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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 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) 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) 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

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

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 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) 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 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 feasibility of variational quantum algorithms, the most popular correspondent of neural networks on noisy, near-term quantum hardware, is highly impacted by the circuit depth of the involved parametrized quantum circuits (PQCs). Higher…

Machine Learning · Computer Science 2024-11-01 Philipp Schleich , Marta Skreta , Lasse B. Kristensen , Rodrigo A. Vargas-Hernández , Alán Aspuru-Guzik

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

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

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 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

Many recent state-of-the-art (SOTA) optical flow models use finite-step recurrent update operations to emulate traditional algorithms by encouraging iterative refinements toward a stable flow estimation. However, these RNNs impose large…

Computer Vision and Pattern Recognition · Computer Science 2022-04-19 Shaojie Bai , Zhengyang Geng , Yash Savani , J. Zico Kolter

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

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 (DEQ) Models, an emerging class of implicit models that maps inputs to fixed points of neural networks, are of growing interest in the deep learning community. However, training and applying DEQ models is currently done in…

Machine Learning · Computer Science 2023-10-31 Zhengyang Geng , J. Zico Kolter

Multimodal fusion integrates the complementary information present in multiple modalities and has gained much attention recently. Most existing fusion approaches either learn a fixed fusion strategy during training and inference, or are…

Computer Vision and Pattern Recognition · Computer Science 2023-06-30 Jinhong Ni , Yalong Bai , Wei Zhang , Ting Yao , Tao Mei
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