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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 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 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

Deep Equilibrium Models (DEQs) are implicit neural networks with fixed points, which have recently gained attention for learning image regularization functionals, particularly in settings involving Gaussian fidelities, where assumptions on…

Optimization and Control · Mathematics 2025-11-19 Christian Daniele , Silvia Villa , Samuel Vaiter , Luca Calatroni

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

In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…

Numerical Analysis · Mathematics 2024-03-18 Matthias Beckmann , Nick Heilenkötter

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

Equivariant Imaging (EI) regularization has become the de-facto technique for unsupervised training of deep imaging networks, without any need of ground-truth data. Observing that the EI-based unsupervised training paradigm currently has…

Image and Video Processing · Electrical Eng. & Systems 2025-12-12 Guixian Xu , Jinglai Li , Junqi Tang

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

Ill-posed image reconstruction problems appear in many scenarios such as remote sensing, where obtaining high quality images is crucial for environmental monitoring, disaster management and urban planning. Deep learning has seen great…

Computer Vision and Pattern Recognition · Computer Science 2024-11-21 Andrew Wang , Mike Davies

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 (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

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

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 equilibrium networks (DEQs) are a promising way to construct models which trade off memory for compute. However, theoretical understanding of these models is still lacking compared to traditional networks, in part because of the…

Machine Learning · Computer Science 2022-07-20 Atish Agarwala , Samuel S. Schoenholz

Deep networks provide state-of-the-art performance in multiple imaging inverse problems ranging from medical imaging to computational photography. However, most existing networks are trained with clean signals which are often hard or…

Computer Vision and Pattern Recognition · Computer Science 2022-03-17 Dongdong Chen , Julián Tachella , Mike E. Davies

Deep equilibrium models (DEQs) refrain from the traditional layer-stacking paradigm and turn to find the fixed point of a single layer. DEQs have achieved promising performance on different applications with featured memory efficiency. At…

Machine Learning · Computer Science 2023-06-05 Zonghan Yang , Tianyu Pang , Yang Liu

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

Electrical Impedance Tomography (EIT) is a powerful imaging modality widely used in medical diagnostics, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity distribution of…

Image and Video Processing · Electrical Eng. & Systems 2025-08-11 Alexander Denker , Fabio Margotti , Jianfeng Ning , Kim Knudsen , Derick Nganyu Tanyu , Bangti Jin , Andreas Hauptmann , Peter Maass
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