English
Related papers

Related papers: Stabilizing Equilibrium Models by Jacobian Regular…

200 papers

Cascaded computation, whereby predictions are recurrently refined over several stages, has been a persistent theme throughout the development of landmark detection models. In this work, we show that the recently proposed Deep Equilibrium…

Computer Vision and Pattern Recognition · Computer Science 2023-04-04 Paul Micaelli , Arash Vahdat , Hongxu Yin , Jan Kautz , Pavlo Molchanov

Plug-and-Play Priors (PnP) and Regularization by Denoising (RED) are widely-used frameworks for solving imaging inverse problems by computing fixed-points of operators combining physical measurement models and learned image priors. While…

Image and Video Processing · Electrical Eng. & Systems 2022-05-27 Jiaming Liu , Xiaojian Xu , Weijie Gan , Shirin Shoushtari , Ulugbek S. Kamilov

Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…

Machine Learning · Computer Science 2020-06-16 Mao Li , Yingyi Ma , Xinhua Zhang

Efficient gradient computation of the Jacobian determinant term is a core problem in many machine learning settings, and especially so in the normalizing flow framework. Most proposed flow models therefore either restrict to a function…

Machine Learning · Computer Science 2021-06-10 T. Anderson Keller , Jorn W. T. Peters , Priyank Jaini , Emiel Hoogeboom , Patrick Forré , Max Welling

Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…

Image and Video Processing · Electrical Eng. & Systems 2021-06-04 Davis Gilton , Gregory Ongie , Rebecca Willett

Powerful deep neural networks are vulnerable to adversarial attacks. To obtain adversarially robust models, researchers have separately developed adversarial training and Jacobian regularization techniques. There are abundant theoretical…

Machine Learning · Statistics 2024-12-18 Dongya Wu , Xin Li

Deep neural networks are known to suffer from exploding or vanishing gradients as depth increases, a phenomenon closely tied to the spectral behavior of the input-output Jacobian. Prior work has identified critical initialization schemes…

Machine Learning · Computer Science 2025-11-25 Benjamin Dadoun , Soufiane Hayou , Hanan Salam , Mohamed El Amine Seddik , Pierre Youssef

Implicit equilibrium models, i.e., deep neural networks (DNNs) defined by implicit equations, have been becoming more and more attractive recently. In this paper, we investigate an emerging question: can an implicit equilibrium model's…

Machine Learning · Computer Science 2021-06-08 Xingyu Xie , Qiuhao Wang , Zenan Ling , Xia Li , Yisen Wang , Guangcan Liu , Zhouchen Lin

It's well-known that inverse problems are ill-posed and to solve them meaningfully one has to employ regularization methods. Traditionally, popular regularization methods have been the penalized Variational approaches. In recent years, the…

Machine Learning · Computer Science 2022-02-17 Abinash Nayak

Implicit layer deep learning techniques, like Neural Differential Equations, have become an important modeling framework due to their ability to adapt to new problems automatically. Training a neural differential equation is effectively a…

Machine Learning · Computer Science 2023-06-05 Avik Pal , Alan Edelman , Chris Rackauckas

Weight-tied models have attracted attention in the modern development of neural networks. The deep equilibrium model (DEQ) represents infinitely deep neural networks with weight-tying, and recent studies have shown the potential of this…

Machine Learning · Computer Science 2023-06-21 Takuya Konishi , Yoshinobu Kawahara

A promising trend in deep learning replaces traditional feedforward networks with implicit networks. Unlike traditional networks, implicit networks solve a fixed point equation to compute inferences. Solving for the fixed point varies in…

Machine Learning · Computer Science 2021-12-28 Samy Wu Fung , Howard Heaton , Qiuwei Li , Daniel McKenzie , Stanley Osher , Wotao Yin

We develop a new method for regularising neural networks. We learn a probability distribution over the activations of all layers of the model and then insert imputed values into the network during training. We obtain a posterior for an…

Machine Learning · Computer Science 2019-10-14 Matthew Willetts , Alexander Camuto , Stephen Roberts , Chris Holmes

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

Machine Learning · Computer Science 2025-12-19 Maria Matveev , Vit Fojtik , Hung-Hsu Chou , Gitta Kutyniok , Johannes Maly

Implicit deep learning has recently gained popularity with applications ranging from meta-learning to Deep Equilibrium Networks (DEQs). In its general formulation, it relies on expressing some components of deep learning pipelines…

Machine Learning · Computer Science 2023-05-25 Zaccharie Ramzi , Pierre Ablin , Gabriel Peyré , Thomas Moreau

We develop a unified matrix-spectral framework for analyzing stability and interpretability in deep neural networks. Representing networks as data-dependent products of linear operators reveals spectral quantities governing sensitivity to…

Machine Learning · Computer Science 2026-02-03 Ronald Katende

Solving image reconstruction problems of the form \(\mathbf{A} \mathbf{x} = \mathbf{y}\) remains challenging due to ill-posedness and the lack of large-scale supervised datasets. Deep Equilibrium (DEQ) models have been used successfully but…

Computer Vision and Pattern Recognition · Computer Science 2026-01-06 Markus Haltmeier , Lukas Neumann , Nadja Gruber , Johannes Schwab , Gyeongha Hwang

A key challenge for the machine learning community is to understand and accelerate the training dynamics of deep networks that lead to delayed generalisation and emergent robustness to input perturbations, also known as grokking. Prior work…

Machine Learning · Computer Science 2025-08-01 Thomas Walker , Ahmed Imtiaz Humayun , Randall Balestriero , Richard Baraniuk

One major challenge in training Deep Neural Networks is preventing overfitting. Many techniques such as data augmentation and novel regularizers such as Dropout have been proposed to prevent overfitting without requiring a massive amount of…

Machine Learning · Computer Science 2016-06-13 Michael Cogswell , Faruk Ahmed , Ross Girshick , Larry Zitnick , Dhruv Batra

Neural networks with wide layers have attracted significant attention due to their equivalence to Gaussian processes, enabling perfect fitting of training data while maintaining generalization performance, known as benign overfitting.…

Machine Learning · Computer Science 2023-10-18 Tianxiang Gao , Xiaokai Huo , Hailiang Liu , Hongyang Gao