# Single Domain Generalization via Normalised Cross-correlation Based Convolutions

arXiv: https://arxiv.org/abs/2307.05901 · HTML: https://mlsanity.com/paper/2307.05901/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 43 references that are in the map.
- First posted on arXiv 12 Jul 2023.

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

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Measuring Robustness to Natural Distribution Shifts in Image Classification](https://mlsanity.com/paper/2007.00644/) (2020)
- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [A Survey of Unsupervised Deep Domain Adaptation](https://mlsanity.com/paper/1812.02849/) (2018)
- [Learning to Learn Single Domain Generalization](https://mlsanity.com/paper/2003.13216/) (2020)
- [Evaluating Prediction-Time Batch Normalization for Robustness under Covariate Shift](https://mlsanity.com/paper/2006.10963/) (2020)
- [Learning to Diversify for Single Domain Generalization](https://mlsanity.com/paper/2108.11726/) (2021)
- [Learning to Optimize Domain Specific Normalization for Domain Generalization](https://mlsanity.com/paper/1907.04275/) (2019)
- [Robust and Generalizable Visual Representation Learning via Random Convolutions](https://mlsanity.com/paper/2007.13003/) (2020)
- [Maximum-Entropy Adversarial Data Augmentation for Improved Generalization and Robustness](https://mlsanity.com/paper/2010.08001/) (2020)
- [Causality-inspired Single-source Domain Generalization for Medical Image Segmentation](https://mlsanity.com/paper/2111.12525/) (2021)
- [Progressive Domain Expansion Network for Single Domain Generalization](https://mlsanity.com/paper/2103.16050/) (2021)
- [B-cos Networks: Alignment is All We Need for Interpretability](https://mlsanity.com/paper/2205.10268/) (2022)
- [OoD-Bench: Quantifying and Understanding Two Dimensions of Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.03721/) (2021)
- [Adversarially Adaptive Normalization for Single Domain Generalization](https://mlsanity.com/paper/2106.01899/) (2021)
- [Cosine Normalization: Using Cosine Similarity Instead of Dot Product in Neural Networks](https://mlsanity.com/paper/1702.05870/) (2017)
- [Deep Hyperspherical Learning](https://mlsanity.com/paper/1711.03189/) (2017)
- [Decoupled Networks](https://mlsanity.com/paper/1804.08071/) (2018)
- [Meta-causal Learning for Single Domain Generalization](https://mlsanity.com/paper/2304.03709/) (2023)
- [Non-linear Convolution Filters for CNN-based Learning](https://mlsanity.com/paper/1708.07038/) (2017)
- [Kervolutional Neural Networks](https://mlsanity.com/paper/1904.03955/) (2019)

## Built on by (most cited first, 2 of 2)

- [Enhanced Online Test-time Adaptation with Feature-Weight Cosine Alignment](https://mlsanity.com/paper/2405.07171/) (2024)
- [VFM4SDG: Unveiling the Power of VFMs for Single-Domain Generalized Object Detection](https://mlsanity.com/paper/2604.21502/) (2026)

## Abstract (arXiv)

Deep learning techniques often perform poorly in the presence of domain shift, where the test data follows a different distribution than the training data. The most practically desirable approach to address this issue is Single Domain Generalization (S-DG), which aims to train robust models using data from a single source. Prior work on S-DG has primarily focused on using data augmentation techniques to generate diverse training data. In this paper, we explore an alternative approach by investigating the robustness of linear operators, such as convolution and dense layers commonly used in deep learning. We propose a novel operator called XCNorm that computes the normalized cross-correlation between weights and an input feature patch. This approach is invariant to both affine shifts and changes in energy within a local feature patch and eliminates the need for commonly used non-linear activation functions. We show that deep neural networks composed of this operator are robust to common semantic distribution shifts. Furthermore, our empirical results on single-domain generalization benchmarks demonstrate that our proposed technique performs comparably to the state-of-the-art methods.