@article{Gray1993dithered,
	title={Dithered quantizers},
	author={Gray, Robert M. and Stockham, T. G.},
	journal={IEEE Trans. Information Theory},
	volume={39},
	number={3},
	pages={805--812},
	month={May},
	year={1993},
}

@inproceedings{Alistarh2017qsgd,
	title={{QSGD}: Communication-efficient {SGD} via gradient quantization and encoding},
	author={Alistarh, Dan and Grubic, Demjan and Li, Jerry and Tomioka, Ryota and Vojnovic, Milan},
	booktitle={Advances in Neural Information Processing Systems (NeurIPS)},
	year={2017},
}

@article{Shlezinger2020uveqfed,
	title={{UVeQFed}: Universal vector quantization for federated learning},
	author={Shlezinger, Nir and Chen, Mingzhe and Eldar, Yonina C. and Poor, H. Vincent and Cui, Shuguang},
	journal={IEEE Trans. Signal Processing},
	volume={69},
	pages={500--514},
	month={Dec.},
	year={2020},
}

@article{Kar2012distributed,
	title={Distributed parameter estimation in sensor networks: Nonlinear observation models and imperfect communication},
	author={Kar, Soummya and Moura, Jos\'{e} M. F. and Ramanan, Kavita},
	journal={IEEE Trans. Information Theory},
	volume={58},
	number={6},
	month={June},
	year={2012},
	pages={3575--3605},
}

@article{Schuchman1964dither,
	title={Dither signals and their effect on quantization noise},
	author={Schuchman, Leonard},
	journal={IEEE Trans. Communication Technology},
	volume={12},
	number={4},
	pages={162--165},
	month={Dec.},
	year={1964},
}

@article{Luo2005universal,
	title={Universal decentralized estimation in a bandwidth constrained sensor network},
	author={Luo, Zhi-Quan},
	journal={IEEE Trans. Information Theory},
	volume={51},
	number={6},
	pages={2210--2219},
	month={June},
	year={2005},
}

@article{Aysal2008distributed,
	title={Distributed average consensus with dithered quantization},
	author={Aysal, T. Can and Coates, Mark J. and Rabbat, Michael G.},
	journal={IEEE Trans. Signal Processing},
	volume={56},
	number={10},
	month={Oct.},
	year={2008},
	pages={4905--4918},
}

@article{Lipshitz1992quantization,
	title={Quantization and dither: A theoretical survey},
	author={Lipshitz, Stanley P. and Wannamaker, Robert A. and Vanderkooy, John},
	journal={Journal of the Audio Engineering Society},
	volume={40},
	number={5},
	pages={355--375},
	month={May},
	year={1992},
}

@article{sinha1979multiple,
  title={The multiple-choice knapsack problem},
  author={Sinha, Prabhakant and Zoltners, Andris A},
  journal={Operations Research},
  volume={27},
  number={3},
  pages={503--515},
  year={1979},
  publisher={INFORMS}
}

@inproceedings{Amiri2021compressive,
	title={Compressive Differentially-Private Federated Learning Through Universal Vector Quantization},
	author={Amiri, Saba and Belloum, Adam and Klous, Sander and Gommans, Leon},
	booktitle={AAAI Workshop on Privacy-Preserving Artificial Intelligence},
	year={2021},
}

@article{Cormode2021bit,
	title={Bit-efficient Numerical Aggregation and Stronger Privacy for Trust in Federated Analytics},
	author={Cormode, Graham and Markov, Igor L.},
	journal={arXiv preprint arXiv:2108.01521},
	month={Aug.},
	year={2021}
}

@inproceedings{girgis2021shuffled,
  title={Shuffled model of differential privacy in federated learning},
  author={Girgis, Antonious and Data, Deepesh and Diggavi, Suhas and Kairouz, Peter and Suresh, Ananda Theertha},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={2521--2529},
  year={2021},
  organization={PMLR}
}

@inproceedings{balle2018improving,
  title={Improving the gaussian mechanism for differential privacy: Analytical calibration and optimal denoising},
  author={Balle, Borja and Wang, Yu-Xiang},
  booktitle={International Conference on Machine Learning},
  pages={394--403},
  year={2018},
  organization={PMLR}
}

@article{canonne2020discrete,
  title={The discrete gaussian for differential privacy},
  author={Canonne, Cl{\'e}ment L and Kamath, Gautam and Steinke, Thomas},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  pages={15676--15688},
  year={2020}
}

@article{papernot2020tempered,
  title={Tempered sigmoid activations for deep learning with differential privacy},
  author={Papernot, Nicolas and Thakurta, Abhradeep and Song, Shuang and Chien, Steve and Erlingsson, Ulfar},
  journal={arXiv preprint arXiv:2007.14191},
  pages={10},
  year={2020}
}

@article{tramer2020differentially,
  title={Differentially private learning needs better features (or much more data)},
  author={Tramer, Florian and Boneh, Dan},
  journal={arXiv preprint arXiv:2011.11660},
  year={2020}
}

@inproceedings{oyallon2015deep,
  title={Deep roto-translation scattering for object classification},
  author={Oyallon, Edouard and Mallat, St{\'e}phane},
  booktitle={Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition},
  pages={2865--2873},
  year={2015}
}

