# MinBackProp -- Backpropagating through Minimal Solvers

arXiv: https://arxiv.org/abs/2404.17993 · HTML: https://mlsanity.com/paper/2404.17993/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 34 references that are in the map.
- First posted on arXiv 27 Apr 2024.

## Builds on (most cited first, 14 of 14)

- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [DSAC - Differentiable RANSAC for Camera Localization](https://mlsanity.com/paper/1611.05705/) (2016)
- [Image Matching across Wide Baselines: From Paper to Practice](https://mlsanity.com/paper/2003.01587/) (2020)
- [MAGSAC++, a fast, reliable and accurate robust estimator](https://mlsanity.com/paper/1912.05909/) (2019)
- [Neural-Guided RANSAC: Learning Where to Sample Model Hypotheses](https://mlsanity.com/paper/1905.04132/) (2019)
- [EPro-PnP: Generalized End-to-End Probabilistic Perspective-n-Points for Monocular Object Pose Estimation](https://mlsanity.com/paper/2303.12787/) (2023)
- [Deep Declarative Networks: A New Hope](https://mlsanity.com/paper/1909.04866/) (2019)
- [End-to-End Learnable Geometric Vision by Backpropagating PnP Optimization](https://mlsanity.com/paper/1909.06043/) (2019)
- [Progressive Correspondence Pruning by Consensus Learning](https://mlsanity.com/paper/2101.00591/) (2021)
- [Generalized Differentiable RANSAC](https://mlsanity.com/paper/2212.13185/) (2022)
- [Beyond Gr"obner Bases: Basis Selection for Minimal Solvers](https://mlsanity.com/paper/1803.04360/) (2018)
- [Eigendecomposition-free Training of Deep Networks with Zero Eigenvalue-based Losses](https://mlsanity.com/paper/1803.08071/) (2018)
- [Optimizing Elimination Templates by Greedy Parameter Search](https://mlsanity.com/paper/2203.14901/) (2022)
- [Implicitly Defined Layers in Neural Networks](https://mlsanity.com/paper/2003.01822/) (2020)

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

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)

## Abstract (arXiv)

We present an approach to backpropagating through minimal problem solvers in end-to-end neural network training. Traditional methods relying on manually constructed formulas, finite differences, and autograd are laborious, approximate, and unstable for complex minimal problem solvers. We show that using the Implicit function theorem (IFT) to calculate derivatives to backpropagate through the solution of a minimal problem solver is simple, fast, and stable. We compare our approach to (i) using the standard autograd on minimal problem solvers and relate it to existing backpropagation formulas through SVD-based and Eig-based solvers and (ii) implementing the backprop with an existing PyTorch Deep Declarative Networks (DDN) framework. We demonstrate our technique on a toy example of training outlier-rejection weights for 3D point registration and on a real application of training an outlier-rejection and RANSAC sampling network in image matching. Our method provides 100% stability and is 10 times faster compared to autograd, which is unstable and slow, and compared to DDN, which is stable but also slow.