---
references:
- id: ArjovskyUnitary2016
  author:
    - family: Arjovsky
      given: Martin
    - family: Shah
      given: Amar
    - family: Bengio
      given: Yoshua
  citation-key: ArjovskyUnitary2016
  collection-title: ICML'16
  container-title: >-
    Proceedings of the 33rd International Conference on International Conference
    on Machine Learning - Volume 48
  event-place: New York, NY, USA
  event-title: International Conference on Machine Learning
  issued:
    - year: 2016
      month: 6
      day: 11
  language: en
  page: 1120-1128
  publisher: JMLR.org
  publisher-place: New York, NY, USA
  title: Unitary Evolution Recurrent Neural Networks
  type: paper-conference
  URL: http://arxiv.org/abs/1511.06464

- id: AtalHistory2006
  author:
    - family: Atal
      given: B. S.
  citation-key: AtalHistory2006
  container-title: IEEE Signal Processing Magazine
  DOI: 10.1109/MSP.2006.1598091
  ISSN: 1053-5888
  issue: '2'
  issued:
    - year: 2006
      month: 3
  page: 154-161
  title: The history of linear prediction
  type: article-journal
  URL: >-
    http://www.uncini.com/dida/aacp/dida_mat/2006_Atal_The%20history%20of%20linear%20prediction.pdf
  volume: '23'

- id: BengioLearning1994
  author:
    - family: Bengio
      given: Y.
    - family: Simard
      given: P.
    - family: Frasconi
      given: P.
  citation-key: BengioLearning1994
  container-title: IEEE Transactions on Neural Networks
  DOI: 10.1109/72.279181
  ISSN: 1045-9227
  issue: '2'
  issued:
    - year: 1994
      month: 3
  page: 157-166
  title: Learning long-term dependencies with gradient descent is difficult
  type: article-journal
  URL: http://dsii.dsi.unifi.it/~paolo/ps/tnn-94-gradient.pdf
  volume: '5'

- id: BenTaiebBias2016
  author:
    - family: Ben Taieb
      given: Souhaib
    - family: Atiya
      given: Amir F.
  citation-key: BenTaiebBias2016
  container-title: IEEE transactions on neural networks and learning systems
  container-title-short: IEEE Trans Neural Netw Learn Syst
  DOI: 10.1109/TNNLS.2015.2411629
  ISSN: 2162-2388
  issue: '1'
  issued:
    - year: 2016
      month: 1
  language: eng
  page: 62-76
  PMID: '25807572'
  title: A Bias and Variance Analysis for Multistep-Ahead Time Series Forecasting
  type: article-journal
  volume: '27'

- id: BordesSGDQN2009
  accessed:
    - year: 2015
      month: 6
      day: 18
  author:
    - family: Bordes
      given: Antoine
    - family: Bottou
      given: Léon
    - family: Gallinari
      given: Patrick
  citation-key: BordesSGDQN2009
  container-title: Journal of Machine Learning Research
  ISSN: 1532-4435
  issued:
    - year: 2009
      month: 12
  page: 1737–1754
  title: 'SGD-QN: Careful Quasi-Newton Stochastic Gradient Descent'
  type: article-journal
  URL: http://jmlr.org/papers/volume10/bordes09a/bordes09a.pdf
  volume: '10'

- id: CaiMambaTS2024
  accessed:
    - year: 2024
      month: 6
      day: 5
  author:
    - family: Cai
      given: Xiuding
    - family: Zhu
      given: Yaoyao
    - family: Wang
      given: Xueyao
    - family: Yao
      given: Yu
  citation-key: CaiMambaTS2024
  issued:
    - year: 2024
      month: 5
      day: 26
  language: en
  number: arXiv:2405.16440
  publisher: arXiv
  title: >-
    MambaTS: Improved Selective State Space Models for Long-term Time Series
    Forecasting
  type: article
  URL: http://arxiv.org/abs/2405.16440

- id: CakirFilterbank2016
  accessed:
    - year: 2017
      month: 4
      day: 10
  author:
    - family: Cakir
      given: Emre
    - family: Ozan
      given: Ezgi Can
    - family: Virtanen
      given: Tuomas
  citation-key: CakirFilterbank2016
  container-title: Neural Networks (IJCNN), 2016 International Joint Conference on
  issued:
    - year: 2016
  page: 3399–3406
  publisher: IEEE
  title: >-
    Filterbank learning for deep neural network based polyphonic sound event
    detection
  type: paper-conference
  URL: http://ieeexplore.ieee.org/abstract/document/7727634/

- id: ChangAntisymmetricRNN2019
  accessed:
    - year: 2019
      month: 3
      day: 20
  author:
    - family: Chang
      given: Bo
    - family: Chen
      given: Minmin
    - family: Haber
      given: Eldad
    - family: Chi
      given: Ed H.
  citation-key: ChangAntisymmetricRNN2019
  container-title: Proceedings of ICLR
  event-title: Seventh International Conference on Learning Representations
  issued:
    - year: 2019
      month: 2
      day: 25
  title: 'AntisymmetricRNN: A Dynamical System View on Recurrent Neural Networks'
  type: paper-conference
  URL: http://arxiv.org/abs/1902.09689

- id: ChangMultilevel2018
  accessed:
    - year: 2018
      month: 4
      day: 23
  author:
    - family: Chang
      given: Bo
    - family: Meng
      given: Lili
    - family: Haber
      given: Eldad
    - family: Tung
      given: Frederick
    - family: Begert
      given: David
  citation-key: ChangMultilevel2018
  container-title: PRoceedings of ICLR
  event-title: ICLR
  issued:
    - year: 2018
  title: Multi-level Residual Networks from Dynamical Systems View
  type: paper-conference
  URL: http://arxiv.org/abs/1710.10348

- id: ChangReversible2018
  accessed:
    - year: 2018
      month: 4
      day: 23
  author:
    - family: Chang
      given: Bo
    - family: Meng
      given: Lili
    - family: Haber
      given: Eldad
    - family: Ruthotto
      given: Lars
    - family: Begert
      given: David
    - family: Holtham
      given: Elliot
  citation-key: ChangReversible2018
  container-title: arXiv:1709.03698 [cs, stat]
  event-title: AAAI
  issued:
    - year: 2018
  title: Reversible Architectures for Arbitrarily Deep Residual Neural Networks
  type: paper-conference
  URL: http://arxiv.org/abs/1709.03698

- id: ChungHierarchical2016
  author:
    - family: Chung
      given: Junyoung
    - family: Ahn
      given: Sungjin
    - family: Bengio
      given: Yoshua
  citation-key: ChungHierarchical2016
  container-title: arXiv:1609.01704 [cs]
  issued:
    - year: 2016
      month: 9
      day: 6
  title: Hierarchical Multiscale Recurrent Neural Networks
  type: article-journal
  URL: http://arxiv.org/abs/1609.01704

