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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…

机器学习 · 计算机科学 2019-10-30 Shaojie Bai , J. Zico Kolter , Vladlen Koltun

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…

机器学习 · 计算机科学 2026-02-04 Junchao Lin , Zenan Ling , Jingwen Xu , Robert C. Qiu

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…

机器学习 · 计算机科学 2023-03-30 Zenan Ling , Xingyu Xie , Qiuhao Wang , Zongpeng Zhang , Zhouchen Lin

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…

机器学习 · 计算机科学 2025-12-04 Sam McCallum , Kamran Arora , James Foster

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…

机器学习 · 计算机科学 2023-04-25 Bac Nguyen , Lukas Mauch

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…

机器学习 · 计算机科学 2024-06-25 Mateusz Gabor , Tomasz Piotrowski , Renato L. G. Cavalcante

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…

机器学习 · 计算机科学 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.…

机器学习 · 计算机科学 2025-03-25 Jonathan Geuter , Clément Bonet , Anna Korba , David Alvarez-Melis

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…

机器学习 · 计算机科学 2023-06-05 Zonghan Yang , Tianyu Pang , Yang Liu

Implicit equilibrium models, i.e., deep neural networks (DNNs) defined by implicit equations, have been becoming more and more attractive recently. In this paper, we investigate an emerging question: can an implicit equilibrium model's…

机器学习 · 计算机科学 2021-06-08 Xingyu Xie , Qiuhao Wang , Zenan Ling , Xia Li , Yisen Wang , Guangcan Liu , Zhouchen Lin

Deep equilibrium (DEQ) models replace the multiple-layer stacking of conventional deep networks with a fixed-point iteration of a single-layer transformation. Having been demonstrated to be competitive in a variety of real-world scenarios,…

机器学习 · 计算机科学 2023-06-05 Zonghan Yang , Peng Li , Tianyu Pang , Yang Liu

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…

机器学习 · 计算机科学 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…

量子物理 · 物理学 2026-05-12 Pengyuan Xu , Tristan Zaborniak , Luis F. Rivera , Hausi A. Müller

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…

机器学习 · 计算机科学 2022-07-20 Atish Agarwala , Samuel S. Schoenholz

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…

计算机视觉与模式识别 · 计算机科学 2022-04-19 Shaojie Bai , Zhengyang Geng , Yash Savani , J. Zico Kolter

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…

最优化与控制 · 数学 2026-05-20 Antonin Clerc , Marien Renaud , Baudouin Denis De Seneville , Nicolas Papadakis

Deep equilibrium models (DEQs) have recently emerged as a powerful paradigm for training infinitely deep weight-tied neural networks that achieve state of the art performance across many modern machine learning tasks. Despite their…

机器学习 · 计算机科学 2026-01-13 Sanjit Dandapanthula , Aaditya Ramdas

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…

图像与视频处理 · 电气工程与系统科学 2022-10-11 Weijie Gan , Chunwei Ying , Parna Eshraghi , Tongyao Wang , Cihat Eldeniz , Yuyang Hu , Jiaming Liu , Yasheng Chen , Hongyu An , Ulugbek S. Kamilov

We propose a new technique that boosts the convergence of training generative adversarial networks. Generally, the rate of training deep models reduces severely after multiple iterations. A key reason for this phenomenon is that a deep…

机器学习 · 统计学 2018-06-15 Atsushi Nitanda , Taiji Suzuki

Neural networks with wide layers have attracted significant attention due to their equivalence to Gaussian processes, enabling perfect fitting of training data while maintaining generalization performance, known as benign overfitting.…

机器学习 · 计算机科学 2023-10-18 Tianxiang Gao , Xiaokai Huo , Hailiang Liu , Hongyang Gao
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