# Normalized Matching Transformer

arXiv: https://arxiv.org/abs/2503.17715 · HTML: https://mlsanity.com/paper/2503.17715/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 60 references that are in the map.
- First posted on arXiv 22 Mar 2025.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [Random Erasing Data Augmentation](https://mlsanity.com/paper/1708.04896/) (2017)
- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [LightGlue: Local Feature Matching at Light Speed](https://mlsanity.com/paper/2306.13643/) (2023)
- [Albumentations: fast and flexible image augmentations](https://mlsanity.com/paper/1809.06839/) (2018)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [SPair-71k: A Large-scale Benchmark for Semantic Correspondence](https://mlsanity.com/paper/1908.10543/) (2019)
- [Learning Combinatorial Embedding Networks for Deep Graph Matching](https://mlsanity.com/paper/1904.00597/) (2019)
- [Hyperspherical Prototype Networks](https://mlsanity.com/paper/1901.10514/) (2019)
- [Deep Graph Matching Consensus](https://mlsanity.com/paper/2001.09621/) (2020)
- [Neural Graph Matching Network: Learning Lawler's Quadratic Assignment Problem with Extension to Hypergraph and Multiple-graph Matching](https://mlsanity.com/paper/1911.11308/) (2019)
- [Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers](https://mlsanity.com/paper/2003.11657/) (2020)
- [nGPT: Normalized Transformer with Representation Learning on the Hypersphere](https://mlsanity.com/paper/2410.01131/) (2024)
- [DGC-Net: Dense Geometric Correspondence Network](https://mlsanity.com/paper/1810.08393/) (2018)
- [Graph Matching with Bi-level Noisy Correspondence](https://mlsanity.com/paper/2212.04085/) (2022)
- [A Study of Lagrangean Decompositions and Dual Ascent Solvers for Graph Matching](https://mlsanity.com/paper/1612.05476/) (2016)
- [LayoutGMN: Neural Graph Matching for Structural Layout Similarity](https://mlsanity.com/paper/2012.06547/) (2020)
- [Deep Graph Matching under Quadratic Constraint](https://mlsanity.com/paper/2103.06643/) (2021)
- [Fusion Moves for Graph Matching](https://mlsanity.com/paper/2101.12085/) (2021)
- [A Comparative Study of Graph Matching Algorithms in Computer Vision](https://mlsanity.com/paper/2207.00291/) (2022)
- [GLMNet: Graph Learning-Matching Networks for Feature Matching](https://mlsanity.com/paper/1911.07681/) (2019)

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

- [RBF-GNN: Rational Basis Functions for Pseudo-Coordinate based Graph Convolutions](https://mlsanity.com/paper/2609.37015/) (2026)

## Abstract (arXiv)

We introduce the Normalized Matching Transformer (NMT), a deep learning approach for efficient and accurate sparse semantic keypoint matching between image pairs. NMT consists of a strong visual backbone, geometric feature refinement via SplineCNN, followed by a normalized Transformer for computing matching features. Central to NMT is our hyperspherical normalization strategy: we enforce unit-norm embeddings at every Transformer layer and train with a combined contrastive InfoNCE and hyperspherical uniformity loss to yield more discriminative keypoint representations. This novel architecture/loss combination encourages close alignment of matching image features and large distances between non-matching ones not only at the output level, but for each layer. Despite its architectural simplicity, NMT sets a new state-of-the-art performance on PascalVOC and SPair-71k, outperforming BBGM, ASAR, COMMON and GMTR by 5.1% and 2.2%, respectively, while converging in at least 1.7x fewer epochs compared to other state-of-the-art baselines. These results underscore the power of combining pervasive normalization with hyperspherical learning for matching tasks.