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Explaining the output of a deep network remains a challenge. In the case of an image classifier, one type of explanation is to identify pixels that strongly influence the final decision. A starting point for this strategy is the gradient of…

Machine Learning · Computer Science 2017-06-14 Daniel Smilkov , Nikhil Thorat , Been Kim , Fernanda Viégas , Martin Wattenberg

Many efforts have been made for revealing the decision-making process of black-box learning machines such as deep neural networks, resulting in useful local and global explanation methods. For local explanation, stochasticity is known to…

Machine Learning · Computer Science 2023-03-29 Kirill Bykov , Anna Hedström , Shinichi Nakajima , Marina M. -C. Höhne

Integrated Gradients as an attribution method for deep neural network models offers simple implementability. However, it suffers from noisiness of explanations which affects the ease of interpretability. The SmoothGrad technique is proposed…

Computer Vision and Pattern Recognition · Computer Science 2021-09-03 Gary S. W. Goh , Sebastian Lapuschkin , Leander Weber , Wojciech Samek , Alexander Binder

Gradient Smoothing is an efficient approach to reducing noise in gradient-based model explanation method. SmoothGrad adds Gaussian noise to mitigate much of these noise. However, the crucial hyper-parameter in this method, the variance…

Machine Learning · Computer Science 2025-10-23 Linjiang Zhou , Chao Ma , Zepeng Wang , Libing Wu , Xiaochuan Shi

Binarized Neural Networks (BNNs) have the potential to revolutionize the way that deep learning is carried out in edge computing platforms. However, the effectiveness of interpretability methods on these networks has not been assessed. In…

Computer Vision and Pattern Recognition · Computer Science 2021-06-24 Amy Widdicombe , Simon J. Julier

Techniques for generating saliency maps continue to be used for explainability of deep learning models, with efforts primarily applied to the image classification task. Such techniques, however, can also be applied to object detectors, not…

Computer Vision and Pattern Recognition · Computer Science 2023-04-18 Chul Gwon , Steven C. Howell

We present Smooth Grad-CAM++, a technique which combines two recent techniques: SMOOTHGRAD and Grad-CAM++. Smooth Grad-CAM++ has the capability of either visualizing a layer, subset of feature maps, or subset of neurons within a feature map…

Computer Vision and Pattern Recognition · Computer Science 2019-12-05 Daniel Omeiza

Saliency Map, the gradient of the score function with respect to the input, is the most basic technique for interpreting deep neural network decisions. However, saliency maps are often visually noisy. Although several hypotheses were…

Machine Learning · Computer Science 2019-09-17 Beomsu Kim , Junghoon Seo , SeungHyun Jeon , Jamyoung Koo , Jeongyeol Choe , Taegyun Jeon

Gradient-based saliency methods such as Vanilla Gradient (VG) and Integrated Gradients (IG) are widely used to explain image classifiers, yet the resulting maps are often noisy and unstable, limiting their usefulness in high-stakes…

Computer Vision and Pattern Recognition · Computer Science 2026-03-10 Dipkamal Bhusal , Md Tanvirul Alam , Nidhi Rastogi

Gradients play a pivotal role in neural networks explanation. The inherent high dimensionality and structural complexity of neural networks result in the original gradients containing a significant amount of noise. While several approaches…

Machine Learning · Computer Science 2024-07-02 Linjiang Zhou , Xiaochuan Shi , Chao Ma , Zepeng Wang

This paper formalizes and analyzes Gaussian smoothing applied to two prominent optimization methods: Stochastic Gradient Descent (GSmoothSGD) and Adam (GSmoothAdam) in deep learning. By attenuating small fluctuations, Gaussian smoothing…

Optimization and Control · Mathematics 2024-11-19 Andrew Starnes , Clayton Webster

In this work, we investigate methods to reduce the noise in deep saliency maps coming from convolutional downsampling. Those methods make the investigated models more interpretable for gradient-based saliency maps, computed in hidden…

Computer Vision and Pattern Recognition · Computer Science 2024-08-09 Rudolf Herdt , Maximilian Schmidt , Daniel Otero Baguer , Peter Maaß

Gaining insight into how deep convolutional neural network models perform image classification and how to explain their outputs have been a concern to computer vision researchers and decision makers. These deep models are often referred to…

Computer Vision and Pattern Recognition · Computer Science 2019-08-06 Daniel Omeiza , Skyler Speakman , Celia Cintas , Komminist Weldermariam

Saliency maps have been widely used to interpret the decisions of neural network classifiers and discover phenomena from their learned functions. However, standard gradient-based maps are frequently observed to be highly sensitive to the…

Computer Vision and Pattern Recognition · Computer Science 2025-03-12 Zhuorui Ye , Farzan Farnia

Gradient-based saliency methods are widely used to interpret deep neural networks, yet they often produce noisy and unstable explanations that poorly align with semantically meaningful input features. We argue that a fundamental cause of…

Computer Vision and Pattern Recognition · Computer Science 2026-04-29 Ali Karkehabadi , Jamshid Hassanpour , Houman Homayoun , Avesta Sasan

The gradient noise of SGD is considered to play a central role in the observed strong generalization abilities of deep learning. While past studies confirm that the magnitude and the covariance structure of gradient noise are critical for…

Machine Learning · Computer Science 2020-06-22 Jingfeng Wu , Wenqing Hu , Haoyi Xiong , Jun Huan , Vladimir Braverman , Zhanxing Zhu

Simulated DAG models may exhibit properties that, perhaps inadvertently, render their structure identifiable and unexpectedly affect structure learning algorithms. Here, we show that marginal variance tends to increase along the causal…

Machine Learning · Statistics 2021-11-11 Alexander G. Reisach , Christof Seiler , Sebastian Weichwald

Adaptive gradient methods have been widely adopted in training large-scale deep neural networks, especially large foundation models. Despite the huge success in practice, their theoretical advantages over classical gradient methods with…

Machine Learning · Computer Science 2024-10-15 Yuxing Liu , Rui Pan , Tong Zhang

Randomized smoothing is a technique for providing provable robustness guarantees against adversarial attacks while making minimal assumptions about a classifier. This method relies on taking a majority vote of any base classifier over…

Machine Learning · Computer Science 2023-05-09 Ambar Pal , Jeremias Sulam

Saliency methods can make deep neural network predictions more interpretable by identifying a set of critical features in an input sample, such as pixels that contribute most strongly to a prediction made by an image classifier.…

Machine Learning · Computer Science 2021-06-15 Yang Lu , Wenbo Guo , Xinyu Xing , William Stafford Noble
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