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Algebraic model counting unifies many inference tasks on logic formulas by exploiting semirings. Rather than focusing on inference, we consider learning, especially in statistical-relational and neurosymbolic AI, which combine logical,…

Artificial Intelligence · Computer Science 2025-02-26 Jaron Maene , Luc De Raedt

This paper studies interpretability of convolutional networks by means of saliency maps. Most approaches based on Class Activation Maps (CAM) combine information from fully connected layers and gradient through variants of backpropagation.…

Computer Vision and Pattern Recognition · Computer Science 2024-04-24 Felipe Torres Figueroa , Hanwei Zhang , Ronan Sicre , Yannis Avrithis , Stephane Ayache

While backpropagation--reverse-mode automatic differentiation--has been extraordinarily successful in deep learning, it requires two passes (forward and backward) through the neural network and the storage of intermediate activations.…

Machine Learning · Computer Science 2025-11-06 Daniel Wang , Evan Markou , Dylan Campbell

Neural networks are trained primarily based on their inputs and outputs, without regard for their internal mechanisms. These neglected mechanisms determine properties that are critical for safety, like (i) transparency; (ii) the absence of…

Machine Learning · Computer Science 2024-12-02 Alex Cloud , Jacob Goldman-Wetzler , Evžen Wybitul , Joseph Miller , Alexander Matt Turner

Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic…

Machine Learning · Computer Science 2022-02-18 Atılım Güneş Baydin , Barak A. Pearlmutter , Don Syme , Frank Wood , Philip Torr

Interpretability methods for deep neural networks mainly focus on the sensitivity of the class score with respect to the original or perturbed input, usually measured using actual or modified gradients. Some methods also use a…

Computer Vision and Pattern Recognition · Computer Science 2022-06-20 Md Mahfuzur Rahman , Noah Lewis , Sergey Plis

The goal of this document is to provide a pedagogical introduction to the main concepts underpinning the training of deep neural networks using gradient descent; a process known as backpropagation. Although we focus on a very influential…

Machine Learning · Computer Science 2018-11-30 Laurent Boué

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

Current methods for the interpretability of discriminative deep neural networks commonly rely on the model's input-gradients, i.e., the gradients of the output logits w.r.t. the inputs. The common assumption is that these input-gradients…

Machine Learning · Computer Science 2021-03-04 Suraj Srinivas , Francois Fleuret

Saliency methods seek to explain the predictions of a model by producing an importance map across each input sample. A popular class of such methods is based on backpropagating a signal and analyzing the resulting gradient. Despite much…

Computer Vision and Pattern Recognition · Computer Science 2020-04-07 Sylvestre-Alvise Rebuffi , Ruth Fong , Xu Ji , Andrea Vedaldi

Backpropagation algorithm is the cornerstone for neural network analysis. Paper extends it for training any derivatives of neural network's output with respect to its input. By the dint of it feedforward networks can be used to solve or…

Neural and Evolutionary Computing · Computer Science 2017-12-13 V. I. Avrutskiy

Visualizing the features captured by Convolutional Neural Networks (CNNs) is one of the conventional approaches to interpret the predictions made by these models in numerous image recognition applications. Grad-CAM is a popular solution…

Computer Vision and Pattern Recognition · Computer Science 2021-02-17 Sam Sattarzadeh , Mahesh Sudhakar , Konstantinos N. Plataniotis , Jongseong Jang , Yeonjeong Jeong , Hyunwoo Kim

Gradients have been used to quantify feature importance in machine learning models. Unfortunately, in nonlinear deep networks, not only individual neurons but also the whole network can saturate, and as a result an important input feature…

Machine Learning · Computer Science 2016-11-16 Mukund Sundararajan , Ankur Taly , Qiqi Yan

In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external…

Machine Learning · Computer Science 2016-01-06 John Schulman , Nicolas Heess , Theophane Weber , Pieter Abbeel

Saliency methods interpret the prediction of a neural network by showing the importance of input elements for that prediction. A popular family of saliency methods utilize gradient information. In this work, we empirically show that two…

Machine Learning · Computer Science 2020-12-02 Ashkan Khakzar , Soroosh Baselizadeh , Nassir Navab

In this paper, we utilize weight gradients from backpropagation to characterize the representation space learned by deep learning algorithms. We demonstrate the utility of such gradients in applications including perceptual image quality…

Computer Vision and Pattern Recognition · Computer Science 2019-08-28 Gukyeong Kwon , Mohit Prabhushankar , Dogancan Temel , Ghassan AlRegib

Despite tremendous success of modern neural networks, they are known to be overconfident even when the model encounters inputs with unfamiliar conditions. Detecting such inputs is vital to preventing models from making naive predictions…

Computer Vision and Pattern Recognition · Computer Science 2020-09-07 Jinsol Lee , Ghassan AlRegib

This paper introduces feature gradient flow, a new technique for interpreting deep learning models in terms of features that are understandable to humans. The gradient flow of a model locally defines nonlinear coordinates in the input data…

Image and Video Processing · Electrical Eng. & Systems 2023-07-26 Yinzhu Jin , Jonathan C. Garneau , P. Thomas Fletcher

We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a…

Machine Learning · Statistics 2014-06-02 Danilo Jimenez Rezende , Shakir Mohamed , Daan Wierstra

Backpropagation is the core learning mechanism underlying deep learning. However, whether and how this algorithm is implemented in the brain remains highly debated. In particular, while forward activations of pretrained models reliably map…

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