- id: ChungRecurrent2015
  author:
    - family: Chung
      given: Junyoung
    - family: Kastner
      given: Kyle
    - family: Dinh
      given: Laurent
    - family: Goel
      given: Kratarth
    - family: Courville
      given: Aaron C
    - family: Bengio
      given: Yoshua
  citation-key: ChungRecurrent2015
  container-title: Advances in Neural Information Processing Systems 28
  editor:
    - family: Cortes
      given: C.
    - family: Lawrence
      given: N. D.
    - family: Lee
      given: D. D.
    - family: Sugiyama
      given: M.
    - family: Garnett
      given: R.
  issued:
    - year: 2015
  page: 2980–2988
  publisher: Curran Associates, Inc.
  title: A Recurrent Latent Variable Model for Sequential Data
  type: paper-conference
  URL: >-
    http://papers.nips.cc/paper/5653-a-recurrent-latent-variable-model-for-sequential-data.pdf

- id: CollinsCapacity2016
  author:
    - family: Collins
      given: Jasmine
    - family: Sohl-Dickstein
      given: Jascha
    - family: Sussillo
      given: David
  citation-key: CollinsCapacity2016
  container-title: arXiv:1611.09913 [cs, stat]
  issued:
    - year: 2016
      month: 11
      day: 29
  title: Capacity and Trainability in Recurrent Neural Networks
  type: paper-conference
  URL: http://arxiv.org/abs/1611.09913

- id: CooijmansRecurrent2016
  accessed:
    - year: 2017
      month: 10
      day: 6
  author:
    - family: Cooijmans
      given: Tim
    - family: Ballas
      given: Nicolas
    - family: Laurent
      given: César
    - family: Gülçehre
      given: Çağlar
    - family: Courville
      given: Aaron
  citation-key: CooijmansRecurrent2016
  container-title: arXiv preprint arXiv:1603.09025
  issued:
    - year: 2016
  title: Recurrent batch normalization
  type: article-journal
  URL: https://arxiv.org/abs/1603.09025

- id: DaiReexamination2019
  accessed:
    - year: 2019
      month: 3
      day: 4
  author:
    - family: Dai
      given: Zihang
    - family: Lai
      given: Guokun
    - family: Yang
      given: Yiming
    - family: Yoo
      given: Shinjae
  citation-key: DaiReexamination2019
  container-title: arXiv:1902.01388 [cs, stat]
  issued:
    - year: 2019
      month: 2
      day: 4
  title: Re-examination of the Role of Latent Variables in Sequence Modeling
  type: article-journal
  URL: http://arxiv.org/abs/1902.01388

- id: DoucetSequential2001
  accessed:
    - year: 2017
      month: 9
      day: 1
  author:
    - family: Doucet
      given: Arnaud
    - family: Freitas
      given: Nando
    - family: Gordon
      given: Neil
  citation-key: DoucetSequential2001
  event-place: New York, NY
  ISBN: 978-1-4757-3437-9
  issued:
    - year: 2001
  language: English
  publisher: Springer New York
  publisher-place: New York, NY
  title: Sequential Monte Carlo Methods in Practice
  type: book
  URL: http://public.eblib.com/choice/publicfullrecord.aspx?p=3087052

- id: FengWere2024
  accessed:
    - year: 2024
      month: 10
      day: 6
  author:
    - family: Feng
      given: Leo
    - family: Tung
      given: Frederick
    - family: Ahmed
      given: Mohamed Osama
    - family: Bengio
      given: Yoshua
    - family: Hajimirsadegh
      given: Hossein
  citation-key: FengWere2024
  issued:
    - year: 2024
      month: 10
      day: 2
  language: en
  title: Were RNNs All We Needed?
  type: article
  URL: https://arxiv.org/abs/2410.01201v1

- id: FraccaroSequential2016
  accessed:
    - year: 2016
      month: 12
      day: 7
  author:
    - family: Fraccaro
      given: Marco
    - family: Sø nderby
      given: Sø ren Kaae
    - family: Paquet
      given: Ulrich
    - family: Winther
      given: Ole
  citation-key: FraccaroSequential2016
  container-title: Advances in Neural Information Processing Systems 29
  editor:
    - family: Lee
      given: D. D.
    - family: Sugiyama
      given: M.
    - family: Luxburg
      given: U. V.
    - family: Guyon
      given: I.
    - family: Garnett
      given: R.
  issued:
    - year: 2016
  page: 2199–2207
  publisher: Curran Associates, Inc.
  title: Sequential Neural Models with Stochastic Layers
  type: paper-conference
  URL: >-
    http://papers.nips.cc/paper/6039-sequential-neural-models-with-stochastic-layers.pdf

- id: GoodwinMatching1999
  author:
    - family: Goodwin
      given: M M
    - family: Vetterli
      given: M
  citation-key: GoodwinMatching1999
  container-title: IEEE Transactions on Signal Processing
  DOI: 10.1109/78.771038
  ISSN: 1053-587X
  issue: '7'
  issued:
    - year: 1999
      month: 7
  number: '7'
  page: 1890-1902
  title: Matching pursuit and atomic signal models based on recursive filter banks
  type: article-journal
  URL: >-
    https://www.researchgate.net/profile/Michael_Goodwin4/publication/3317287_Matching_pursuit_and_atomic_signal_models_based_on_recursive_filter_banks/links/543416db0cf2dc341daf33ed.pdf
  volume: '47'

- id: GrosseShiftInvariant2007
  accessed:
    - year: 2016
      month: 3
      day: 28
  author:
    - family: Grosse
      given: Roger
    - family: Raina
      given: Rajat
    - family: Kwong
      given: Helen
    - family: Ng
      given: Andrew Y.
  citation-key: GrosseShiftInvariant2007
  container-title: >-
    The Twenty-Third Conference on Uncertainty in Artificial Intelligence
    (UAI2007)
  event-title: >-
    Proceedings of the Twenty-Third Conference on Uncertainty in Artificial
    Intelligence (UAI2007)
  issued:
    - year: 2007
  page: '8'
  title: Shift-Invariant Sparse Coding for Audio Classification
  type: paper-conference
  URL: http://arxiv.org/abs/1206.5241
  volume: '9'

- id: GuCombining2021
  accessed:
    - year: 2022
      month: 8
      day: 6
  author:
    - family: Gu
      given: Albert
    - family: Johnson
      given: Isys
    - family: Goel
      given: Karan
    - family: Saab
      given: Khaled
    - family: Dao
      given: Tri
    - family: Rudra
      given: Atri
    - family: Ré
      given: Christopher
  citation-key: GuCombining2021
  container-title: Advances in Neural Information Processing Systems
  DOI: 10.48550/arXiv.2110.13985
  event-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2021
  page: 572–585
  publisher: Curran Associates, Inc.
  title: >-
    Combining Recurrent, Convolutional, and Continuous-time Models with Linear
    State Space Layers
  type: paper-conference
  URL: http://arxiv.org/abs/2110.13985
  volume: '34'

