[47] A.-H. Phan, K. Sobolev, K. Sozykin, D. Ermilov, J. Gusak, P. Tichavsky, V. Glukhov, I. Oseledets, and A. Cichocki. Stable low-rank tensor decomposition for compression of convolutional neural network. In A. Vedaldi, H. Bischof, T. Brox, and J.-M. Frahm, editors, Computer Vision – ECCV 2020, pages 522–539, Cham, 2020. Springer International Publishing. (Cited on page 1)
[48] M. Pilanci. Lecture notes: Large scale matrix computation, optimization, and learning (ee 270), 2020. URL https://web.stanford.edu/class/ee270/Lecture18.pdf. (Cited on page 29)
[49] Pinecone. Vector database for vector search | pinecone. https://www.pinecone.io/, 2023. (Accessed on 05/16/2023). (Cited on page 8)
[50] Y. Plan and R. Vershynin. Dimension reduction by random hyperplane tessellations. Discrete & Computational Geometry, 51(2):438-461, 2014. (Cited on page 4)
[51] Y. Qi, D. S. Sachan, M. Felix, S. J. Padmanabhan, and G. Neubig. When and why are pre-trained word embeddings useful for neural machine translation? arXiv preprint arXiv:1804.06323, 2018. (Cited on page 8)
[52] S. M. Rezaeinia, R. Rahmani, A. Ghodsi, and H. Veisi. Sentiment analysis based on improved pre-trained word embeddings. Expert Systems with Applications, 117:139-147, 2019. (Cited on page 8)
[53] M. Rudelson and R. Vershynin. Smallest singular value of a random rectangular matrix. Communications on Pure and Applied Mathematics, 62, 2008. (Cited on page 5)
[54] M. Safaryan, E. Shulgin, and P. Richtárik. Uncertainty principle for communication compression in distributed and federated learning and the search for an optimal compressor. Information and Inference: A Journal of the IMA, Apr 2021. (Cited on page 3)
[55] M. Safaryan, R. Islamov, X. Qian, and P. Richtárik. FedNL: Making newton-type methods applicable to federated learning. In International Conference on Machine Learning, ICML 2022, 17-23 July 2022, Baltimore, Maryland, USA, volume 162 of Proceedings of Machine Learning Research, pages 18959-19010. PMLR, 2022. URL https://proceedings.mlrpress/v162/safaryan22a.html. (Cited on page 2)
[56] R. Saha, M. Pilanci, and A. J. Goldsmith. Minimax optimal quantization of linear models: Information-theoretic limits and efficient algorithms, 2022. URL https://arxiv.org/abs/2202.11277. (Cited on page 3)
[57] R. Saha, M. Pilanci, and A. J. Goldsmith. Efficient randomized subspace embeddings for distributed optimization under a communication budget. IEEE Journal on Selected Areas in Information Theory, 3(2):183-196, 2022. doi: 10.1109/JSAIT.2022.3198412. (Cited on pages 3 and 4)
[58] R. Saha, M. Pilanci, and A. J. Goldsmith. Low precision representations for high dimensional models. In ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1-5, 2023. doi: 10.1109/ICASSP49357.2023.10095529. (Cited on pages 3 and 4)
[59] V. Siskind. Second moments of inverse wishart-matrix elements. Biometrika, 59(3):690-691, 12 1972. ISSN 0006-3444. doi: 10.1093/biomet/59.3.690. URL https://doi.org/10.1093/ biomet/59.3.690. (Cited on page 21)
[60] C. Studer, W. Yin, and R. G. Baraniuk. Signal representations with minimum  $\ell_{\infty}$ -norm. In 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 1270-1277, 2012. (Cited on page 3)
[61] A. T. Suresh, F. X. Yu, S. Kumar, and H. B. McMahan. Distributed mean estimation with limited communication. In Proceedings of the 34th International Conference on Machine Learning - Volume 70, ICML '17, page 3329-3337. JMLR.org, 2017. (Cited on pages 3 and 4)