# Recurrence without Recurrence: Stable Video Landmark Detection with Deep Equilibrium Models

arXiv: https://arxiv.org/abs/2304.00600 · HTML: https://mlsanity.com/paper/2304.00600/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 89 references that are in the map.
- First posted on arXiv 2 Apr 2023.

## Builds on (most cited first, 30 of 46)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep High-Resolution Representation Learning for Human Pose Estimation](https://mlsanity.com/paper/1902.09212/) (2019)
- [Stacked Hourglass Networks for Human Pose Estimation](https://mlsanity.com/paper/1603.06937/) (2016)
- [Joint Face Detection and Alignment using Multi-task Cascaded Convolutional Networks](https://mlsanity.com/paper/1604.02878/) (2016)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [WIDER FACE: A Face Detection Benchmark](https://mlsanity.com/paper/1511.06523/) (2015)
- ["Zero-Shot" Super-Resolution using Deep Internal Learning](https://mlsanity.com/paper/1712.06087/) (2017)
- [Deep Face Recognition: A Survey](https://mlsanity.com/paper/1804.06655/) (2018)
- [Deep Facial Expression Recognition: A Survey](https://mlsanity.com/paper/1804.08348/) (2018)
- [VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning](https://mlsanity.com/paper/1705.07761/) (2017)
- [General Facial Representation Learning in a Visual-Linguistic Manner](https://mlsanity.com/paper/2112.03109/) (2021)
- [Adaptive Risk Minimization: Learning to Adapt to Domain Shift](https://mlsanity.com/paper/2007.02931/) (2020)
- [Recasting Gradient-Based Meta-Learning as Hierarchical Bayes](https://mlsanity.com/paper/1801.08930/) (2018)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [Hand-Object Contact Consistency Reasoning for Human Grasps Generation](https://mlsanity.com/paper/2104.03304/) (2021)
- [Multiscale Deep Equilibrium Models](https://mlsanity.com/paper/2006.08656/) (2020)
- [HRFormer: High-Resolution Transformer for Dense Prediction](https://mlsanity.com/paper/2110.09408/) (2021)
- [Look at Boundary: A Boundary-Aware Face Alignment Algorithm](https://mlsanity.com/paper/1805.10483/) (2018)
- [Adaptive Wing Loss for Robust Face Alignment via Heatmap Regression](https://mlsanity.com/paper/1904.07399/) (2019)
- [Self-Supervised Policy Adaptation during Deployment](https://mlsanity.com/paper/2007.04309/) (2020)
- [A-SDF: Learning Disentangled Signed Distance Functions for Articulated Shape Representation](https://mlsanity.com/paper/2104.07645/) (2021)
- [Wing Loss for Robust Facial Landmark Localisation with Convolutional Neural Networks](https://mlsanity.com/paper/1711.06753/) (2017)
- [Monotone operator equilibrium networks](https://mlsanity.com/paper/2006.08591/) (2020)
- [LUVLi Face Alignment: Estimating Landmarks' Location, Uncertainty, and Visibility Likelihood](https://mlsanity.com/paper/2004.02980/) (2020)
- [On Training Implicit Models](https://mlsanity.com/paper/2111.05177/) (2021)
- [Stabilizing Equilibrium Models by Jacobian Regularization](https://mlsanity.com/paper/2106.14342/) (2021)
- [Deep Equilibrium Optical Flow Estimation](https://mlsanity.com/paper/2204.08442/) (2022)
- [Facial Landmark Detection: a Literature Survey](https://mlsanity.com/paper/1805.05563/) (2018)

