@article{seddik2021random,
  title={When Random Tensors meet Random Matrices},
  author={Seddik, Mohamed El Amine and Guillaud, Maxime and Couillet, Romain},
  journal={arXiv preprint arXiv:2112.12348},
  year={2021}
}

@article{hillar2013most,
  title={Most tensor problems are NP-hard},
  author={Hillar, Christopher J and Lim, Lek-Heng},
  journal={Journal of the ACM (JACM)},
  volume={60},
  number={6},
  pages={1--39},
  year={2013},
  publisher={ACM New York, NY, USA}
}

@article{auddy2021estimating,
  title={On estimating rank-one spiked tensors in the presence of heavy tailed errors},
  author={Auddy, Arnab and Yuan, Ming},
  journal={IEEE Transactions on Information Theory},
  volume={68},
  number={12},
  pages={8053--8075},
  year={2022},
  publisher={IEEE}
}

@article{o2016eigenvectors,
  title={Eigenvectors of random matrices: a survey},
  author={O'Rourke, Sean and Vu, Van and Wang, Ke},
  journal={Journal of Combinatorial Theory, Series A},
  volume={144},
  pages={361--442},
  year={2016},
  publisher={Elsevier}
}

@article{wang2022binary,
  title={Binary classification of gaussian mixtures: Abundance of support vectors, benign overfitting, and regularization},
  author={Wang, Ke and Thrampoulidis, Christos},
  journal={SIAM Journal on Mathematics of Data Science},
  volume={4},
  number={1},
  pages={260--284},
  year={2022},
  publisher={SIAM}
}

@article{ge2021understanding,
  title={Understanding deflation process in over-parametrized tensor decomposition},
  author={Ge, Rong and Ren, Yunwei and Wang, Xiang and Zhou, Mo},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={1299--1311},
  year={2021}
}

@inproceedings{pennington2017nonlinear,
  title={Nonlinear random matrix theory for deep learning},
  author={Pennington, Jeffrey and Worah, Pratik},
  booktitle={Advances in neural information processing systems},
  volume={30},
  year={2017}
}

@article{rontogiannis2021block,
  title={Block-term tensor decomposition: Model selection and computation},
  author={Rontogiannis, Athanasios A and Kofidis, Eleftherios and Giampouras, Paris V},
  journal={IEEE Journal of Selected Topics in Signal Processing},
  volume={15},
  number={3},
  pages={464--475},
  year={2021},
  publisher={IEEE}
}

@article{louart2018random,
  title={A random matrix approach to neural networks},
  author={Louart, Cosme and Liao, Zhenyu and Couillet, Romain},
  journal={The Annals of Applied Probability},
  volume={28},
  number={2},
  pages={1190--1248},
  year={2018},
  publisher={Institute of Mathematical Statistics}
}

@article{tiomoko2020large,
  title={Large dimensional analysis and improvement of multi task learning},
  author={Tiomoko, Malik and Couillet, Romain and Tiomoko, Hafiz},
  journal={arXiv preprint arXiv:2009.01591},
  year={2020}
}

@article{mai2018random,
  title={A random matrix analysis and improvement of semi-supervised learning for large dimensional data},
  author={Mai, Xiaoyi and Couillet, Romain},
  journal={The Journal of Machine Learning Research},
  volume={19},
  number={1},
  pages={3074--3100},
  year={2018},
  publisher={JMLR. org}
}

@article{ali2017improved,
  title={Improved spectral community detection in large heterogeneous networks},
  author={Ali, Hafiz Tiomoko and Couillet, Romain},
  journal={The Journal of Machine Learning Research},
  volume={18},
  number={1},
  pages={8344--8392},
  year={2017},
  publisher={JMLR. org}
}

@article{couillet2016kernel,
  title={Kernel spectral clustering of large dimensional data},
  author={Couillet, Romain and Benaych-Georges, Florent},
  journal={Electronic journal of statistics},
  volume={10},
  number={1},
  pages={1393--1454},
  year={2016},
  publisher={Institute of Mathematical Statistics and Bernoulli Society}
}

@inproceedings{seddik2021unexpected,
  title={The Unexpected Deterministic and Universal Behavior of Large Softmax Classifiers},
  author={Seddik, Mohamed El Amine and Louart, Cosme and Couillet, Romain and Tamaazousti, Mohamed},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={1045--1053},
  year={2021},
  organization={PMLR}
}

