# Heatmap Regression without Soft-Argmax for Facial Landmark Detection

arXiv: https://arxiv.org/abs/2508.14929 · HTML: https://mlsanity.com/paper/2508.14929/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 100 references that are in the map.
- First posted on arXiv 19 Aug 2025.

## Builds on (most cited first, 30 of 61)

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Deep High-Resolution Representation Learning for Visual Recognition](https://mlsanity.com/paper/1908.07919/) (2019)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Stacked Hourglass Networks for Human Pose Estimation](https://mlsanity.com/paper/1603.06937/) (2016)
- [Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFs](https://mlsanity.com/paper/1412.7062/) (2014)
- [How far are we from solving the 2D & 3D Face Alignment problem? (and a dataset of 230,000 3D facial landmarks)](https://mlsanity.com/paper/1703.07332/) (2017)
- [Accurate 3D Face Reconstruction with Weakly-Supervised Learning: From Single Image to Image Set](https://mlsanity.com/paper/1903.08527/) (2019)
- [Learning an Animatable Detailed 3D Face Model from In-The-Wild Images](https://mlsanity.com/paper/2012.04012/) (2020)
- [Regularizing Neural Networks by Penalizing Confident Output Distributions](https://mlsanity.com/paper/1701.06548/) (2017)
- [Bag of Tricks for Image Classification with Convolutional Neural Networks](https://mlsanity.com/paper/1812.01187/) (2018)
- [Deep Face Recognition: A Survey](https://mlsanity.com/paper/1804.06655/) (2018)
- [EMOCA: Emotion Driven Monocular Face Capture and Animation](https://mlsanity.com/paper/2204.11312/) (2022)
- [Conditional Random Fields as Recurrent Neural Networks](https://mlsanity.com/paper/1502.03240/) (2015)
- [General Facial Representation Learning in a Visual-Linguistic Manner](https://mlsanity.com/paper/2112.03109/) (2021)
- [Look at Boundary: A Boundary-Aware Face Alignment Algorithm](https://mlsanity.com/paper/1805.10483/) (2018)
- [Joint Training of a Convolutional Network and a Graphical Model for Human Pose Estimation](https://mlsanity.com/paper/1406.2984/) (2014)
- [Adaptive Wing Loss for Robust Face Alignment via Heatmap Regression](https://mlsanity.com/paper/1904.07399/) (2019)
- [Wing Loss for Robust Facial Landmark Localisation with Convolutional Neural Networks](https://mlsanity.com/paper/1711.06753/) (2017)
- [LUVLi Face Alignment: Estimating Landmarks' Location, Uncertainty, and Visibility Likelihood](https://mlsanity.com/paper/2004.02980/) (2020)
- [Towards Open-Set Identity Preserving Face Synthesis](https://mlsanity.com/paper/1803.11182/) (2018)
- [Pixel-in-Pixel Net: Towards Efficient Facial Landmark Detection in the Wild](https://mlsanity.com/paper/2003.03771/) (2020)
- [Numerical Coordinate Regression with Convolutional Neural Networks](https://mlsanity.com/paper/1801.07372/) (2018)
- [3D face reconstruction with dense landmarks](https://mlsanity.com/paper/2204.02776/) (2022)
- [Mask-Guided Portrait Editing with Conditional GANs](https://mlsanity.com/paper/1905.10346/) (2019)
- [Style Aggregated Network for Facial Landmark Detection](https://mlsanity.com/paper/1803.04108/) (2018)
- [Structured Landmark Detection via Topology-Adapting Deep Graph Learning](https://mlsanity.com/paper/2004.08190/) (2020)
- [Supervision-by-Registration: An Unsupervised Approach to Improve the Precision of Facial Landmark Detectors](https://mlsanity.com/paper/1807.00966/) (2018)
- [Sparse Local Patch Transformer for Robust Face Alignment and Landmarks Inherent Relation Learning](https://mlsanity.com/paper/2203.06541/) (2022)
- [DeCaFA: Deep Convolutional Cascade for Face Alignment In The Wild](https://mlsanity.com/paper/1904.02549/) (2019)

## Built on by (most cited first, 1 of 1)

- [MARCO: Navigating the Unseen Space of Semantic Correspondence](https://mlsanity.com/paper/2604.18267/) (2026)

## Abstract (arXiv)

Facial landmark detection is an important task in computer vision with numerous applications, such as head pose estimation, expression analysis, face swapping, etc. Heatmap regression-based methods have been widely used to achieve state-of-the-art results in this task. These methods involve computing the argmax over the heatmaps to predict a landmark. Since argmax is not differentiable, these methods use a differentiable approximation, Soft-argmax, to enable end-to-end training on deep-nets. In this work, we revisit this long-standing choice of using Soft-argmax and demonstrate that it is not the only way to achieve strong performance. Instead, we propose an alternative training objective based on the classic structured prediction framework. Empirically, our method achieves state-of-the-art performance on three facial landmark benchmarks (WFLW, COFW, and 300W), converging 2.2x faster during training while maintaining better/competitive accuracy. Our code is available here: https://github.com/ca-joe-yang/regression-without-softarg.