- id: GuEfficiently2021
  accessed:
    - year: 2023
      month: 5
      day: 22
  author:
    - family: Gu
      given: Albert
    - family: Goel
      given: Karan
    - family: Ré
      given: Christopher
  citation-key: GuEfficiently2021
  issued:
    - year: 2021
      month: 10
      day: 31
  language: en
  title: Efficiently Modeling Long Sequences with Structured State Spaces
  type: article
  URL: https://arxiv.org/abs/2111.00396v3

- id: GuMamba2023
  accessed:
    - year: 2024
      month: 3
      day: 5
  author:
    - family: Gu
      given: Albert
    - family: Dao
      given: Tri
  citation-key: GuMamba2023
  DOI: 10.48550/arXiv.2312.00752
  issued:
    - year: 2023
      month: 12
      day: 1
  number: arXiv:2312.00752
  publisher: arXiv
  title: 'Mamba: Linear-Time Sequence Modeling with Selective State Spaces'
  type: article
  URL: http://arxiv.org/abs/2312.00752

- id: HaberStable2018
  author:
    - family: Haber
      given: Eldad
    - family: Ruthotto
      given: Lars
  citation-key: HaberStable2018
  container-title: Inverse Problems
  container-title-short: Inverse Problems
  DOI: 10.1088/1361-6420/aa9a90
  ISSN: 0266-5611
  issue: '1'
  issued:
    - year: 2018
  language: en
  page: '014004'
  title: Stable architectures for deep neural networks
  type: article-journal
  URL: http://arxiv.org/abs/1705.03341
  volume: '34'

- id: HardtGradient2018
  author:
    - family: Hardt
      given: Moritz
    - family: Ma
      given: Tengyu
    - family: Recht
      given: Benjamin
  citation-key: HardtGradient2018
  container-title: The Journal of Machine Learning Research
  container-title-short: J. Mach. Learn. Res.
  ISSN: 1532-4435
  issue: '1'
  issued:
    - year: 2018
      month: 1
      day: 1
  page: 1025–1068
  title: Gradient descent learns linear dynamical systems
  type: article-journal
  URL: http://arxiv.org/abs/1609.05191
  volume: '19'

- id: HaykinKalman2001
  call-number: QA76.87 .K35 2001
  citation-key: HaykinKalman2001
  collection-title: >-
    Adaptive and learning systems for signal processing, communications, and
    control
  editor:
    - family: Haykin
      given: Simon S.
  event-place: New York
  ISBN: 978-0-471-36998-1
  issued:
    - year: 2001
  number-of-pages: '284'
  publisher: Wiley
  publisher-place: New York
  title: Kalman filtering and neural networks
  type: book
  URL: >-
    http://booksbw.com/books/mathematical/hayking-s/2001/files/kalmanfilteringneuralnetworks2001.pdf

- id: HazanLearning2017
  author:
    - family: Hazan
      given: Elad
    - family: Singh
      given: Karan
    - family: Zhang
      given: Cyril
  citation-key: HazanLearning2017
  container-title: NIPS
  issued:
    - year: 2017
  title: Learning Linear Dynamical Systems via Spectral Filtering
  type: paper-conference
  URL: http://arxiv.org/abs/1711.00946

- id: HeapsEnforcing2020
  accessed:
    - year: 2021
      month: 2
      day: 15
  author:
    - family: Heaps
      given: Sarah E.
  citation-key: HeapsEnforcing2020
  container-title: arXiv:2004.09455 [stat]
  issued:
    - year: 2020
      month: 4
      day: 20
  title: Enforcing stationarity through the prior in vector autoregressions
  type: article-journal
  URL: http://arxiv.org/abs/2004.09455

- id: HochreiterGradient2001
  author:
    - family: Hochreiter
      given: Sepp
    - family: Bengio
      given: Yoshua
    - family: Frasconi
      given: Paolo
    - family: Schmidhuber
      given: Jürgen
  citation-key: HochreiterGradient2001
  container-title: A field guide to dynamical recurrent neural networks
  issued:
    - year: 2001
  publisher: IEEE Press
  title: >-
    Gradient Flow in Recurrent Nets: the Difficulty of Learning Long-Term
    Dependencies
  type: chapter
  URL: http://www.bioinf.jku.at/publications/older/ch7.pdf

- id: HochreiterLong1997
  accessed:
    - year: 2016
      month: 3
      day: 30
  author:
    - family: Hochreiter
      given: Sepp
    - family: Schmidhuber
      given: Jürgen
  citation-key: HochreiterLong1997
  container-title: Neural Computation
  container-title-short: Neural Computation
  DOI: 10.1162/neco.1997.9.8.1735
  ISSN: 0899-7667
  issue: '8'
  issued:
    - year: 1997
      month: 11
      day: 1
  page: 1735-1780
  title: Long Short-Term Memory
  type: article-journal
  URL: >-
    http://didawiki.di.unipi.it/lib/exe/fetch.php/magistraleinformatica/aa2/lstm.pdf
  volume: '9'

- id: HochreiterVanishing1998
  accessed:
    - year: 2017
      month: 7
      day: 24
  author:
    - family: Hochreiter
      given: Sepp
  citation-key: HochreiterVanishing1998
  container-title: International Journal of Uncertainty Fuzziness and Knowledge Based Systems
  DOI: 10.1142/S0218488598000094
  issued:
    - year: 1998
  page: 107–115
  title: >-
    The vanishing gradient problem during learning recurrent neural nets and
    problem solutions
  type: article-journal
  volume: '6'

- id: HurzelerApproximating2001
  accessed:
    - year: 2017
      month: 8
      day: 30
  author:
    - family: Hürzeler
      given: Markus
    - family: Künsch
      given: Hans R.
  citation-key: HurzelerApproximating2001
  collection-title: Statistics for Engineering and Information Science
  container-title: Sequential Monte Carlo Methods in Practice
  DOI: 10.1007/978-1-4757-3437-9_8
  ISBN: 978-1-4419-2887-0
  issued:
    - year: 2001
  language: en
  page: 159-175
  publisher: Springer, New York, NY
  title: Approximating and Maximising the Likelihood for a General State-Space Model
  type: chapter
  URL: http://www.umiacs.umd.edu/users/aravinds/documents/fall02enee698a.pdf

