# Improving Predictive Performance and Calibration by Weight Fusion in Semantic Segmentation

arXiv: https://arxiv.org/abs/2207.11211 · HTML: https://mlsanity.com/paper/2207.11211/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 46 references that are in the map.
- First posted on arXiv 22 Jul 2022.

## Builds on (most cited first, 30 of 37)

- [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)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [Deep High-Resolution Representation Learning for Visual Recognition](https://mlsanity.com/paper/1908.07919/) (2019)
- [Rethinking Semantic Segmentation from a Sequence-to-Sequence Perspective with Transformers](https://mlsanity.com/paper/2012.15840/) (2020)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Segmenter: Transformer for Semantic Segmentation](https://mlsanity.com/paper/2105.05633/) (2021)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)
- [Panoptic-DeepLab](https://mlsanity.com/paper/1910.04751/) (2019)
- [Calibrating Deep Neural Networks using Focal Loss](https://mlsanity.com/paper/2002.09437/) (2020)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [Dilated Residual Networks](https://mlsanity.com/paper/1705.09914/) (2017)
- [ENet: A Deep Neural Network Architecture for Real-Time Semantic Segmentation](https://mlsanity.com/paper/1606.02147/) (2016)
- [ICNet for Real-Time Semantic Segmentation on High-Resolution Images](https://mlsanity.com/paper/1704.08545/) (2017)

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

- [A Re-Parameterized Vision Transformer (ReVT) for Domain-Generalized Semantic Segmentation](https://mlsanity.com/paper/2308.13331/) (2023)

## Abstract (arXiv)

Averaging predictions of a deep ensemble of networks is apopular and effective method to improve predictive performance andcalibration in various benchmarks and Kaggle competitions. However, theruntime and training cost of deep ensembles grow linearly with the size ofthe ensemble, making them unsuitable for many applications. Averagingensemble weights instead of predictions circumvents this disadvantageduring inference and is typically applied to intermediate checkpoints ofa model to reduce training cost. Albeit effective, only few works haveimproved the understanding and the performance of weight averaging.Here, we revisit this approach and show that a simple weight fusion (WF)strategy can lead to a significantly improved predictive performance andcalibration. We describe what prerequisites the weights must meet interms of weight space, functional space and loss. Furthermore, we presenta new test method (called oracle test) to measure the functional spacebetween weights. We demonstrate the versatility of our WF strategy acrossstate of the art segmentation CNNs and Transformers as well as real worlddatasets such as BDD100K and Cityscapes. We compare WF with similarapproaches and show our superiority for in- and out-of-distribution datain terms of predictive performance and calibration.