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Related papers: Efficient Training of Deep Equilibrium Models

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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

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

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, implicit deep learning has emerged as a method to increase the effective depth of deep neural networks. While their training is memory-efficient, they are still significantly slower to train than their explicit…

Machine Learning · Computer Science 2023-03-13 Zaccharie Ramzi , Florian Mannel , Shaojie Bai , Jean-Luc Starck , Philippe Ciuciu , Thomas Moreau

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

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

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

Implicit models separate the definition of a layer from the description of its solution process. While implicit layers allow features such as depth to adapt to new scenarios and inputs automatically, this adaptivity makes its computational…

Machine Learning · Computer Science 2023-03-06 Avik Pal , Alan Edelman , Christopher Rackauckas

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) 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 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 (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) 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 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

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

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

Recent efforts in applying implicit networks to solve inverse problems in imaging have achieved competitive or even superior results when compared to feedforward networks. These implicit networks only require constant memory during…

Machine Learning · Computer Science 2024-02-06 Linghai Liu , Shuaicheng Tong , Lisa Zhao

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

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
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