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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

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 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 (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) 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 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

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

Many tasks in deep learning involve optimizing over the \emph{inputs} to a network to minimize or maximize some objective; examples include optimization over latent spaces in a generative model to match a target image, or adversarially…

Machine Learning · Computer Science 2021-11-29 Swaminathan Gurumurthy , Shaojie Bai , Zachary Manchester , J. Zico Kolter

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

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

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

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

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

Diffusion-based generative models are extremely effective in generating high-quality images, with generated samples often surpassing the quality of those produced by other models under several metrics. One distinguishing feature of these…

Machine Learning · Computer Science 2022-10-25 Ashwini Pokle , Zhengyang Geng , Zico Kolter

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

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) replace a stack of explicit layers with a single operator whose fixed point defines the output, giving the expressive power of an arbitrarily deep network at the memory cost of a single layer. Quantum Deep…

Quantum Physics · Physics 2026-05-12 Pengyuan Xu , Tristan Zaborniak , Luis F. Rivera , Hausi A. Müller

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

Diffusion model-based image restoration (IR) aims to use diffusion models to recover high-quality (HQ) images from degraded images, achieving promising performance. Due to the inherent property of diffusion models, most existing methods…

Computer Vision and Pattern Recognition · Computer Science 2024-04-01 Jiezhang Cao , Yue Shi , Kai Zhang , Yulun Zhang , Radu Timofte , Luc Van Gool

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
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