@article{kadmon2019statistical,
  title={Statistical mechanics of low-rank tensor decomposition},
  author={Kadmon, Jonathan and Ganguli, Surya},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  volume={2019},
  number={12},
  pages={124016},
  year={2019},
  publisher={IOP Publishing}
}

@article{tiomoko2021pca,
  title={Pca-based multi task learning: a random matrix approach},
  author={Tiomoko, Malik and Couillet, Romain and Pascal, Fr{\'e}d{\'e}ric},
  journal={arXiv preprint arXiv:2111.00924},
  year={2021}
}

@inproceedings{ng2002spectral,
  title={On spectral clustering: Analysis and an algorithm},
  author={Ng, Andrew Y and Jordan, Michael I and Weiss, Yair},
  booktitle={Advances in neural information processing systems},
  pages={849--856},
  year={2002}
}

@article{zhouIEEE2013,
  title={Tensor regression with applications in neuroimaging data analysis},
  author={Zhou, H. and Li, L. and Zhu, H.},
  journal={Journal of the American Statistical Association},
  volume={108},
  year={2013},
}

@inproceedings{chen2020tensor,
  title={Tensor low-rank reconstruction for semantic segmentation},
  author={Chen, Wanli and Zhu, Xinge and Sun, Ruoqi and He, Junjun and Li, Ruiyu and Shen, Xiaoyong and Yu, Bei},
  booktitle={European Conference on Computer Vision},
  pages={52--69},
  year={2020},
  organization={Springer}
}

@article{sunandli2019,
  title={Dynamic tensor clustering},
  author={Sun, W. and Li, L.},
  journal={Journal of the American Statistical Association},
  volume={114},
  pages={1894--1907},
  year={2019},
}

@article{koldabader2009,
  title={Tensor decompositions and applications},
  author={Kolda, T. G. and Bader, B. W.},
  journal={SIAM Review},
  volume={51},
  pages={455--500},
  year={2019},
}



@article{kossaifi2020tensor,
  title={Tensor regression networks},
  author={Kossaifi, Jean and Lipton, Zachary C and Kolbeinsson, Arinbj{\"o}rn and Khanna, Aran and Furlanello, Tommaso and Anandkumar, Anima},
  journal={Journal of Machine Learning Research},
  volume={21},
  pages={1--21},
  year={2020},
  publisher={Journal of Machine Learning Research}
}

@inproceedings{liang2019learning,
  title={Learning Representations from Imperfect Time Series Data via Tensor Rank Regularization},
  author={Liang, Paul Pu and Liu, Zhun and Tsai, Yao-Hung Hubert and Zhao, Qibin and Salakhutdinov, Ruslan and Morency, Louis-Philippe},
  booktitle={Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics},
  pages={1569--1576},
  year={2019}
}

@inproceedings{huangfNIRS2MW2021,
    title = {The Tufts fNIRS Mental Workload Dataset and Benchmark for Brain-Computer Interfaces that Generalize},
    booktitle = {Proceedings of the Neural Information Processing Systems (NeurIPS) Track on Datasets and Benchmarks},
    author = {Huang, Zhe and Wang, Liang and Blaney, Giles and Slaughter, Christopher and McKeon, Devon and Zhou, Ziyu and Jacob, Robert J. K. and Hughes, Michael C.},
    year = {2021},
    url = {https://openreview.net/pdf?id=QzNHE7QHhut},
}


@inproceedings{lim2005singular,
  title={Singular values and eigenvalues of tensors: a variational approach},
  author={Lim, Lek-Heng},
  booktitle={Proc. IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing},
  pages={129--132},
  year={2005}
}

@article{arous2021long,
  title={Long Random Matrices and Tensor Unfolding},
  author={Ben Arous, G{\'e}rard and Huang, Daniel Zhengyu and Huang, Jiaoyang},
  journal={arXiv preprint arXiv:2110.10210},
  year={2021}
}

@article{rabanser2017introduction,
  title={Introduction to tensor decompositions and their applications in machine learning},
  author={Rabanser, Stephan and Shchur, Oleksandr and G{\"u}nnemann, Stephan},
  journal={arXiv preprint arXiv:1711.10781},
  year={2017}
}

@article{sun2014tensors,
  title={Tensors in Modern Statistical Learning},
  author={Sun, Will Wei and Hao, Botao and Li, Lexin},
  journal={Wiley StatsRef: Statistics Reference Online},
  pages={1--25},
  year={2014},
  publisher={John Wiley \& Sons, Ltd Chichester, UK}
}

