@inproceedings{zhang2020does,
  author       = {Linjun Zhang and
                  Zhun Deng and
                  Kenji Kawaguchi and
                  Amirata Ghorbani and
                  James Zou},
  title        = {How Does Mixup Help With Robustness and Generalization?},
  booktitle    = {9th International Conference on Learning Representations, {ICLR} 2021,
                  Virtual Event, Austria, May 3-7, 2021},
  year         = {2021},
  url          = {https://openreview.net/forum?id=8yKEo06dKNo}
}
@inproceedings{zhang2017mixup,
  author       = {Hongyi Zhang and
                  Moustapha Ciss{\'{e}} and
                  Yann N. Dauphin and
                  David Lopez{-}Paz},
  title        = {mixup: Beyond Empirical Risk Minimization},
  booktitle    = {6th International Conference on Learning Representations, {ICLR} 2018,
                  Vancouver, BC, Canada, April 30 - May 3, 2018, Conference Track Proceedings},
  year         = {2018},
  url          = {https://openreview.net/forum?id=r1Ddp1-Rb}
}
}
@inproceedings{verma2019manifold,
  title={Manifold mixup: Better representations by interpolating hidden states},
  author={Verma, Vikas and Lamb, Alex and Beckham, Christopher and Najafi, Amir and Mitliagkas, Ioannis and Lopez-Paz, David and Bengio, Yoshua},
  booktitle={International conference on machine learning},
  pages={6438--6447},
  year={2019},
  organization={PMLR}
}
@article{mcinnes2018umap,
  title={Umap: Uniform manifold approximation and projection for dimension reduction},
  author={McInnes, Leland and Healy, John and Melville, James},
  journal={arXiv preprint arXiv:1802.03426},
  year={2018}
}
@article{vapnik1999overview,
  title={An overview of statistical learning theory},
  author={Vapnik, Vladimir N},
  journal={IEEE transactions on neural networks},
  volume={10},
  number={5},
  pages={988--999},
  year={1999},
  publisher={IEEE}
}
@article{chapelle2000vicinal,
  title={Vicinal risk minimization},
  author={Chapelle, Olivier and Weston, Jason and Bottou, L{\'e}on and Vapnik, Vladimir},
  journal={Advances in neural information processing systems},
  volume={13},
  year={2000}
}
@inproceedings{el-laham2023deep,
title={Deep Gaussian Mixture Ensembles},
author={Yousef El-Laham and Niccolo Dalmasso and Elizabeth Fons and Svitlana Vyetrenko},
booktitle={The 39th Conference on Uncertainty in Artificial Intelligence},
year={2023},
url={https://openreview.net/forum?id=_Qwp7ATIa6P}
}

@article{baena2022preventing,
  title={Preventing manifold intrusion with locality: Local mixup},
  author={Baena, Raphael and Drumetz, Lucas and Gripon, Vincent},
  journal={arXiv preprint arXiv:2201.04368},
  year={2022}
}
@inproceedings{guo2019mixup,
  title={Mixup as locally linear out-of-manifold regularization},
  author={Guo, Hongyu and Mao, Yongyi and Zhang, Richong},
  booktitle={Proceedings of the AAAI conference on artificial intelligence},
  volume={33},
  pages={3714--3722},
  year={2019}
}
@article{carratino2022mixup,
  title={On mixup regularization},
  author={Carratino, Luigi and Ciss{\'e}, Moustapha and Jenatton, Rodolphe and Vert, Jean-Philippe},
  journal={Journal of Machine Learning Research},
  volume={23},
  number={325},
  pages={1--31},
  year={2022}
}
@article{jin2024survey,
  title={A Survey on Mixup Augmentations and Beyond},
  author={Jin, Xin and Zhu, Hongyu and Li, Siyuan and Wang, Zedong and Liu, Zicheng and Yu, Chang and Qin, Huafeng and Li, Stan Z},
  journal={arXiv preprint arXiv:2409.05202},
  year={2024}
}
@inproceedings{el2024augment,
  title={Augment on Manifold: Mixup Regularization with UMAP},
  author={El-Laham, Yousef and Fons, Elizabeth and Daudert, Dillon and Vyetrenko, Svitlana},
  booktitle={ICASSP 2024-2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
  pages={7040--7044},
  year={2024},
  organization={IEEE}
}
@article{cai2024survey,
  author={Cai, Weilin and Jiang, Juyong and Wang, Fan and Tang, Jing and Kim, Sunghun and Huang, Jiayi},
  journal={IEEE Transactions on Knowledge and Data Engineering}, 
  title={A Survey on Mixture of Experts in Large Language Models}, 
  year={2025},
  volume={37},
  number={7},
  pages={3896-3915},
  doi={10.1109/TKDE.2025.3554028}}
@article{jacobs1991adaptive,
  title={Adaptive mixtures of local experts},
  author={Jacobs, Robert A and Jordan, Michael I and Nowlan, Steven J and Hinton, Geoffrey E},
  journal={Neural computation},
  volume={3},
  number={1},
  pages={79--87},
  year={1991},
  publisher={MIT Press}
}
@article{hinton2002training,
