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Deep Equilibrium Models (DEQs) are an interesting class of implicit model where the model output is implicitly defined as the fixed point of a learned function. These models have been shown to outperform explicit (fixed-depth) models in…

Machine Learning · Computer Science 2025-12-04 Sam McCallum , Kamran Arora , James Foster

Deep Equilibrium Models (DEQs) are an established framework for image restoration that learn a problem-adapted regularization by solving a fixed-point (i.e. equilibrium) problem. While flexible and expressive, DEQs are often hindered by…

Optimization and Control · Mathematics 2026-05-20 Antonin Clerc , Marien Renaud , Baudouin Denis De Seneville , Nicolas Papadakis

Equivariant imaging (EI) enables training signal reconstruction models without requiring ground truth data by leveraging signal symmetries. Deep equilibrium models (DEQs) are a powerful class of neural networks where the output is a fixed…

Image and Video Processing · Electrical Eng. & Systems 2025-11-25 Alexander Mehta , Ruangrawee Kitichotkul , Vivek K Goyal , Julián Tachella

Deep equilibrium models (DEQs) achieve infinitely deep network representations without stacking layers by exploring fixed points of layer transformations in neural networks. Such models constitute an innovative approach that achieves…

Machine Learning · Computer Science 2026-02-04 Naoki Sato , Hideaki Iiduka

Deep equilibrium models (DEQs) have proven to be very powerful for learning data representations. The idea is to replace traditional (explicit) feedforward neural networks with an implicit fixed-point equation, which allows to decouple the…

Machine Learning · Computer Science 2023-04-25 Bac Nguyen , Lukas Mauch

Deep equilibrium networks (DEQs) are a new class of models that eschews traditional depth in favor of finding the fixed point of a single nonlinear layer. These models have been shown to achieve performance competitive with the…

Machine Learning · Computer Science 2021-06-29 Shaojie Bai , Vladlen Koltun , J. Zico Kolter

We present a new approach to modeling sequential data: the deep equilibrium model (DEQ). Motivated by an observation that the hidden layers of many existing deep sequence models converge towards some fixed point, we propose the DEQ approach…

Machine Learning · Computer Science 2019-10-30 Shaojie Bai , J. Zico Kolter , Vladlen Koltun

Deep equilibrium (DEQ) models are widely recognized as a memory efficient alternative to standard neural networks, achieving state-of-the-art performance in language modeling and computer vision tasks. These models solve a fixed point…

Machine Learning · Computer Science 2024-06-25 Mateusz Gabor , Tomasz Piotrowski , Renato L. G. Cavalcante

Deep equilibrium models (DEQ) have emerged as a powerful alternative to deep unfolding (DU) for image reconstruction. DEQ models-implicit neural networks with effectively infinite number of layers-were shown to achieve state-of-the-art…

Image and Video Processing · Electrical Eng. & Systems 2022-10-11 Weijie Gan , Chunwei Ying , Parna Eshraghi , Tongyao Wang , Cihat Eldeniz , Yuyang Hu , Jiaming Liu , Yasheng Chen , Hongyu An , Ulugbek S. Kamilov

Deep Equilibrium Models (DEQs) are a class of implicit neural networks that solve for a fixed point of a neural network in their forward pass. Traditionally, DEQs take sequences as inputs, but have since been applied to a variety of data.…

Machine Learning · Computer Science 2025-03-25 Jonathan Geuter , Clément Bonet , Anna Korba , David Alvarez-Melis

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

The ability of snapshot compressive imaging (SCI) systems to efficiently capture high-dimensional (HD) data has led to an inverse problem, which consists of recovering the HD signal from the compressed and noisy measurement. While…

Image and Video Processing · Electrical Eng. & Systems 2023-03-01 Yaping Zhao , Siming Zheng , Xin Yuan

Deep model-based architectures (DMBAs) are widely used in imaging inverse problems to integrate physical measurement models and learned image priors. Plug-and-play priors (PnP) and deep equilibrium models (DEQ) are two DMBA frameworks that…

Image and Video Processing · Electrical Eng. & Systems 2022-11-02 Junhao Hu , Shirin Shoushtari , Zihao Zou , Jiaming Liu , Zhixin Sun , Ulugbek S. Kamilov

Deep Equilibrium Models (DEQs) have emerged as a powerful paradigm in deep learning, offering the ability to model infinite-depth networks with constant memory usage. However, DEQs incur significant inference latency due to the iterative…

Machine Learning · Computer Science 2026-02-04 Junchao Lin , Zenan Ling , Jingwen Xu , Robert C. Qiu

There has been significant recent interest in the use of deep learning for regularizing imaging inverse problems. Most work in the area has focused on regularization imposed implicitly by convolutional neural networks (CNNs) pre-trained for…

Image and Video Processing · Electrical Eng. & Systems 2023-03-10 Zihao Zou , Jiaming Liu , Brendt Wohlberg , Ulugbek S. Kamilov

A deep equilibrium model (DEQ) is implicitly defined through an equilibrium point of an infinite-depth weight-tied model with an input-injection. Instead of infinite computations, it solves an equilibrium point directly with root-finding…

Machine Learning · Computer Science 2023-03-30 Zenan Ling , Xingyu Xie , Qiuhao Wang , Zongpeng Zhang , Zhouchen Lin

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

Query-based object detectors directly decode image features into object instances with a set of learnable queries. These query vectors are progressively refined to stable meaningful representations through a sequence of decoder layers, and…

Computer Vision and Pattern Recognition · Computer Science 2023-08-21 Shuai Wang , Yao Teng , Limin Wang

Magnetic particle imaging (MPI) offers unparalleled contrast and resolution for tracing magnetic nanoparticles. A common imaging procedure calibrates a system matrix (SM) that is used to reconstruct data from subsequent scans. The ill-posed…

Image and Video Processing · Electrical Eng. & Systems 2023-09-07 Alper Güngör , Baris Askin , Damla Alptekin Soydan , Can Barış Top , Emine Ulku Saritas , Tolga Çukur

Deep Equilibrium Model (DEQ), which serves as a typical implicit neural network, emphasizes their memory efficiency and competitive performance compared to explicit neural networks. However, there has been relatively limited theoretical…

Machine Learning · Computer Science 2024-12-05 Haixiang Sun , Ye Shi
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