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The optimization algorithms are crucial in training physics-informed neural networks (PINNs), as unsuitable methods may lead to poor solutions. Compared to the common gradient descent (GD) algorithm, implicit gradient descent (IGD)…

Machine Learning · Computer Science 2025-08-04 Xianliang Xu , Ting Du , Wang Kong , Bin Shan , Ye Li , Zhongyi Huang

Despite the recent progress in Graph Neural Networks (GNNs), it remains challenging to explain the predictions made by GNNs. Existing explanation methods mainly focus on post-hoc explanations where another explanatory model is employed to…

Machine Learning · Computer Science 2021-12-03 Zaixi Zhang , Qi Liu , Hao Wang , Chengqiang Lu , Cheekong Lee

Neural networks have achieved remarkable success across various fields. However, the lack of interpretability limits their practical use, particularly in critical decision-making scenarios. Post-hoc interpretability, which provides…

Machine Learning · Computer Science 2025-11-21 Yang Ji , Ying Sun , Yuting Zhang , Zhigaoyuan Wang , Yuanxin Zhuang , Zheng Gong , Dazhong Shen , Chuan Qin , Hengshu Zhu , Hui Xiong

This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…

Numerical Analysis · Mathematics 2024-05-14 Foivos Alimisis , Yousef Saad , Bart Vandereycken

In machine learning, accurately predicting the probability that a specific input is correct is crucial for risk management. This process, known as uncertainty (or confidence) estimation, is particularly important in mission-critical…

Machine Learning · Computer Science 2023-01-12 Gabriella Chouraqui , Liron Cohen , Gil Einziger , Liel Leman

Understanding specifically where a model focuses on within an image is critical for human interpretability of the decision-making process. Deep learning-based solutions are prone to learning coincidental correlations in training datasets,…

Computer Vision and Pattern Recognition · Computer Science 2024-10-22 Aidan Boyd , Mohamed Trabelsi , Huseyin Uzunalioglu , Dan Kushnir

An influential line of recent work has focused on the generalization properties of unregularized gradient-based learning procedures applied to separable linear classification with exponentially-tailed loss functions. The ability of such…

Machine Learning · Computer Science 2022-06-24 Matan Schliserman , Tomer Koren

In this paper, we visualize and quantify the predictive uncertainty of gradient-based post hoc visual explanations for neural networks. Predictive uncertainty refers to the variability in the network predictions under perturbations to the…

Machine Learning · Computer Science 2024-06-04 Mohit Prabhushankar , Ghassan AlRegib

Graph neural networks (GNNs) are powerful graph-based deep-learning models that have gained significant attention and demonstrated remarkable performance in various domains, including natural language processing, drug discovery, and…

Machine Learning · Computer Science 2023-06-06 Jaykumar Kakkad , Jaspal Jannu , Kartik Sharma , Charu Aggarwal , Sourav Medya

Urban land use inference is a critically important task that aids in city planning and policy-making. Recently, the increased use of sensor and location technologies has facilitated the collection of multi-modal mobility data, offering…

Artificial Intelligence · Computer Science 2026-05-11 Xuehao Zhai , Junqi Jiang , Adam Dejl , Antonio Rago , Fangce Guo , Francesca Toni , Aruna Sivakumar

We propose the first unsupervised and learning-based method to identify interpretable directions in h-space of pre-trained diffusion models. Our method is derived from an existing technique that operates on the GAN latent space.…

Computer Vision and Pattern Recognition · Computer Science 2023-12-01 Zijian Zhang , Luping Liu , Zhijie Lin , Yichen Zhu , Zhou Zhao

In this paper, an enhancement technique for the class activation mapping methods such as gradient-weighted class activation maps or excitation backpropagation is proposed to present the visual explanations of decisions from convolutional…

Computer Vision and Pattern Recognition · Computer Science 2021-07-08 Tomasz Szandala

While numerous approaches have been developed to embed graphs into either Euclidean or hyperbolic spaces, they do not fully utilize the information available in graphs, or lack the flexibility to model intrinsic complex graph geometry. To…

Machine Learning · Computer Science 2020-10-26 Shichao Zhu , Shirui Pan , Chuan Zhou , Jia Wu , Yanan Cao , Bin Wang

Any prediction from a model is made by a combination of learning history and test stimuli. This provides significant insights for improving model interpretability: {\it because of which part(s) of which training example(s), the model…

Computation and Language · Computer Science 2020-11-03 Yuxian Meng , Chun Fan , Zijun Sun , Eduard Hovy , Fei Wu , Jiwei Li

As the use of deep learning techniques has grown across various fields over the past decade, complaints about the opaqueness of the black-box models have increased, resulting in an increased focus on transparency in deep learning models.…

Computation and Language · Computer Science 2024-03-19 Siwen Luo , Hamish Ivison , Caren Han , Josiah Poon

Prototype learning, a popular machine learning method designed for inherently interpretable decisions, leverages similarities to learned prototypes for classifying new data. While it is mainly applied in computer vision, in this work, we…

Computation and Language · Computer Science 2023-12-14 Claudio Fanconi , Moritz Vandenhirtz , Severin Husmann , Julia E. Vogt

Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of…

Machine Learning · Computer Science 2023-06-28 Haitz Sáez de Ocáriz Borde , Anees Kazi , Federico Barbero , Pietro Liò

In deep learning, it is common to use more network parameters than training points. In such scenarioof over-parameterization, there are usually multiple networks that achieve zero training error so that thetraining algorithm induces an…

Machine Learning · Computer Science 2023-08-22 Hung-Hsu Chou , Carsten Gieshoff , Johannes Maly , Holger Rauhut

Even for the gradient descent (GD) method applied to neural network training, understanding its optimization dynamics, including convergence rate, iterate trajectories, function value oscillations, and especially its implicit acceleration,…

Machine Learning · Computer Science 2026-05-22 Alexander Tyurin

Graph neural networks (GNNs) have demonstrated a significant boost in prediction performance on graph data. At the same time, the predictions made by these models are often hard to interpret. In that regard, many efforts have been made to…

Machine Learning · Computer Science 2023-05-24 Yiqiao Li , Jianlong Zhou , Sunny Verma , Fang Chen