtasun

Despite deep-learning being state-of-the-art for data-driven model predictions, it has not yet found frequent application in ecology. Given the low sample size typical in many environmental research fields, the default choice for the…

Loss functions are at the heart of deep learning, shaping how models learn and perform across diverse tasks. They are used to quantify the difference between predicted outputs and ground truth labels, guiding the optimization process to…

We introduce a novel loss function, Covariance Loss, which is conceptually equivalent to conditional neural processes and has a form of regularization so that is applicable to many kinds of neural networks. With the proposed loss, mappings…

机器学习 · 计算机科学 2025-04-02 Boseon Yoo , Jiwoo Lee , Janghoon Ju , Seijun Chung , Soyeon Kim , Jaesik Choi

Most state-of-the-art machine learning techniques revolve around the optimisation of loss functions. Defining appropriate loss functions is therefore critical to successfully solving problems in this field. In this survey, we present a…

机器学习 · 计算机科学 2024-11-19 Lorenzo Ciampiconi , Adam Elwood , Marco Leonardi , Ashraf Mohamed , Alessandro Rozza

Supervised training of neural networks for classification is typically performed with a global loss function. The loss function provides a gradient for the output layer, and this gradient is back-propagated to hidden layers to dictate an…

机器学习 · 统计学 2019-05-09 Arild Nøkland , Lars Hiller Eidnes

Applications of neural networks to data analyses in natural sciences are complicated by the fact that many inputs are subject to systematic uncertainties. To control the dependence of the neural network function to variations of the input…

数据分析、统计与概率 · 物理学 2020-02-25 Stefan Wunsch , Simon Jörger , Roger Wolf , Günter Quast

This paper presents a comprehensive review of loss functions and performance metrics in deep learning, highlighting key developments and practical insights across diverse application areas. We begin by outlining fundamental considerations…

Typically, loss functions, regularization mechanisms and other important aspects of training parametric models are chosen heuristically from a limited set of options. In this paper, we take the first step towards automating this process,…

In machine learning and statistical modeling, the mean square or absolute error is commonly used as an error metric, also called a "loss function." While effective in reducing the average error, this approach may fail to address localized…

最优化与控制 · 数学 2025-09-10 John M. Hanna , Hugues Talbot , Irene E. Vignon-Clementel

Neural network emulators have become an invaluable tool for a wide variety of climate and weather prediction tasks. While showing incredibly promising results, these networks do not have an inherent ability to produce equitable predictions.…

大气与海洋物理 · 物理学 2024-07-01 William Yik , Sam J. Silva

Many neural networks deployed in the real world scenarios are trained using cross entropy based loss functions. From the optimization perspective, it is known that the behavior of first order methods such as gradient descent crucially…

机器学习 · 计算机科学 2023-10-09 Zhu Wang , Praveen Raj Veluswami , Harsh Mishra , Sathya N. Ravi

Recent advances in deep learning have pushed the performances of visual saliency models way further than it has ever been. Numerous models in the literature present new ways to design neural networks, to arrange gaze pattern data, or to…

计算机视觉与模式识别 · 计算机科学 2019-07-05 Alexandre Bruckert , Hamed R. Tavakoli , Zhi Liu , Marc Christie , Olivier Le Meur

The choice of a loss function is an important factor when training neural networks for image restoration problems, such as single image super resolution. The loss function should encourage natural and perceptually pleasing results. A…

图像与视频处理 · 电气工程与系统科学 2021-10-19 Aamir Mustafa , Aliaksei Mikhailiuk , Dan Andrei Iliescu , Varun Babbar , Rafal K. Mantiuk

Neural networks have become increasingly prevalent within the geosciences, although a common limitation of their usage has been a lack of methods to interpret what the networks learn and how they make decisions. As such, neural networks…

大气与海洋物理 · 物理学 2020-10-28 Benjamin A. Toms , Elizabeth A. Barnes , Imme Ebert-Uphoff

Neural networks are becoming central in several areas of computer vision and image processing and different architectures have been proposed to solve specific problems. The impact of the loss layer of neural networks, however, has not…

计算机视觉与模式识别 · 计算机科学 2018-04-24 Hang Zhao , Orazio Gallo , Iuri Frosio , Jan Kautz

Learning with noisy labels is a common challenge in supervised learning. Existing approaches often require practitioners to specify noise rates, i.e., a set of parameters controlling the severity of label noises in the problem, and the…

机器学习 · 计算机科学 2020-08-18 Yang Liu , Hongyi Guo

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…

机器学习 · 计算机科学 2025-10-14 Christian Raymond , Qi Chen , Bing Xue , Mengjie Zhang
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