- id: HuZigMa2024
  accessed:
    - year: 2024
      month: 6
      day: 5
  author:
    - family: Hu
      given: Vincent Tao
    - family: Baumann
      given: Stefan Andreas
    - family: Gui
      given: Ming
    - family: Grebenkova
      given: Olga
    - family: Ma
      given: Pingchuan
    - family: Fischer
      given: Johannes
    - family: Ommer
      given: Björn
  citation-key: HuZigMa2024
  issued:
    - year: 2024
      month: 4
      day: 1
  language: en
  number: arXiv:2403.13802
  publisher: arXiv
  title: 'ZigMa: A DiT-style Zigzag Mamba Diffusion Model'
  type: article
  URL: http://arxiv.org/abs/2403.13802

- id: IonidesInference2006
  accessed:
    - year: 2014
      month: 2
      day: 20
  author:
    - family: Ionides
      given: E. L.
    - family: Bretó
      given: C.
    - family: King
      given: A. A.
  citation-key: IonidesInference2006
  container-title: Proceedings of the National Academy of Sciences
  container-title-short: PNAS
  DOI: 10.1073/pnas.0603181103
  ISSN: 0027-8424, 1091-6490
  issue: '49'
  issued:
    - year: 2006
      month: 5
      day: 12
  language: en
  page: 18438-18443
  PMID: '17121996'
  title: Inference for nonlinear dynamical systems
  type: article-journal
  volume: '103'

- id: IonidesIterated2011
  accessed:
    - year: 2015
      month: 12
      day: 15
  author:
    - family: Ionides
      given: Edward L.
    - family: Bhadra
      given: Anindya
    - family: Atchadé
      given: Yves
    - family: King
      given: Aaron
  citation-key: IonidesIterated2011
  container-title: The Annals of Statistics
  DOI: 10.1214/11-AOS886
  ISSN: 0090-5364
  issue: '3'
  issued:
    - year: 2011
      month: 6
  page: 1776-1802
  title: Iterated filtering
  type: article-journal
  URL: http://arxiv.org/abs/0902.0347
  volume: '39'

- id: JaegerTutorial2002
  accessed:
    - year: 2017
      month: 10
      day: 6
  author:
    - family: Jaeger
      given: Herbert
  citation-key: JaegerTutorial2002
  issued:
    - year: 2002
  publisher: GMD-Forschungszentrum Informationstechnik
  title: >-
    Tutorial on training recurrent neural networks, covering BPPT, RTRL, EKF and
    the" echo state network" approach
  type: book
  URL: >-
    http://minds.jacobs-university.de/sites/default/files/uploads/papers/ESNTutorialRev.pdf
  volume: '5'

- id: JingTunable2017
  author:
    - family: Jing
      given: Li
    - family: Shen
      given: Yichen
    - family: Dubcek
      given: Tena
    - family: Peurifoy
      given: John
    - family: Skirlo
      given: Scott
    - family: LeCun
      given: Yann
    - family: Tegmark
      given: Max
    - family: Soljačić
      given: Marin
  citation-key: JingTunable2017
  container-title: PMLR
  event-title: International Conference on Machine Learning
  issued:
    - year: 2017
      month: 7
      day: 17
  language: en
  page: 1733-1741
  title: >-
    Tunable Efficient Unitary Neural Networks (EUNN) and their application to
    RNNs
  type: paper-conference
  URL: http://proceedings.mlr.press/v70/jing17a.html

- id: KailathLinear1980
  author:
    - family: Kailath
      given: Thomas
  call-number: QA402 .K295 1980
  citation-key: KailathLinear1980
  collection-title: Prentice-Hall information and system science series
  event-place: Englewood Cliffs, N.J
  ISBN: 978-0-13-536961-6
  issued:
    - year: 1980
  number-of-pages: '682'
  publisher: Prentice-Hall
  publisher-place: Englewood Cliffs, N.J
  title: Linear systems
  type: book

- id: KailathLinear2000
  author:
    - family: Kailath
      given: Thomas
    - family: Sayed
      given: Ali H.
    - family: Hassibi
      given: Babak
  call-number: QA276.8 .K33 2000
  citation-key: KailathLinear2000
  collection-title: Prentice Hall information and system sciences series
  event-place: Upper Saddle River, N.J
  ISBN: 978-0-13-022464-4
  issued:
    - year: 2000
  number-of-pages: '854'
  publisher: Prentice Hall
  publisher-place: Upper Saddle River, N.J
  title: Linear estimation
  type: book

- id: KaulLinear2020
  accessed:
    - year: 2020
      month: 12
      day: 13
  author:
    - family: Kaul
      given: Shiva
  citation-key: KaulLinear2020
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2020
  language: en
  title: Linear Dynamical Systems as a Core Computational Primitive
  type: paper-conference
  URL: >-
    https://proceedings.neurips.cc//paper_files/paper/2020/hash/c3581d2150ff68f3b33b22634b8adaea-Abstract.html
  volume: '33'

- id: KingmaImproving2016
  author:
    - family: Kingma
      given: Diederik P.
    - family: Salimans
      given: Tim
    - family: Jozefowicz
      given: Rafal
    - family: Chen
      given: Xi
    - family: Sutskever
      given: Ilya
    - family: Welling
      given: Max
  citation-key: KingmaImproving2016
  container-title: Advances in Neural Information Processing Systems 29
  issued:
    - year: 2016
      month: 6
      day: 15
  publisher: Curran Associates, Inc.
  title: Improving Variational Inference with Inverse Autoregressive Flow
  type: paper-conference
  URL: http://arxiv.org/abs/1606.04934

- id: KolterLearning2019
  author:
    - family: Kolter
      given: J Zico
    - family: Manek
      given: Gaurav
  citation-key: KolterLearning2019
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2019
  language: en
  page: '9'
  title: Learning Stable Deep Dynamics Models
  type: paper-conference
  URL: http://arxiv.org/abs/2001.06116

- id: KrishnamurthyTheory2022
  author:
    - family: Krishnamurthy
      given: Kamesh
    - family: Can
      given: Tankut
    - family: Schwab
      given: David J.
  citation-key: KrishnamurthyTheory2022
  container-title: Physical Review. X
  container-title-short: Phys Rev X
  DOI: 10.1103/physrevx.12.011011
  ISSN: 2160-3308
  issue: '1'
  issued:
    - year: 2022
  language: eng
  page: '011011'
  PMCID: PMC9762509
  PMID: '36545030'
  title: Theory of Gating in Recurrent Neural Networks
  type: article-journal
  URL: http://arxiv.org/abs/2007.14823
  volume: '12'

- id: KrishnanDeep2015
  accessed:
    - year: 2017
      month: 8
      day: 11
  author:
    - family: Krishnan
      given: Rahul G.
    - family: Shalit
      given: Uri
    - family: Sontag
      given: David
  citation-key: KrishnanDeep2015
  container-title: arXiv preprint arXiv:1511.05121
  issued:
    - year: 2015
  title: Deep kalman filters
  type: article-journal
  URL: https://arxiv.org/abs/1511.05121