## Built on by (most cited first, 27 of 27)

- [One-Step Diffusion Distillation via Deep Equilibrium Models](https://mlsanity.com/paper/2401.08639/) (2023)
- [FaceXFormer: A Unified Transformer for Facial Analysis](https://mlsanity.com/paper/2403.12960/) (2024)
- [Deep Equilibrium Models are Almost Equivalent to Not-so-deep Explicit Models for High-dimensional Gaussian Mixtures](https://mlsanity.com/paper/2402.02697/) (2024)
- [Cascaded Dual Vision Transformer for Accurate Facial Landmark Detection](https://mlsanity.com/paper/2411.07167/) (2024)
- [Test like you Train in Implicit Deep Learning](https://mlsanity.com/paper/2305.15042/) (2023)
- [Automated Detection of Cat Facial Landmarks](https://mlsanity.com/paper/2310.09793/) (2023)
- [Subhomogeneous Deep Equilibrium Models](https://mlsanity.com/paper/2403.00720/) (2024)
- [Self-supervised Adaptive Pre-training of Multilingual Speech Models for Language and Dialect Identification](https://mlsanity.com/paper/2312.07338/) (2023)
- [ORFormer: Occlusion-Robust Transformer for Accurate Facial Landmark Detection](https://mlsanity.com/paper/2412.13174/) (2024)
- [Recovering Pulse Waves from Video Using Deep Unrolling and Deep Equilibrium Models](https://mlsanity.com/paper/2503.17269/) (2025)
- [Local Scale Equivariance with Latent Deep Equilibrium Canonicalizer](https://mlsanity.com/paper/2508.14187/) (2025)
- [Heatmap Regression without Soft-Argmax for Facial Landmark Detection](https://mlsanity.com/paper/2508.14929/) (2025)
- [Event-based Facial Keypoint Alignment via Cross-Modal Fusion Attention and Self-Supervised Multi-Event Representation Learning](https://mlsanity.com/paper/2509.24968/) (2025)
- [Lipschitz Multiscale Deep Equilibrium Models: A Theoretically Guaranteed and Accelerated Approach](https://mlsanity.com/paper/2602.03297/) (2026)
- [Enhancing Multilingual Speech Recognition through Language Prompt Tuning and Frame-Level Language Adapter](https://mlsanity.com/paper/2309.09443/) (2023)
- [GMTR: Graph Matching Transformers](https://mlsanity.com/paper/2311.08141/) (2023)
- [DarkShot: Lighting Dark Images with Low-Compute and High-Quality](https://mlsanity.com/paper/2312.16805/) (2023)
- [TRLS: A Time Series Representation Learning Framework via Spectrogram for Medical Signal Processing](https://mlsanity.com/paper/2401.05431/) (2024)
- [TEN-GUARD: Tensor Decomposition for Backdoor Attack Detection in Deep Neural Networks](https://mlsanity.com/paper/2401.05432/) (2024)
- [T-Pixel2Mesh: Combining Global and Local Transformer for 3D Mesh Generation from a Single Image](https://mlsanity.com/paper/2403.13663/) (2024)
- [Strategic Arms with Side Communication Prevail Over Low-Regret MAB Algorithms](https://mlsanity.com/paper/2408.17101/) (2024)
- [Towards General Deepfake Detection with Dynamic Curriculum](https://mlsanity.com/paper/2410.11162/) (2024)
- [Attr-Int: A Simple and Effective Entity Alignment Framework for Heterogeneous Knowledge Graphs](https://mlsanity.com/paper/2410.13409/) (2024)
- [Mask6D: Masked Pose Priors For 6D Object Pose Estimation](https://mlsanity.com/paper/2507.06486/) (2025)
- [Uncertainty-quantified Pulse Signal Recovery from Facial Video using Regularized Stochastic Interpolants](https://mlsanity.com/paper/2604.10777/) (2026)
- [FAHCD-Net: Frequency-Adaptive Heatmap-Conditional Diffusion Networks for Robust Facial Landmark Detection](https://mlsanity.com/paper/2609.16842/) (2026)
- [DIME: Scaling Facial Representation Learning via Differential Masked Autoencoding](https://mlsanity.com/paper/2610.17015/) (2026)

## Abstract (arXiv)

Cascaded computation, whereby predictions are recurrently refined over several stages, has been a persistent theme throughout the development of landmark detection models. In this work, we show that the recently proposed Deep Equilibrium Model (DEQ) can be naturally adapted to this form of computation. Our Landmark DEQ (LDEQ) achieves state-of-the-art performance on the challenging WFLW facial landmark dataset, reaching 3.92 NME with fewer parameters and a training memory cost of O(1) in the number of recurrent modules. Furthermore, we show that DEQs are particularly suited for landmark detection in videos. In this setting, it is typical to train on still images due to the lack of labelled videos. This can lead to a ``flickering'' effect at inference time on video, whereby a model can rapidly oscillate between different plausible solutions across consecutive frames. By rephrasing DEQs as a constrained optimization, we emulate recurrence at inference time, despite not having access to temporal data at training time. This Recurrence without Recurrence (RwR) paradigm helps in reducing landmark flicker, which we demonstrate by introducing a new metric, normalized mean flicker (NMF), and contributing a new facial landmark video dataset (WFLW-V) targeting landmark uncertainty. On the WFLW-V hard subset made up of 500 videos, our LDEQ with RwR improves the NME and NMF by 10 and 13% respectively, compared to the strongest previously published model using a hand-tuned conventional filter.