Correction: Break a Lag: Triple Exponential Moving Average for Enhanced Optimization (Machine Learning, (2026), 115, 3, (58), 10.1007/s10994-025-06992-x)

In this article, the current version contains major formatting errors in the tables. The structures of Tables 1–3 appear distorted and compressed to half a page. The values overlap in multiple tables and extend beyond the margins in Tables 4–6. For completeness and transparency, the corrected versions of Tables 1, 2, 3, 4, 5, 6 are displayed below. The original article has been corrected. Performance comparison of various models using different optimization techniques on CIFAR-100 and ImageNet datasets Dataset Type Model Our FAME Adam SGD + Momentum CIFAR-100 CNN EfficientNet-B0 (Tan and Le, 2019) EfficientNet-B3 (Tan and Le, 2019) MobileNetV3-Large (Howard et al., 2019) DenseNet-121 (Huang et al., 2017) DenseNet-201 (Huang et al., 2017) SE-ResNet-50 (Hu et al., 2018) PyramidNet-272 (Han et al., 2017) Transformer ViT-Base (Dosovitskiy et al., 2020) Swin-T (Liu et al., 2021) CvT-13 (Wu et al., 2021) T2T-ViT-14 (Yuan et al., 2021) ImageNet CNN MobileNetV3-Large (Howard et al., 2019) EfficientNet-B0 (Tan and Le, 2019) EfficientNet-B5 (Tan and Le, 2019) Transformer CvT-13 (Wu et al., 2021) CAFormer-S18 (Yu et al., 2024) CAFormer-S36 (Yu et al., 2024) The bold values means 1st place in performance The mean values over 3 different initializations are in standard font, and std values are presented as subscripts Object detection results on MS-COCO using YOLOv5-s (Li et al., 2023) and different optimization techniques Metric Our FAME SGD Adam AdamW [email protected] [email protected]:0.95 Precision Recall F1-Score The bold values means 1st place in performance The mean accuracy values over 3 different initializations are in standard font, and std values are presented as subscripts. The results match those of training from scratch, as reported in the literature Pascal Visual Object Classes (VOC) for detection/classification tasks using various models and different optimization techniques Our Fame SGD Adam AdamW Yolov5-s (Li et al., 2023) ([email protected]) - Detection Yolov5-m (Sadiq et al., 2022) ([email protected]) - Detection ReViT (Diko et al., 2024) (AUC) - Classification The bold values means 1st place in performance The mean values over 3 different initializations are in standard font, and std values are presented as subscripts. The results match those for training from scratch as reported in literature Cityscapes semantic segmentation. Performance comparison of various deep models using different optimization techniques Model Our FAME Adam SGD DL-V3+ResNet50* DL-V3+ResNet101* DL-V3+MobileNetV2* HANet-ResNet101* DL-V3+Xception "DL" - DeepLab (Chen et al., 2018). Comparison of classification mIoU (Mean ± Std) supplied by different optimizers across models. Best results for each model are bolded. All SGD and Adam results are comparable to the literature results when training from scratch. The mean values over 3 different initializations are in standard font, and std values are presented as subscripts. * indicated pretrained on ImageNet to show FAME’s strength also in pretrained scenarios, otherwise - training from scratch (DL-V3+Xception) Effect of the EMA order on the model’s performance Dataset Model EMA DEMA Our FAME CIFAR-100 ResNet34 MS-COCO YOLOv5-s (Li et al., 2023) PASCAL-VOC YOLOv5-m (Sadiq et al., 2022) Cityscapes DL-V3+ResNet50* Comparison of model performance (Mean and Std) supplied by different optimizers across datasets. The mean values over 3 different initializations are in standard font, and std values are presented as subscripts Ablation study Dataset Adam (Original EMA) Partial FAME Our FAME CIFAR-100 (Accuracy) MS-COCO (mAP) PASCAL-VOC (mAP) CityScapes (mean IoU) "Partial FAME" means using TEMA for only, while "Our FAME" means using TEMA for both and. CIFAR100: ResNet50, MS-COCO: YOLOv5-s, Pascal-VOC: YOLOv5-m, and Cityscapes: ResNet50+ DeepLabV3.