@article{arous2019landscape,
  title={The landscape of the spiked tensor model},
  author={Ben Arous, Gerard and Mei, Song and Montanari, Andrea and Nica, Mihai},
  journal={Communications on Pure and Applied Mathematics},
  volume={72},
  number={11},
  pages={2282--2330},
  year={2019},
  publisher={Wiley Online Library}
}

@book{nocedal2006numerical,
  title={Numerical optimization},
  author={Nocedal, Jorge and Wright, Stephen},
  year={2006},
  publisher={Springer Science \& Business Media}
}

@article{huang2020power,
  title={Power iteration for tensor pca},
  author={Huang, Jiaoyang and Huang, Daniel Z and Yang, Qing and Cheng, Guang},
  journal={arXiv preprint arXiv:2012.13669},
  year={2020}
}

@article{marvcenko1967distribution,
  title={Distribution of eigenvalues for some sets of random matrices},
  author={Mar{\v{c}}enko, Vladimir A and Pastur, Leonid Andreevich},
  journal={Mathematics of the USSR-Sbornik},
  volume={1},
  number={4},
  pages={457},
  year={1967},
  publisher={IOP Publishing}
}

@article{zare2018extension,
  title={Extension of PCA to higher order data structures: An introduction to tensors, tensor decompositions, and tensor PCA},
  author={Zare, Ali and Ozdemir, Alp and Iwen, Mark A and Aviyente, Selin},
  journal={Proceedings of the IEEE},
  volume={106},
  number={8},
  pages={1341--1358},
  year={2018},
  publisher={IEEE}
}

@article{baik2005phase,
  title={Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices},
  author={Baik, Jinho and Arous, G{\'e}rard Ben and P{\'e}ch{\'e}, Sandrine},
  journal={The Annals of Probability},
  volume={33},
  number={5},
  pages={1643--1697},
  year={2005},
  publisher={Institute of Mathematical Statistics}
}

@article{benaych2011eigenvalues,
  title={The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices},
  author={Benaych-Georges, Florent and Nadakuditi, Raj Rao},
  journal={Advances in Mathematics},
  volume={227},
  number={1},
  pages={494--521},
  year={2011},
  publisher={Elsevier}
}

@article{biroli2020iron,
  title={How to iron out rough landscapes and get optimal performances: averaged gradient descent and its application to tensor PCA},
  author={Biroli, Giulio and Cammarota, Chiara and Ricci-Tersenghi, Federico},
  journal={Journal of Physics A: Mathematical and Theoretical},
  volume={53},
  number={17},
  pages={174003},
  year={2020},
  publisher={IOP Publishing}
}

@article{sympy,
 title = {SymPy: symbolic computing in Python},
 author = {Meurer, Aaron and Smith, Christopher P. and Paprocki, Mateusz and \v{C}ert\'{i}k, Ond\v{r}ej and Kirpichev, Sergey B. and Rocklin, Matthew and Kumar, AMiT and Ivanov, Sergiu and Moore, Jason K. and Singh, Sartaj and Rathnayake, Thilina and Vig, Sean and Granger, Brian E. and Muller, Richard P. and Bonazzi, Francesco and Gupta, Harsh and Vats, Shivam and Johansson, Fredrik and Pedregosa, Fabian and Curry, Matthew J. and Terrel, Andy R. and Rou\v{c}ka, \v{S}t\v{e}p\'{a}n and Saboo, Ashutosh and Fernando, Isuru and Kulal, Sumith and Cimrman, Robert and Scopatz, Anthony},
 year = 2017,
 month = jan,
 keywords = {Python, Computer algebra system, Symbolics},
 abstract = {
            SymPy is an open source computer algebra system written in pure Python. It is built with a focus on extensibility and ease of use, through both interactive and programmatic applications. These characteristics have led SymPy to become a popular symbolic library for the scientific Python ecosystem. This paper presents the architecture of SymPy, a description of its features, and a discussion of select submodules. The supplementary material provide additional examples and further outline details of the architecture and features of SymPy.
         },
 volume = 3,
 pages = {e103},
 journal = {PeerJ Computer Science},
 issn = {2376-5992},
 url = {https://doi.org/10.7717/peerj-cs.103},
 doi = {10.7717/peerj-cs.103}
}

@article{peche2006largest,
  title={The largest eigenvalue of small rank perturbations of Hermitian random matrices},
  author={P{\'e}ch{\'e}, Sandrine},
  journal={Probability Theory and Related Fields},
  volume={134},
  number={1},
  pages={127--173},
  year={2006},
  publisher={Springer}
}