- id: KrishnanStructured2017
  accessed:
    - year: 2016
      month: 10
      day: 6
  author:
    - family: Krishnan
      given: Rahul G.
    - family: Shalit
      given: Uri
    - family: Sontag
      given: David
  citation-key: KrishnanStructured2017
  container-title: Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence
  event-title: Thirty-First AAAI Conference on Artificial Intelligence
  issued:
    - year: 2017
  page: 2101–2109
  title: Structured Inference Networks for Nonlinear State Space Models
  type: paper-conference
  URL: http://arxiv.org/abs/1609.09869

- id: KutschireiterApproximate2015
  accessed:
    - year: 2017
      month: 1
      day: 10
  author:
    - family: Kutschireiter
      given: Anna
    - family: Surace
      given: Simone C
    - family: Sprekeler
      given: Henning
    - family: Pfister
      given: Jean-Pascal
  citation-key: KutschireiterApproximate2015
  container-title: BMC Neuroscience
  DOI: 10.1186/1471-2202-16-S1-P196
  ISSN: 1471-2202
  issue: Suppl 1
  issued:
    - year: 2015
  language: en
  page: P196
  title: Approximate nonlinear filtering with a recurrent neural network
  type: article-journal
  URL: http://bmcneurosci.biomedcentral.com/articles/10.1186/1471-2202-16-S1-P196
  volume: '16'

- id: KutschireiterNeural2015
  author:
    - family: Kutschireiter
      given: Anna
    - family: Surace
      given: Simone Carlo
    - family: Sprekeler
      given: Henning
    - family: Pfister
      given: Jean-Pascal
  citation-key: KutschireiterNeural2015
  container-title: arXiv preprint arXiv:1508.06818
  issued:
    - year: 2015
  title: A Neural Implementation for Nonlinear Filtering
  type: article-journal

- id: LambProfessor2016
  accessed:
    - year: 2018
      month: 1
      day: 13
  author:
    - family: Lamb
      given: Alex
    - family: Goyal
      given: Anirudh
    - family: Zhang
      given: Ying
    - family: Zhang
      given: Saizheng
    - family: Courville
      given: Aaron
    - family: Bengio
      given: Yoshua
  citation-key: LambProfessor2016
  container-title: Advances In Neural Information Processing Systems
  event-title: NIPS
  issued:
    - year: 2016
      month: 10
      day: 27
  title: 'Professor Forcing: A New Algorithm for Training Recurrent Networks'
  type: paper-conference
  URL: http://arxiv.org/abs/1610.09038

- id: LaurentRecurrent2016
  author:
    - family: Laurent
      given: Thomas
    - family: Brecht
      given: James
      non-dropping-particle: von
  citation-key: LaurentRecurrent2016
  container-title: arXiv:1612.06212 [cs]
  issued:
    - year: 2016
      month: 12
      day: 19
  title: A recurrent neural network without chaos
  type: article-journal
  URL: http://arxiv.org/abs/1612.06212

- id: LiODE2021
  accessed:
    - year: 2024
      month: 7
      day: 22
  author:
    - family: Li
      given: Bei
    - family: Du
      given: Quan
    - family: Zhou
      given: Tao
    - family: Zhou
      given: Shuhan
    - family: Zeng
      given: Xin
    - family: Xiao
      given: Tong
    - family: Zhu
      given: Jingbo
  citation-key: LiODE2021
  DOI: 10.48550/arXiv.2104.02308
  issued:
    - year: 2021
      month: 4
      day: 6
  number: arXiv:2104.02308
  publisher: arXiv
  title: >-
    ODE Transformer: An Ordinary Differential Equation-Inspired Model for Neural
    Machine Translation
  type: article
  URL: http://arxiv.org/abs/2104.02308

- id: LiptonStuck2016
  author:
    - family: Lipton
      given: Zachary C.
  citation-key: LiptonStuck2016
  container-title: arXiv:1602.07320 [cs]
  issued:
    - year: 2016
      month: 2
      day: 23
  title: Stuck in a What? Adventures in Weight Space
  type: article-journal
  URL: http://arxiv.org/abs/1602.07320

- id: LiWhat2022
  accessed:
    - year: 2022
      month: 11
      day: 14
  author:
    - family: Li
      given: Yuhong
    - family: Cai
      given: Tianle
    - family: Zhang
      given: Yi
    - family: Chen
      given: Deming
    - family: Dey
      given: Debadeepta
  citation-key: LiWhat2022
  DOI: 10.48550/arXiv.2210.09298
  issued:
    - year: 2022
      month: 10
      day: 17
  number: arXiv:2210.09298
  publisher: arXiv
  title: What Makes Convolutional Models Great on Long Sequence Modeling?
  type: article
  URL: http://arxiv.org/abs/2210.09298

- id: LjungSystem1999
  author:
    - family: Ljung
      given: Lennart
  call-number: QA402 .L59 1999
  citation-key: LjungSystem1999
  collection-title: Prentice Hall information and system sciences series
  edition: 2nd ed
  event-place: Upper Saddle River, NJ
  ISBN: 978-0-13-656695-3
  issued:
    - year: 1999
  number-of-pages: '609'
  publisher: Prentice Hall PTR
  publisher-place: Upper Saddle River, NJ
  title: 'System identification: theory for the user'
  type: book

- id: LjungTheory1983
  author:
    - family: Ljung
      given: Lennart
    - family: Söderström
      given: Torsten
  call-number: QA402 .L6 1983
  citation-key: LjungTheory1983
  collection-number: '4'
  collection-title: The MIT Press series in signal processing, optimization, and control
  event-place: Cambridge, Mass
  ISBN: 978-0-262-12095-1
  issued:
    - year: 1983
  number-of-pages: '529'
  publisher: MIT Press
  publisher-place: Cambridge, Mass
  title: Theory and practice of recursive identification
  type: book

- id: MacKayReversible2018
  accessed:
    - year: 2019
      month: 1
      day: 14
  author:
    - family: MacKay
      given: Matthew
    - family: Vicol
      given: Paul
    - family: Ba
      given: Jimmy
    - family: Grosse
      given: Roger
  citation-key: MacKayReversible2018
  container-title: Advances In Neural Information Processing Systems
  issued:
    - year: 2018
      month: 10
      day: 25
  title: Reversible Recurrent Neural Networks
  type: paper-conference
  URL: http://arxiv.org/abs/1810.10999

- id: MarelliRecursive2010
  accessed:
    - year: 2018
      month: 4
      day: 20
  author:
    - family: Marelli
      given: D.
    - family: Fu
      given: Minyue
  citation-key: MarelliRecursive2010
  container-title: IEEE Transactions on Signal Processing
  DOI: 10.1109/TSP.2009.2034933
  ISSN: 1053-587X, 1941-0476
  issue: '3'
  issued:
    - year: 2010
      month: 3
  language: en
  page: 1025-1034
  title: >-
    A Recursive Method for the Approximation of LTI Systems Using Subband
    Processing
  type: article-journal
  URL: http://www.eng.newcastle.edu.au/~mf140/home/Papers/LTISystem_TSP.pdf
  volume: '58'

