# Deep Equilibrium Object Detection

arXiv: https://arxiv.org/abs/2308.09564 · HTML: https://mlsanity.com/paper/2308.09564/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 47 references that are in the map.
- First posted on arXiv 18 Aug 2023.

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [FCOS: Fully Convolutional One-Stage Object Detection](https://mlsanity.com/paper/1904.01355/) (2019)
- [Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression](https://mlsanity.com/paper/1902.09630/) (2019)
- [Objects as Points](https://mlsanity.com/paper/1904.07850/) (2019)
- [CornerNet: Detecting Objects as Paired Keypoints](https://mlsanity.com/paper/1808.01244/) (2018)
- [Focal Loss for Dense Object Detection](https://mlsanity.com/paper/1708.02002/) (2017)
- [CenterNet: Keypoint Triplets for Object Detection](https://mlsanity.com/paper/1904.08189/) (2019)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [DAB-DETR: Dynamic Anchor Boxes are Better Queries for DETR](https://mlsanity.com/paper/2201.12329/) (2022)
- [Sparse R-CNN: End-to-End Object Detection with Learnable Proposals](https://mlsanity.com/paper/2011.12450/) (2020)
- [DN-DETR: Accelerate DETR Training by Introducing Query DeNoising](https://mlsanity.com/paper/2203.01305/) (2022)
- [Cascade R-CNN: High Quality Object Detection and Instance Segmentation](https://mlsanity.com/paper/1906.09756/) (2019)
- [Conditional DETR for Fast Training Convergence](https://mlsanity.com/paper/2108.06152/) (2021)
- [DiffusionDet: Diffusion Model for Object Detection](https://mlsanity.com/paper/2211.09788/) (2022)
- [Visual Attention Network](https://mlsanity.com/paper/2202.09741/) (2022)
- [Dynamic Head: Unifying Object Detection Heads with Attentions](https://mlsanity.com/paper/2106.08322/) (2021)
- [Fast Convergence of DETR with Spatially Modulated Co-Attention](https://mlsanity.com/paper/2101.07448/) (2021)
- [Multiscale Deep Equilibrium Models](https://mlsanity.com/paper/2006.08656/) (2020)

## Built on by (most cited first, 10 of 10)

- [Accelerating Auto-regressive Text-to-Image Generation with Training-free Speculative Jacobi Decoding](https://mlsanity.com/paper/2410.01699/) (2024)
- [One-Step Diffusion Distillation via Deep Equilibrium Models](https://mlsanity.com/paper/2401.08639/) (2023)
- [Deep Equilibrium Diffusion Restoration with Parallel Sampling](https://mlsanity.com/paper/2311.11600/) (2023)
- [Positive concave deep equilibrium models](https://mlsanity.com/paper/2402.04029/) (2024)
- [Differentiable Solver Search for Fast Diffusion Sampling](https://mlsanity.com/paper/2505.21114/) (2025)
- [Physics-Guided Detector for SAR Airplanes](https://mlsanity.com/paper/2411.12301/) (2024)
- [Adaptive 1D Video Diffusion Autoencoder](https://mlsanity.com/paper/2602.04220/) (2026)
- [SJD++: Improved Speculative Jacobi Decoding for Training-free Acceleration of Discrete Auto-regressive Text-to-Image Generation](https://mlsanity.com/paper/2512.07503/) (2025)
- [Consistency Deep Equilibrium Models](https://mlsanity.com/paper/2602.03024/) (2026)
- [Lipschitz Multiscale Deep Equilibrium Models: A Theoretically Guaranteed and Accelerated Approach](https://mlsanity.com/paper/2602.03297/) (2026)

## Abstract (arXiv)

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 then used to directly predict object locations and categories with simple FFN heads. In this paper, we present a new query-based object detector (DEQDet) by designing a deep equilibrium decoder. Our DEQ decoder models the query vector refinement as the fixed point solving of an implicit layer and is equivalent to applying infinite steps of refinement. To be more specific to object decoding, we use a two-step unrolled equilibrium equation to explicitly capture the query vector refinement. Accordingly, we are able to incorporate refinement awareness into the DEQ training with the inexact gradient back-propagation (RAG). In addition, to stabilize the training of our DEQDet and improve its generalization ability, we devise the deep supervision scheme on the optimization path of DEQ with refinement-aware perturbation~(RAP). Our experiments demonstrate DEQDet converges faster, consumes less memory, and achieves better results than the baseline counterpart (AdaMixer). In particular, our DEQDet with ResNet50 backbone and 300 queries achieves the 49.5 mAP and 33.0 APs on the MS COCO benchmark under 2× training scheme (24 epochs).