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State-space models (SSMs) that utilize linear, time-invariant (LTI) systems are known for their effectiveness in learning long sequences.
Analytic properties of schmidt pairs for a hankel operator and the generalized schur–takagi problem
Vadim Movsesovich Adamyan, Damir Zyamovich Arov, and Mark Grigor’evich Krein · 1971
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All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ {\infty} -error bounds
Keith Glover · 1984
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Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms
Alan J. Laub, Michaelt Heath, C Paige, and R Ward · 1987
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Kemin Zhou and John Comstock Doyle · 1998
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An introduction to hankel operators
Vladimir Peller · 2003
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Accelerating the nonuniform fast fourier transform
Leslie Greengard and June-Yub Lee · 2004
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Spectral measure of large random Hankel, Markov and Toeplitz matrices
Włodzimierz Bryc, Amir Dembo, and Tiefeng Jiang · 2006
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Learning multiple layers of features from tiny images
Alex Krizhevsky, Geoffrey Hinton, et al · 2009
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Remark on the norm of random hankel matrices
VV Nekrutkin · 2013
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Fast singular value decay for lyapunov solutions with nonnormal coefficients
Jonathan Baker, Mark Embree, and John Sabino · 2015
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Patterned random matrices
Arup Bose · 2018
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Gradient descent learns linear dynamical systems
Moritz Hardt, Tengyu Ma, and Benjamin Recht · 2018
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System identification via cur-factored hankel approximation
Boris Kramer and Alex A Gorodetsky · 2018
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The aaa algorithm for rational approximation
Yuji Nakatsukasa, Olivier Sète, and Lloyd N Trefethen · 2018
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Legendre memory units: Continuous-time representation in recurrent neural networks
Aaron Voelker, Ivana Kajić, and Chris Eliasmith · 2019
Cited alongside, same era.
Hippo: Recurrent memory with optimal polynomial projections
Albert Gu, Tri Dao, Stefano Ermon, Atri Rudra, and Christopher Ré · 2020
Cited alongside, same era.
Implicit self-regularization in deep neural networks: Evidence from random matrix theory and implications for learning
Charles H Martin and Michael W Mahoney · 2021
Cited alongside, same era.
Predicting trends in the quality of state-of-the-art neural networks without access to training or testing data
Charles H Martin, Tongsu Peng, and Michael W Mahoney · 2021
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Long range arena: A benchmark for efficient transformers
Yi Tay, Mostafa Dehghani, Samira Abnar, Yikang Shen, Dara Bahri, Philip Pham, Jinfeng Rao, Liu Yang, Sebastian Ruder, and Donald Metzler · 2021
Cited alongside, same era.
How to train your hippo: State space models with generalized orthogonal basis projections
Albert Gu, Isys Johnson, Aman Timalsina, Atri Rudra, and Christopher Ré · 2023
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Liquid structural state-space models
Ramin Hasani, Mathias Lechner, Tsun-Hsuan Wang, Makram Chahine, Alexander Amini, and Daniela Rus · 2023
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Resurrecting recurrent neural networks for long sequences
Antonio Orvieto, Samuel L. Smith, Albert Gu, Anushan Fernando, Caglar Gulcehre, Razvan Pascanu, and Soham De · 2023
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Simplified state space layers for sequence modeling
Jimmy T.H. Smith, Andrew Warrington, and Scott Linderman · 2023
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Stablessm: Alleviating the curse of memory in state-space models through stable reparameterization
Shida Wang and Qianxiao Li · 2023
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How exponentially ill-conditioned are contiguous submatrices of the fourier matrix?
Alex H Barnett · 2022
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On the parameterization and initialization of diagonal state space models
Albert Gu, Karan Goel, Ankit Gupta, and Christopher Ré · 2022
Cited alongside, same era.
Efficiently modeling long sequences with structured state spaces
Albert Gu, Karan Goel, and Christopher Re · 2022
Cited alongside, same era.
Diagonal state spaces are as effective as structured state spaces
Ankit Gupta, Albert Gu, and Jonathan Berant · 2022
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Naman Agarwal, Daniel Suo, Xinyi Chen, and Elad Hazan · 2023
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Quirin Aumann and Ion Victor Gosea · 2023
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On trigonometric interpolation in an even number of points
Anthony P Austin · 2023
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On the stability of unevenly spaced samples for interpolation and quadrature
Annan Yu and Alex Townsend · 2023
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From generalization analysis to optimization designs for state space models
Fusheng Liu and Qianxiao Li · 2024
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Universality of linear recurrences followed by non-linear projections: Finite-width guarantees and benefits of complex eigenvalues
Antonio Orvieto, Soham De, Caglar Gulcehre, Razvan Pascanu, and Samuel L Smith · 2024
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S4++: Elevating long sequence modeling with state memory reply
Biqing Qi, Junqi Gao, Dong Li, Kaiyan Zhang, Jianxing Liu, Ligang Wu, and Bowen Zhou · 2024
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State-space models with layer-wise nonlinearity are universal approximators with exponential decaying memory
Shida Wang and Beichen Xue · 2024
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A superfast direct inversion method for the nonuniform discrete fourier transform
Heather Wilber, Ethan N Epperly, and Alex H Barnett · 2024
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Robustifying state-space models for long sequences via approximate diagonalization
Annan Yu, Arnur Nigmetov, Dmitriy Morozov, Michael W. Mahoney, and N. Benjamin Erichson · 2024
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Leveraging the hankel norm approximation and data-driven algorithms in reduced order modeling
Annan Yu and Alex Townsend · 2024
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