- id: MartensLearning2011
  accessed:
    - year: 2018
      month: 4
      day: 2
  author:
    - family: Martens
      given: James
    - family: Sutskever
      given: Ilya
  citation-key: MartensLearning2011
  collection-title: ICML'11
  container-title: >-
    Proceedings of the 28th International Conference on International Conference
    on Machine Learning
  event-place: USA
  ISBN: 978-1-4503-0619-5
  issued:
    - year: 2011
  page: 1033–1040
  publisher: Omnipress
  publisher-place: USA
  title: Learning Recurrent Neural Networks with Hessian-free Optimization
  type: paper-conference
  URL: http://dl.acm.org/citation.cfm?id=3104482.3104612

- id: MattingleyRealTime2010
  author:
    - family: Mattingley
      given: J.
    - family: Boyd
      given: S.
  citation-key: MattingleyRealTime2010
  container-title: IEEE Signal Processing Magazine
  DOI: 10.1109/MSP.2010.936020
  ISSN: 1053-5888
  issue: '3'
  issued:
    - year: 2010
      month: 5
  page: 50-61
  title: Real-Time Convex Optimization in Signal Processing
  type: article-journal
  URL: https://www.stanford.edu/~boyd/papers/pdf/sig_proc_mag.pdf
  volume: '27'

- id: MegretskiPositivity2003
  author:
    - family: Megretski
      given: A.
  citation-key: MegretskiPositivity2003
  container-title: >-
    42nd IEEE International Conference on Decision and Control (IEEE Cat.
    No.03CH37475)
  DOI: 10.1109/CDC.2003.1271743
  event-title: >-
    42nd IEEE International Conference on Decision and Control (IEEE Cat.
    No.03CH37475)
  issued:
    - year: 2003
      month: 12
  page: 3814-3817 vol.4
  title: Positivity of trigonometric polynomials
  type: paper-conference
  volume: '4'

- id: MehriSampleRNN2017
  author:
    - family: Mehri
      given: Soroush
    - family: Kumar
      given: Kundan
    - family: Gulrajani
      given: Ishaan
    - family: Kumar
      given: Rithesh
    - family: Jain
      given: Shubham
    - family: Sotelo
      given: Jose
    - family: Courville
      given: Aaron
    - family: Bengio
      given: Yoshua
  citation-key: MehriSampleRNN2017
  container-title: >-
    Proceedings of International Conference on Learning Representations (ICLR)
    2017
  event-title: International Conference on Learning Representations (ICLR) 2017
  issued:
    - year: 2017
  title: 'SampleRNN: An Unconditional End-to-End Neural Audio Generation Model'
  type: paper-conference
  URL: http://arxiv.org/abs/1612.07837

- id: MhammediEfficient2017
  author:
    - family: Mhammedi
      given: Zakaria
    - family: Hellicar
      given: Andrew
    - family: Rahman
      given: Ashfaqur
    - family: Bailey
      given: James
  citation-key: MhammediEfficient2017
  container-title: PMLR
  event-title: International Conference on Machine Learning
  issued:
    - year: 2017
      month: 7
      day: 17
  language: en
  page: 2401-2409
  title: >-
    Efficient Orthogonal Parametrisation of Recurrent Neural Networks Using
    Householder Reflections
  type: paper-conference
  URL: http://proceedings.mlr.press/v70/mhammedi17a.html

- id: MillerWhen2018
  accessed:
    - year: 2018
      month: 8
      day: 6
  author:
    - family: Miller
      given: John
    - family: Hardt
      given: Moritz
  citation-key: MillerWhen2018
  container-title: arXiv:1805.10369 [cs, stat]
  issued:
    - year: 2018
      month: 5
      day: 25
  title: When Recurrent Models Don't Need To Be Recurrent
  type: article-journal
  URL: http://arxiv.org/abs/1805.10369

- id: MoradkhaniDual2005
  accessed:
    - year: 2017
      month: 8
      day: 30
  author:
    - family: Moradkhani
      given: Hamid
    - family: Sorooshian
      given: Soroosh
    - family: Gupta
      given: Hoshin V.
    - family: Houser
      given: Paul R.
  citation-key: MoradkhaniDual2005
  container-title: Advances in Water Resources
  container-title-short: Advances in Water Resources
  DOI: 10.1016/j.advwatres.2004.09.002
  ISSN: 0309-1708
  issue: '2'
  issued:
    - year: 2005
      month: 2
      day: 1
  page: 135-147
  title: >-
    Dual state–parameter estimation of hydrological models using ensemble Kalman
    filter
  type: article-journal
  URL: http://prhouser.com/houser_files/DualStateParamaterEstimation.pdf
  volume: '28'

- id: NerrandNeural1993
  author:
    - family: Nerrand
      given: O.
    - family: Roussel-Ragot
      given: P.
    - family: Personnaz
      given: L.
    - family: Dreyfus
      given: G.
    - family: Marcos
      given: S.
  citation-key: NerrandNeural1993
  container-title: Neural Computation
  DOI: 10.1162/neco.1993.5.2.165
  ISSN: 0899-7667
  issue: '2'
  issued:
    - year: 1993
      month: 3
  page: 165-199
  title: >-
    Neural Networks and Nonlinear Adaptive Filtering: Unifying Concepts and New
    Algorithms
  type: article-journal
  URL: https://www.neurones.espci.fr/Articles_PS/NeuralComp_Filtrage.pdf
  volume: '5'

- id: NishikawaState2024
  accessed:
    - year: 2024
      month: 5
      day: 30
  author:
    - family: Nishikawa
      given: Naoki
    - family: Suzuki
      given: Taiji
  citation-key: NishikawaState2024
  issued:
    - year: 2024
      month: 5
      day: 29
  number: arXiv:2405.19036
  publisher: arXiv
  title: >-
    State Space Models are Comparable to Transformers in Estimating Functions
    with Dynamic Smoothness
  type: article
  URL: http://arxiv.org/abs/2405.19036

- id: OliveiraStability2001
  accessed:
    - year: 2018
      month: 3
      day: 23
  author:
    - family: Oliveira
      given: Maurício C.
      dropping-particle: de
    - family: Skelton
      given: Robert E.
  citation-key: OliveiraStability2001
  collection-title: Lecture Notes in Control and Information Sciences
  container-title: Perspectives in robust control
  DOI: 10.1007/BFb0110624
  ISBN: 978-1-85233-452-9 978-1-84628-576-9
  issued:
    - year: 2001
  language: en
  page: 241-257
  publisher: Springer, London
  title: Stability tests for constrained linear systems
  type: chapter