@inproceedings{abadi2016deep,
  title={Deep learning with differential privacy},
  author={Abadi, Martin and Chu, Andy and Goodfellow, Ian and McMahan, H Brendan and Mironov, Ilya and Talwar, Kunal and Zhang, Li},
  booktitle={Proceedings of the 2016 ACM SIGSAC conference on computer and communications security},
  pages={308--318},
  year={2016}
}

@article{jin2020stochastic,
  title={Stochastic-sign SGD for federated learning with theoretical guarantees},
  author={Jin, Richeng and Huang, Yufan and He, Xiaofan and Dai, Huaiyu and Wu, Tianfu},
  journal={arXiv preprint arXiv:2002.10940},
  year={2020}
}

@book{conn2000trust,
  title={Trust Region Methods},
  author={Conn, Andrew R. and Gould, Nicholas I. M. and Toint, Philippe L.},
  publisher={SIAM},
  year={2000}
}

@article{stich2020error,
  title={The error-feedback framework: Better rates for {SGD} with delayed gradients and compressed communication},
  author={Stich, Sebastian U. and Karimireddy, Sai Praneeth},
  journal={Journal of Machine Learning Research},
  volume={21},
  number={237},
  pages={1--36},
  year={2020},
}

@inproceedings{haddadpour2021federated,
  title={Federated learning with compression: Unified analysis and sharp guarantees},
  author={Haddadpour, Farzin and Kamani, Mohammad Mahdi and Mokhtari, Aryan and Mahdavi, Mehrdad},
  booktitle={International Conference on Artificial Intelligence and Statistics (AISTATS)},
  pages={2350--2358},
  year={2021}
}

@article{konevcny2016federated,
  title={Federated learning: Strategies for improving communication efficiency},
  author={Kone{\v{c}}n{\`y}, Jakub and McMahan, H Brendan and Yu, Felix X and Richt{\'a}rik, Peter and Suresh, Ananda Theertha and Bacon, Dave},
  journal={arXiv preprint arXiv:1610.05492},
  year={2016}
}

@article{horvath2019stochastic,
  title={Stochastic distributed learning with gradient quantization and variance reduction},
  author={Horv{\'a}th, Samuel and Kovalev, Dmitry and Mishchenko, Konstantin and Stich, Sebastian and Richt{\'a}rik, Peter},
  journal={arXiv preprint arXiv:1904.05115},
  year={2019}
}

@article{das2020faster,
  title={Faster non-convex federated learning via global and local momentum},
  author={Das, Rudrajit and Acharya, Anish and Hashemi, Abolfazl and Sanghavi, Sujay and Dhillon, Inderjit S and Topcu, Ufuk},
  journal={arXiv preprint arXiv:2012.04061},
  year={2020}
}

@InProceedings{gorbunov21marina,
  title = 	 {{MARINA}: Faster Non-Convex Distributed Learning with Compression},
  author =       {Gorbunov, Eduard and Burlachenko, Konstantin P. and Li, Zhize and Richtarik, Peter},
  booktitle = 	 {International Conference on Machine Learning},
  pages = 	 {3788--3798},
  year = 	 {2021},
}

@inproceedings{seide2014one,
  title={1-bit stochastic gradient descent and its application to data-parallel distributed training of speech {DNNs}},
  author={Seide, Frank and Fu, Hao and Droppo, Jasha and Li, Gang and Yu, Dong},
  booktitle={Fifteenth Annual Conference of the International Speech Communication Association},
  year={2014},
}

@inproceedings{chatzikokolakis2013broadening,
  title={Broadening the scope of differential privacy using metrics},
  author={Chatzikokolakis, Konstantinos and Andr{\'e}s, Miguel E and Bordenabe, Nicol{\'a}s Emilio and Palamidessi, Catuscia},
  booktitle={International Symposium on Privacy Enhancing Technologies Symposium},
  pages={82--102},
  year={2013},
  organization={Springer}
}

@inproceedings{mironov2017renyi,
  title={R{\'e}nyi differential privacy},
  author={Mironov, Ilya},
  booktitle={2017 IEEE 30th computer security foundations symposium (CSF)},
  pages={263--275},
  year={2017},
  organization={IEEE}
}

@inproceedings{renyi1961measures,
  title={On measures of entropy and information},
  author={R{\'e}nyi, Alfr{\'e}d},
  booktitle={Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics},
  volume={4},
  pages={547--562},
  year={1961},
  organization={University of California Press}
}

@inproceedings{wu2018group,
  title={Group normalization},
  author={Wu, Yuxin and He, Kaiming},
  booktitle={Proceedings of the European conference on computer vision (ECCV)},
  pages={3--19},
  year={2018}
}

@inproceedings{balle2019privacy,
  title={The privacy blanket of the shuffle model},
  author={Balle, Borja and Bell, James and Gasc{\'o}n, Adri{\`a} and Nissim, Kobbi},
  booktitle={Annual International Cryptology Conference},
  pages={638--667},
  year={2019},
  organization={Springer}
}

@article{krizhevsky2009learning,
  title={Learning multiple layers of features from tiny images},
  author={Krizhevsky, Alex and Hinton, Geoffrey and others},
  year={2009},
  publisher={Citeseer}
}

@inproceedings{mcmahan2017communication,
  title={Communication-efficient learning of deep networks from decentralized data},
  author={McMahan, Brendan and Moore, Eider and Ramage, Daniel and Hampson, Seth and y Arcas, Blaise Aguera},
  booktitle={Artificial intelligence and statistics},
  pages={1273--1282},
  year={2017},
  organization={PMLR}
}