  title={Training products of experts by minimizing contrastive divergence},
  author={Hinton, Geoffrey E},
  journal={Neural computation},
  volume={14},
  number={8},
  pages={1771--1800},
  year={2002},
  publisher={MIT Press}
}
@article{lakshminarayanan2017simple,
  title={Simple and scalable predictive uncertainty estimation using deep ensembles},
  author={Lakshminarayanan, Balaji and Pritzel, Alexander and Blundell, Charles},
  journal={Advances in neural information processing systems},
  volume={30},
  year={2017}
}
@article{koliander2022fusion,
  title={Fusion of probability density functions},
  author={Koliander, G{\"u}nther and El-Laham, Yousef and Djuri{\'c}, Petar M and Hlawatsch, Franz},
  journal={Proceedings of the IEEE},
  volume={110},
  number={4},
  pages={404--453},
  year={2022},
  publisher={IEEE}
}
@inproceedings{lepikhin2020gshard,
  author       = {Dmitry Lepikhin and
                  HyoukJoong Lee and
                  Yuanzhong Xu and
                  Dehao Chen and
                  Orhan Firat and
                  Yanping Huang and
                  Maxim Krikun and
                  Noam Shazeer and
                  Zhifeng Chen},
  title        = {GShard: Scaling Giant Models with Conditional Computation and Automatic
                  Sharding},
  booktitle    = {9th International Conference on Learning Representations, {ICLR} 2021,
                  Virtual Event, Austria, May 3-7, 2021},
  year         = {2021},
  url          = {https://openreview.net/forum?id=qrwe7XHTmYb}
}
@article{jiang2024mixtral,
  title={Mixtral of experts},
  author={Jiang, Albert Q and Sablayrolles, Alexandre and Roux, Antoine and Mensch, Arthur and Savary, Blanche and Bamford, Chris and Chaplot, Devendra Singh and Casas, Diego de las and Hanna, Emma Bou and Bressand, Florian and others},
  journal={arXiv preprint arXiv:2401.04088},
  year={2024}
}
@article{liu2024deepseek,
  title={Deepseek-v3 technical report},
  author={Liu, Aixin and Feng, Bei and Xue, Bing and Wang, Bingxuan and Wu, Bochao and Lu, Chengda and Zhao, Chenggang and Deng, Chengqi and Zhang, Chenyu and Ruan, Chong and others},
  journal={arXiv preprint arXiv:2412.19437},
  year={2024}
}
@article{kingma2013auto,
  title={Auto-encoding variational bayes},
  author={Kingma, Diederik P},
  journal={arXiv preprint arXiv:1312.6114},
  year={2013}
}
@inproceedings{liu2023mixmae,
  title={MixMAE: Mixed and masked autoencoder for efficient pretraining of hierarchical vision transformers},
  author={Liu, Jihao and Huang, Xin and Zheng, Jinliang and Liu, Yu and Li, Hongsheng},
  booktitle={Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  pages={6252--6261},
  year={2023}
}
@inproceedings{islam2024diffusemix,
  title={DiffuseMix: Label-Preserving Data Augmentation with Diffusion Models},
  author={Islam, Khawar and Zaheer, Muhammad Zaigham and Mahmood, Arif and Nandakumar, Karthik},
  booktitle={Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  pages={27621--27630},
  year={2024}
}
@inproceedings{wang2024enhance,
  title={Enhance Image Classification via Inter-Class Image Mixup with Diffusion Model},
  author={Wang, Zhicai and Wei, Longhui and Wang, Tan and Chen, Heyu and Hao, Yanbin and Wang, Xiang and He, Xiangnan and Tian, Qi},
  booktitle={Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  pages={17223--17233},
  year={2024}
}
@inproceedings{tokozume2018between,
  title={Between-class learning for image classification},
  author={Tokozume, Yuji and Ushiku, Yoshitaka and Harada, Tatsuya},
  booktitle={Proceedings of the IEEE conference on computer vision and pattern recognition},
  pages={5486--5494},
  year={2018}
}
@inproceedings{zhang2022contrastive,
  title={Contrastive-mixup learning for improved speaker verification},
  author={Zhang, Xin and Jin, Minho and Cheng, Roger and Li, Ruirui and Han, Eunjung and Stolcke, Andreas},
  booktitle={ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
  pages={7652--7656},
  year={2022},
  organization={IEEE}
}
@inproceedings{sun2020mixup,
    title = "Mixup-Transformer: Dynamic Data Augmentation for {NLP} Tasks",
    author = "Sun, Lichao  and
      Xia, Congying  and
      Yin, Wenpeng  and
      Liang, Tingting  and
      Yu, Philip  and
      He, Lifang",
    editor = "Scott, Donia  and
      Bel, Nuria  and
      Zong, Chengqing",
    booktitle = "Proceedings of the 28th International Conference on Computational Linguistics",
    month = dec,
    year = "2020",
    address = "Barcelona, Spain (Online)",
    publisher = "International Committee on Computational Linguistics",