- id: PatroSiMBA2024
  accessed:
    - year: 2024
      month: 6
      day: 5
  author:
    - family: Patro
      given: Badri N.
    - family: Agneeswaran
      given: Vijay S.
  citation-key: PatroSiMBA2024
  issued:
    - year: 2024
      month: 4
      day: 24
  language: en
  number: arXiv:2403.15360
  publisher: arXiv
  title: >-
    SiMBA: Simplified Mamba-Based Architecture for Vision and Multivariate Time
    series
  type: article
  URL: http://arxiv.org/abs/2403.15360

- id: RobertsHierarchical2018
  accessed:
    - year: 2018
      month: 3
      day: 21
  author:
    - family: Roberts
      given: Adam
    - family: Engel
      given: Jesse
    - family: Raffel
      given: Colin
    - family: Hawthorne
      given: Curtis
    - family: Eck
      given: Douglas
  citation-key: RobertsHierarchical2018
  container-title: arXiv:1803.05428 [cs, eess, stat]
  issued:
    - year: 2018
      month: 3
      day: 13
  title: A Hierarchical Latent Vector Model for Learning Long-Term Structure in Music
  type: article-journal
  URL: http://arxiv.org/abs/1803.05428

- id: RouttenbergBlind2010
  accessed:
    - year: 2016
      month: 4
      day: 14
  author:
    - family: Routtenberg
      given: Tirza
    - family: Tabrikian
      given: Joseph
  citation-key: RouttenbergBlind2010
  container-title: IEEE Transactions on Signal Processing
  DOI: 10.1109/TSP.2009.2036043
  ISSN: 1053-587X
  issue: '3'
  issued:
    - year: 2010
      month: 3
  page: 990–1000
  title: >-
    Blind MIMO-AR System Identification and Source Separation with
    Finite-alphabet
  type: article-journal
  volume: '58'

- id: SeuretWirtingerbased2013
  accessed:
    - year: 2019
      month: 5
      day: 21
  author:
    - family: Seuret
      given: Alexandre
    - family: Gouaisbaut
      given: Frédéric
  citation-key: SeuretWirtingerbased2013
  container-title: Automatica
  issue: '9'
  issued:
    - year: 2013
      month: 9
  page: 2860-2866
  title: 'Wirtinger-based integral inequality: Application to time-delay systems'
  type: article-journal
  URL: https://hal.archives-ouvertes.fr/hal-00855159
  volume: '49'

- id: SimchowitzLearning2019
  accessed:
    - year: 2019
      month: 4
      day: 8
  author:
    - family: Simchowitz
      given: Max
    - family: Boczar
      given: Ross
    - family: Recht
      given: Benjamin
  citation-key: SimchowitzLearning2019
  container-title: arXiv:1902.00768 [cs, math, stat]
  issued:
    - year: 2019
      month: 2
      day: 2
  title: Learning Linear Dynamical Systems with Semi-Parametric Least Squares
  type: article-journal
  URL: http://arxiv.org/abs/1902.00768

- id: SjobergNonlinear1995
  accessed:
    - year: 2017
      month: 9
      day: 19
  author:
    - family: Sjöberg
      given: Jonas
    - family: Zhang
      given: Qinghua
    - family: Ljung
      given: Lennart
    - family: Benveniste
      given: Albert
    - family: Delyon
      given: Bernard
    - family: Glorennec
      given: Pierre-Yves
    - family: Hjalmarsson
      given: Håkan
    - family: Juditsky
      given: Anatoli
  citation-key: SjobergNonlinear1995
  collection-title: Trends in System Identification
  container-title: Automatica
  container-title-short: Automatica
  DOI: 10.1016/0005-1098(95)00120-8
  ISSN: 0005-1098
  issue: '12'
  issued:
    - year: 1995
      month: 12
      day: 1
  page: 1691-1724
  title: 'Nonlinear black-box modeling in system identification: a unified overview'
  type: article-journal
  URL: http://www.diva-portal.org/smash/get/diva2:315882/FULLTEXT02.pdf
  volume: '31'

- id: SmithDisentangling2000
  author:
    - family: Smith
      given: Leonard A
  citation-key: SmithDisentangling2000
  container-title: Nonlinear Dynamics and Statistics
  contributor:
    - family: Mees
      given: Alistair I
  issued:
    - year: 2000
  title: >-
    Disentangling Uncertainty and Error: On the predictability of nonlinear
    systems
  type: chapter

- id: SoderstromSystem1988
  citation-key: SoderstromSystem1988
  editor:
    - family: Söderström
      given: T.
    - family: Stoica
      given: P.
  event-place: Upper Saddle River, NJ, USA
  ISBN: 978-0-13-881236-2
  issued:
    - year: 1988
  publisher: Prentice-Hall, Inc.
  publisher-place: Upper Saddle River, NJ, USA
  title: System Identification
  type: book

- id: StepletonLowpass2018
  accessed:
    - year: 2018
      month: 5
      day: 24
  author:
    - family: Stepleton
      given: Thomas
    - family: Pascanu
      given: Razvan
    - family: Dabney
      given: Will
    - family: Jayakumar
      given: Siddhant M.
    - family: Soyer
      given: Hubert
    - family: Munos
      given: Remi
  citation-key: StepletonLowpass2018
  container-title: arXiv:1805.04955 [cs, stat]
  issued:
    - year: 2018
      month: 5
      day: 13
  title: >-
    Low-pass Recurrent Neural Networks - A memory architecture for longer-term
    correlation discovery
  type: article-journal
  URL: https://arxiv.org/abs/1805.04955v1

- id: SutskeverTraining2013
  author:
    - family: Sutskever
      given: Ilya
  citation-key: SutskeverTraining2013
  event-place: Toronto, Ont., Canada, Canada
  genre: PhD Thesis
  issued:
    - year: 2013
  publisher: University of Toronto
  publisher-place: Toronto, Ont., Canada, Canada
  title: Training Recurrent Neural Networks
  type: thesis
  URL: https://tspace.library.utoronto.ca/handle/1807/36012

- id: SzegedyGoing2015
  accessed:
    - year: 2017
      month: 4
      day: 7
  author:
    - family: Szegedy
      given: Christian
    - family: Liu
      given: Wei
    - family: Jia
      given: Yangqing
    - family: Sermanet
      given: Pierre
    - family: Reed
      given: Scott
    - family: Anguelov
      given: Dragomir
    - family: Erhan
      given: Dumitru
    - family: Vanhoucke
      given: Vincent
    - family: Rabinovich
      given: Andrew
  citation-key: SzegedyGoing2015
  container-title: >-
    Proceedings of the IEEE Conference on Computer Vision and Pattern
    Recognition
  DOI: 10.1109/CVPR.2015.7298594
  event-title: 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
  issued:
    - year: 2015
  page: 1–9
  title: Going deeper with convolutions
  type: paper-conference
  URL: >-
    http://www.cv-foundation.org/openaccess/content_cvpr_2015/html/Szegedy_Going_Deeper_With_2015_CVPR_paper.html

