# Localization with Sampling-Argmax

arXiv: https://arxiv.org/abs/2110.08825 · HTML: https://mlsanity.com/paper/2110.08825/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 57 references that are in the map.
- First posted on arXiv 17 Oct 2021.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Deep High-Resolution Representation Learning for Human Pose Estimation](https://mlsanity.com/paper/1902.09212/) (2019)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Simple Baselines for Human Pose Estimation and Tracking](https://mlsanity.com/paper/1804.06208/) (2018)
- [End-to-End Learning of Geometry and Context for Deep Stereo Regression](https://mlsanity.com/paper/1703.04309/) (2017)
- [HybrIK: A Hybrid Analytical-Neural Inverse Kinematics Solution for 3D Human Pose and Shape Estimation](https://mlsanity.com/paper/2011.14672/) (2020)
- [Deep Imitation Learning for Complex Manipulation Tasks from Virtual Reality Teleoperation](https://mlsanity.com/paper/1710.04615/) (2017)
- [Integral Human Pose Regression](https://mlsanity.com/paper/1711.08229/) (2017)
- [Coarse-to-Fine Volumetric Prediction for Single-Image 3D Human Pose](https://mlsanity.com/paper/1611.07828/) (2016)
- [CrowdPose: Efficient Crowded Scenes Pose Estimation and A New Benchmark](https://mlsanity.com/paper/1812.00324/) (2018)
- [Deep Spatial Autoencoders for Visuomotor Learning](https://mlsanity.com/paper/1509.06113/) (2015)
- [A* Sampling](https://mlsanity.com/paper/1411.0030/) (2014)
- [Camera Distance-aware Top-down Approach for 3D Multi-person Pose Estimation from a Single RGB Image](https://mlsanity.com/paper/1907.11346/) (2019)
- [Human Pose Regression with Residual Log-likelihood Estimation](https://mlsanity.com/paper/2107.11291/) (2021)
- [DeepPruner: Learning Efficient Stereo Matching via Differentiable PatchMatch](https://mlsanity.com/paper/1909.05845/) (2019)
- [2D/3D Pose Estimation and Action Recognition using Multitask Deep Learning](https://mlsanity.com/paper/1802.09232/) (2018)
- [Numerical Coordinate Regression with Convolutional Neural Networks](https://mlsanity.com/paper/1801.07372/) (2018)
- [SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation](https://mlsanity.com/paper/1612.00606/) (2016)
- [SFNet: Learning Object-aware Semantic Correspondence](https://mlsanity.com/paper/1904.01810/) (2019)
- [Human Pose Regression by Combining Indirect Part Detection and Contextual Information](https://mlsanity.com/paper/1710.02322/) (2017)
- [KeypointNet: A Large-scale 3D Keypoint Dataset Aggregated from Numerous Human Annotations](https://mlsanity.com/paper/2002.12687/) (2020)
- [PoseFix: Model-agnostic General Human Pose Refinement Network](https://mlsanity.com/paper/1812.03595/) (2018)
- [HMOR: Hierarchical Multi-Person Ordinal Relations for Monocular Multi-Person 3D Pose Estimation](https://mlsanity.com/paper/2008.00206/) (2020)
- [Improving Landmark Localization with Semi-Supervised Learning](https://mlsanity.com/paper/1709.01591/) (2017)
- [Skeleton Merger: an Unsupervised Aligned Keypoint Detector](https://mlsanity.com/paper/2103.10814/) (2021)
- [Learning to Orient Surfaces by Self-supervised Spherical CNNs](https://mlsanity.com/paper/2011.03298/) (2020)
- [Learning to Linearize Under Uncertainty](https://mlsanity.com/paper/1506.03011/) (2015)

## Built on by (most cited first, 11 of 11)

- [D&D: Learning Human Dynamics from Dynamic Camera](https://mlsanity.com/paper/2209.08790/) (2022)
- [LocLLM: Exploiting Generalizable Human Keypoint Localization via Large Language Model](https://mlsanity.com/paper/2406.04659/) (2024)
- [Deep Reinforcement Learning for Time-Critical Wilderness Search And Rescue Using Drones](https://mlsanity.com/paper/2405.12800/) (2024)
- [TIC-TAC: A Framework for Improved Covariance Estimation in Deep Heteroscedastic Regression](https://mlsanity.com/paper/2310.18953/) (2023)
- [Pixel-Wise Symbol Spotting via Progressive Points Location for Parsing CAD Images](https://mlsanity.com/paper/2404.10985/) (2024)
- [Towards Self-Supervised Covariance Estimation in Deep Heteroscedastic Regression](https://mlsanity.com/paper/2502.10587/) (2025)
- [The Sampling-Gaussian for stereo matching](https://mlsanity.com/paper/2410.06527/) (2024)
- [CornerFormer: Boosting Corner Representation for Fine-Grained Structured Reconstruction](https://mlsanity.com/paper/2304.07072/) (2023)
- [Topology-inspired Cross-domain Network for Developmental Cervical Stenosis Quantification](https://mlsanity.com/paper/2309.06825/) (2023)
- [Incremental Object Keypoint Learning](https://mlsanity.com/paper/2503.20248/) (2025)
- [Diagnose Like A REAL Pathologist: An Uncertainty-Focused Approach for Trustworthy Multi-Resolution Multiple Instance Learning](https://mlsanity.com/paper/2511.06433/) (2025)

## Abstract (arXiv)

Soft-argmax operation is commonly adopted in detection-based methods to localize the target position in a differentiable manner. However, training the neural network with soft-argmax makes the shape of the probability map unconstrained. Consequently, the model lacks pixel-wise supervision through the map during training, leading to performance degradation. In this work, we propose sampling-argmax, a differentiable training method that imposes implicit constraints to the shape of the probability map by minimizing the expectation of the localization error. To approximate the expectation, we introduce a continuous formulation of the output distribution and develop a differentiable sampling process. The expectation can be approximated by calculating the average error of all samples drawn from the output distribution. We show that sampling-argmax can seamlessly replace the conventional soft-argmax operation on various localization tasks. Comprehensive experiments demonstrate the effectiveness and flexibility of the proposed method. Code is available at https://github.com/Jeff-sjtu/sampling-argmax