@article{capitaine2009largest,
  title={The largest eigenvalues of finite rank deformation of large Wigner matrices: convergence and nonuniversality of the fluctuations},
  author={Capitaine, Mireille and Donati-Martin, Catherine and F{\'e}ral, Delphine},
  journal={The Annals of Probability},
  volume={37},
  number={1},
  pages={1--47},
  year={2009},
  publisher={Institute of Mathematical Statistics}
}


@article{hitchcock1927expression,
  title={The expression of a tensor or a polyadic as a sum of products},
  author={Hitchcock, Frank L},
  journal={Journal of Mathematics and Physics},
  volume={6},
  number={1-4},
  pages={164--189},
  year={1927},
  publisher={Wiley Online Library}
}

@article{landsberg2012tensors,
  title={Tensors: geometry and applications},
  author={Landsberg, Joseph M},
  journal={Representation theory},
  volume={381},
  number={402},
  pages={3},
  year={2012}
}

@article{montanari2014statistical,
  title={A statistical model for tensor {PCA}},
  author={Montanari, Andrea and Richard, Emile},
  journal={arXiv preprint arXiv:1411.1076},
  year={2014}
}

@article{jagannath2020statistical,
  title={Statistical thresholds for tensor {PCA}},
  author={Jagannath, Aukosh and Lopatto, Patrick and Miolane, Leo},
  journal={The Annals of Applied Probability},
  volume={30},
  number={4},
  pages={1910--1933},
  year={2020},
  publisher={Institute of Mathematical Statistics}
}

@phdthesis{handschy2019phase,
  title={Phase Transition in Random Tensors with Multiple Spikes},
  author={Handschy, Madeline Curtis},
  year={2019},
  school={University of Minnesota}
}

@inproceedings{lesieur2017statistical,
  title={Statistical and computational phase transitions in spiked tensor estimation},
  author={Lesieur, Thibault and Miolane, L{\'e}o and Lelarge, Marc and Krzakala, Florent and Zdeborov{\'a}, Lenka},
  booktitle={Proc. IEEE International Symposium on Information Theory (ISIT)},
  pages={511--515},
  year={2017}
}

@inproceedings{perry2020statistical,
  title={Statistical limits of spiked tensor models},
  author={Perry, Amelia and Wein, Alexander S and Bandeira, Afonso S},
  booktitle={Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques},
  volume={56},
  number={1},
  pages={230--264},
  year={2020},
  organization={Institut Henri Poincar{\'e}}
}

@article{de2021random,
  title={A Random Matrix Perspective on Random Tensors},
  author={Goulart, Jos{\'e} Henrique and Couillet, Romain and Comon, Pierre},
  journal={stat},
  volume={1050},
  pages={2},
  year={2021}
}

@article{anandkumar2014tensor,
  title={Tensor decompositions for learning latent variable models},
  author={Anandkumar, Animashree and Ge, Rong and Hsu, Daniel and Kakade, Sham M and Telgarsky, Matus},
  journal={Journal of machine learning research},
  volume={15},
  pages={2773--2832},
  year={2014},
  publisher={Journal of Machine Learning Research}
}

@article{stein1981estimation,
  title={Estimation of the mean of a multivariate normal distribution},
  author={Stein, Charles M},
  journal={The annals of Statistics},
  pages={1135--1151},
  year={1981},
  publisher={JSTOR}
}

@article{hachem2007deterministic,
  title={Deterministic equivalents for certain functionals of large random matrices},
  author={Hachem, Walid and Loubaton, Philippe and Najim, Jamal},
  journal={The Annals of Applied Probability},
  volume={17},
  number={3},
  pages={875--930},
  year={2007},
  publisher={Institute of Mathematical Statistics}
}

@book{tao2012topics,
  title={Topics in random matrix theory},
  author={Tao, Terence},
  volume={132},
  year={2012},
  publisher={American Mathematical Soc.}
}

@book{billingsley2008probability,
  title={Probability and measure},
  author={Billingsley, Patrick},
  year={2008},
  publisher={John Wiley \& Sons}
}

@inproceedings{mignacco2020role,
  title={The role of regularization in classification of high-dimensional noisy gaussian mixture},
  author={Mignacco, Francesca and Krzakala, Florent and Lu, Yue and Urbani, Pierfrancesco and Zdeborova, Lenka},
  booktitle={International conference on machine learning},
  pages={6874--6883},
  year={2020},
  organization={PMLR}
}