    doi = "10.18653/v1/2020.coling-main.305",
    pages = "3436--3440"
}
@inproceedings{zhang2020seqmix,
    title = "{S}eq{M}ix: Augmenting Active Sequence Labeling via Sequence Mixup",
    author = "Zhang, Rongzhi  and
      Yu, Yue  and
      Zhang, Chao",
    editor = "Webber, Bonnie  and
      Cohn, Trevor  and
      He, Yulan  and
      Liu, Yang",
    booktitle = "Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)",
    month = nov,
    year = "2020",
    address = "Online",
    publisher = "Association for Computational Linguistics",
    url = "https://aclanthology.org/2020.emnlp-main.691/",
    doi = "10.18653/v1/2020.emnlp-main.691",
    pages = "8566--8579"
}
@article{guo1905augmenting,
  title={Augmenting data with mixup for sentence classification: An empirical study. arXiv 2019},
  author={Guo, Hongyu and Mao, Yongyi and Zhang, Richong},
  journal={arXiv preprint arXiv:1905.08941},
  year={2019}
}
@inproceedings{verma2021graphmix,
  title={Graphmix: Improved training of gnns for semi-supervised learning},
  author={Verma, Vikas and Qu, Meng and Kawaguchi, Kenji and Lamb, Alex and Bengio, Yoshua and Kannala, Juho and Tang, Jian},
  booktitle={Proceedings of the AAAI conference on artificial intelligence},
  volume={35},
  pages={10024--10032},
  year={2021}
}
@inproceedings{han2022g,
  title={G-mixup: Graph data augmentation for graph classification},
  author={Han, Xiaotian and Jiang, Zhimeng and Liu, Ninghao and Hu, Xia},
  booktitle={International Conference on Machine Learning},
  pages={8230--8248},
  year={2022},
  organization={PMLR}
}
@inproceedings{jeongigraphmix,
  title={iGraphMix: Input Graph Mixup Method for Node Classification},
  author={Jeong, Jongwon and Lee, Hoyeop and Yoon, Hyui Geon and Lee, Beomyoung and Heo, Junhee and Kim, Geonsoo and Seon, Kim Jin},
  booktitle={The Twelfth International Conference on Learning Representations},
  year={2023}
}

% Dataset references
% Yacht
@misc{yacht_hydrodynamics_243,
  author       = {Gerritsma, J. and Onnink, R. and Versluis, A.},
  title        = {{Yacht Hydrodynamics}},
  year         = {1981},
  howpublished = {UCI Machine Learning Repository},
  note         = {{DOI}: https://doi.org/10.24432/C5XG7R}
}
% Naval propulsion
@misc{condition_based_maintenance_of_naval_propulsion_plants_316,
  author       = {Coraddu, Andrea and Oneto, Luca and Ghio, Alessandro and Savio, Stefano and Anguita, Davide and Figari, Massimo},
  title        = {{Condition Based Maintenance of Naval Propulsion Plants}},
  year         = {2014},
  howpublished = {UCI Machine Learning Repository},
  note         = {{DOI}: https://doi.org/10.24432/C5K31K}
}
% Concrete
@misc{concrete_compressive_strength_165,
  author       = {Yeh, I-Cheng},
  title        = {{Concrete Compressive Strength}},
  year         = {1998},
  howpublished = {UCI Machine Learning Repository},
  note         = {{DOI}: https://doi.org/10.24432/C5PK67}
}
% Energy
@misc{energy_efficiency_242,
  author       = {Tsanas, Athanasios and Xifara, Angeliki},
  title        = {{Energy Efficiency}},
  year         = {2012},
  howpublished = {UCI Machine Learning Repository},
  note         = {{DOI}: https://doi.org/10.24432/C51307}
}
% Power plant
@misc{combined_cycle_power_plant_294,
  author       = {Tfekci, Pnar and Kaya, Heysem},
  title        = {{Combined Cycle Power Plant}},
  year         = {2014},
  howpublished = {UCI Machine Learning Repository},
  note         = {{DOI}: https://doi.org/10.24432/C5002N}
}
% Wine quality
@misc{wine_quality_186,
  author       = {Cortez, Paulo and Cerdeira, A. and Almeida, F. and Matos, T. and Reis, J.},
  title        = {{Wine Quality}},
  year         = {2009},
  howpublished = {UCI Machine Learning Repository},
  note         = {{DOI}: https://doi.org/10.24432/C56S3T}
}
%C-mixup
@inproceedings{NEURIPS2022_1626be0a,
 author = {Yao, Huaxiu and Wang, Yiping and Zhang, Linjun and Zou, James Y and Finn, Chelsea},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {S. Koyejo and S. Mohamed and A. Agarwal and D. Belgrave and K. Cho and A. Oh},
 pages = {3361--3376},
 publisher = {Curran Associates, Inc.},
 title = {C-Mixup: Improving Generalization in Regression},
 volume = {35},
 year = {2022}
}

@article{levi2022evaluating,
  title={Evaluating and calibrating uncertainty prediction in regression tasks},
  author={Levi, Dan and Gispan, Liran and Giladi, Niv and Fetaya, Ethan},
  journal={Sensors},
  volume={22},
  number={15},
  pages={5540},
  year={2022},
  publisher={MDPI}
}