# Optimal transport unlocks end-to-end learning for single-molecule localization

arXiv: https://arxiv.org/abs/2512.10683 · HTML: https://mlsanity.com/paper/2512.10683/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 67 references that are in the map.
- First posted on arXiv 11 Dec 2025.

## Builds on (most cited first, 18 of 18)

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- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [DINO: DETR with Improved DeNoising Anchor Boxes for End-to-End Object Detection](https://mlsanity.com/paper/2203.03605/) (2022)
- [DN-DETR: Accelerate DETR Training by Introducing Query DeNoising](https://mlsanity.com/paper/2203.01305/) (2022)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Iterative Residual Refinement for Joint Optical Flow and Occlusion Estimation](https://mlsanity.com/paper/1904.05290/) (2019)
- [Human Pose Estimation with Iterative Error Feedback](https://mlsanity.com/paper/1507.06550/) (2015)
- [Recurrent Inference Machines for Solving Inverse Problems](https://mlsanity.com/paper/1706.04008/) (2017)
- [Fractional Correspondence Framework in Detection Transformer](https://mlsanity.com/paper/2503.04107/) (2025)

## Abstract (arXiv)

Single-molecule localization microscopy (SMLM) allows reconstructing biology-relevant structures beyond the diffraction limit by detecting and localizing individual fluorophores -- fluorescent molecules stained onto the observed specimen -- over time to reconstruct super-resolved images. Currently, efficient SMLM requires non-overlapping emitting fluorophores, leading to long acquisition times that hinders live-cell imaging. Recent deep-learning approaches can handle denser emissions, but they rely on variants of non-maximum suppression (NMS) layers, which are unfortunately non-differentiable and may discard true positives with their local fusion strategy. In this presentation, we reformulate the SMLM training objective as a set-matching problem, deriving an optimal-transport loss that eliminates the need for NMS during inference and enables end-to-end training. Additionally, we propose an iterative neural network that integrates knowledge of the microscope's optical system inside our model. Experiments on synthetic benchmarks and real biological data show that both our new loss function and architecture surpass the state of the art at moderate and high emitter densities. Code is available at https://github.com/RSLLES/SHOT.