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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

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

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

Implicit models, an emerging model class, compute outputs by iterating a single parameter block to a fixed point. This architecture realizes an infinite-depth, weight-tied network that trains with constant memory, significantly reducing…

Machine Learning · Computer Science 2026-04-01 Jialin Liu , Lisang Ding , Stanley Osher , Wotao Yin

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

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) 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

A deep equilibrium model uses implicit layers, which are implicitly defined through an equilibrium point of an infinite sequence of computation. It avoids any explicit computation of the infinite sequence by finding an equilibrium point…

Machine Learning · Computer Science 2021-02-19 Kenji Kawaguchi

Implicit models are a general class of learning models that forgo the hierarchical layer structure typical in neural networks and instead define the internal states based on an ``equilibrium'' equation, offering competitive performance and…

Machine Learning · Computer Science 2022-09-21 Alicia Y. Tsai , Juliette Decugis , Laurent El Ghaoui , Alper Atamtürk

In this paper, we investigate the extrapolation capabilities of implicit deep learning models in handling unobserved data, where traditional deep neural networks may falter. Implicit models, distinguished by their adaptability in layer…

Machine Learning · Computer Science 2024-07-22 Juliette Decugis , Alicia Y. Tsai , Max Emerling , Ashwin Ganesh , Laurent El Ghaoui

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) 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

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

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

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) 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

Transferability estimation identifies the best pre-trained models for downstream tasks without incurring the high computational cost of full fine-tuning. This capability facilitates deployment and advances the pre-training and fine-tuning…

Computer Vision and Pattern Recognition · Computer Science 2025-10-28 Yaoyan Zheng , Huiqun Wang , Nan Zhou , Di Huang

We propose a new class of implicit networks, the multiscale deep equilibrium model (MDEQ), suited to large-scale and highly hierarchical pattern recognition domains. An MDEQ directly solves for and backpropagates through the equilibrium…

Machine Learning · Computer Science 2020-11-25 Shaojie Bai , Vladlen Koltun , J. Zico Kolter

The widespread adoption of deep learning models in computer vision has intensified concerns about interpretability. Despite strong performance, these models are often treated as black boxes, with limited systematic investigation of their…

Machine Learning · Computer Science 2026-05-13 Konstantinos P. Panousis , Diego Marcos

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
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