- id: TelgarskyNeural2017
  author:
    - family: Telgarsky
      given: Matus
  citation-key: TelgarskyNeural2017
  container-title: PMLR
  event-title: International Conference on Machine Learning
  issued:
    - year: 2017
      month: 7
      day: 17
  language: en
  page: 3387-3393
  title: Neural Networks and Rational Functions
  type: paper-conference
  URL: http://proceedings.mlr.press/v70/telgarsky17a.html

- id: ThickstunLearning2017
  author:
    - family: Thickstun
      given: John
    - family: Harchaoui
      given: Zaid
    - family: Kakade
      given: Sham
  citation-key: ThickstunLearning2017
  container-title: >-
    Proceedings of International Conference on Learning Representations (ICLR)
    2017
  event-title: International Conference on Learning Representations (ICLR) 2017
  issued:
    - year: 2017
  title: Learning Features of Music from Scratch
  type: paper-conference
  URL: http://arxiv.org/abs/1611.09827

- id: VardasbiState2023
  accessed:
    - year: 2023
      month: 5
      day: 22
  author:
    - family: Vardasbi
      given: Ali
    - family: Pires
      given: Telmo Pessoa
    - family: Schmidt
      given: Robin M.
    - family: Peitz
      given: Stephan
  citation-key: VardasbiState2023
  DOI: 10.48550/arXiv.2304.12776
  issued:
    - year: 2023
      month: 4
      day: 25
  number: arXiv:2304.12776
  publisher: arXiv
  title: 'State Spaces Aren''t Enough: Machine Translation Needs Attention'
  type: article
  URL: http://arxiv.org/abs/2304.12776

- id: WelchUse1967
  accessed:
    - year: 2014
      month: 11
      day: 3
  author:
    - family: Welch
      given: Peter D.
  citation-key: WelchUse1967
  container-title: IEEE Transactions on audio and electroacoustics
  DOI: 10.1109/TAU.1967.1161901
  ISSN: 0018-9278
  issue: '2'
  issued:
    - year: 1967
  number: '2'
  page: 70–73
  title: >-
    The use of fast Fourier transform for the estimation of power spectra: a
    method based on time averaging over short, modified periodograms
  type: article-journal
  URL: >-
    http://web.iaincirebon.ac.id/ebook/luke/ieeeexplore/Audio_and_Electroacoustics_IE/The_use_of_fast_Fourier_transform_for_the_estimation_of_power_spectra_A_method_based_on_time_averagi-P1T.pdf
  volume: '15'

- id: WerbosBackpropagation1990
  author:
    - family: Werbos
      given: Paul J.
  citation-key: WerbosBackpropagation1990
  container-title: Proceedings of the IEEE
  DOI: 10.1109/5.58337
  ISSN: 0018-9219
  issue: '10'
  issued:
    - year: 1990
      month: 10
  page: 1550-1560
  title: 'Backpropagation through time: what it does and how to do it'
  type: article-journal
  URL: http://mail.werbos.com/Neural/BTT.pdf
  volume: '78'

- id: WerbosGeneralization1988
  accessed:
    - year: 2017
      month: 9
      day: 19
  author:
    - family: Werbos
      given: Paul J.
  citation-key: WerbosGeneralization1988
  container-title: Neural Networks
  container-title-short: Neural Networks
  DOI: 10.1016/0893-6080(88)90007-X
  ISSN: 0893-6080
  issue: '4'
  issued:
    - year: 1988
      month: 1
      day: 1
  page: 339-356
  title: >-
    Generalization of backpropagation with application to a recurrent gas market
    model
  type: article-journal
  volume: '1'

- id: WiatowskiEnergy2018
  author:
    - family: Wiatowski
      given: Thomas
    - family: Grohs
      given: Philipp
    - family: Bölcskei
      given: Helmut
  citation-key: WiatowskiEnergy2018
  container-title: IEEE Transactions on Information Theory
  DOI: 10.1109/TIT.2017.2756880
  ISSN: 0018-9448
  issue: '7'
  issued:
    - year: 2018
  page: 1-1
  title: Energy Propagation in Deep Convolutional Neural Networks
  type: article-journal
  URL: http://arxiv.org/abs/1704.03636
  volume: '64'

- id: WilliamsEfficient1990
  accessed:
    - year: 2018
      month: 4
      day: 4
  author:
    - family: Williams
      given: Ronald J.
    - family: Peng
      given: Jing
  citation-key: WilliamsEfficient1990
  container-title: Neural Computation
  container-title-short: Neural Computation
  DOI: 10.1162/neco.1990.2.4.490
  ISSN: 0899-7667
  issue: '4'
  issued:
    - year: 1990
      month: 12
      day: 1
  page: 490-501
  title: >-
    An Efficient Gradient-Based Algorithm for On-Line Training of Recurrent
    Network Trajectories
  type: article-journal
  URL: >-
    https://www.researchgate.net/profile/Jing_Peng2/publication/2343555_An_Efficient_Gradient-Based_Algorithm_for_On-Line_Training_of_Recurrent_Network_Trajectories/links/555ca9a108ae8c0cab2a63ab/An-Efficient-Gradient-Based-Algorithm-for-On-Line-Training-of-Recurrent-Network-Trajectories.pdf
  volume: '2'

- id: WisdomInterpretable2016
  author:
    - family: Wisdom
      given: Scott
    - family: Powers
      given: Thomas
    - family: Pitton
      given: James
    - family: Atlas
      given: Les
  citation-key: WisdomInterpretable2016
  container-title: Advances in Neural Information Processing Systems 29
  issued:
    - year: 2016
      month: 11
      day: 22
  title: Interpretable Recurrent Neural Networks Using Sequential Sparse Recovery
  type: paper-conference
  URL: http://arxiv.org/abs/1611.07252

- id: YuDeep2011
  author:
    - family: Yu
      given: D.
    - family: Deng
      given: L.
  citation-key: YuDeep2011
  container-title: IEEE Signal Processing Magazine
  DOI: 10.1109/MSP.2010.939038
  ISSN: 1053-5888
  issue: '1'
  issued:
    - year: 2011
      month: 1
  page: 145-154
  title: >-
    Deep Learning and Its Applications to Signal and Information Processing
    [Exploratory DSP]
  type: article-journal
  URL: http://msr-waypoint.com/pubs/143620/DeepLearn-SPM2010.pdf
  volume: '28'

- id: ZhangContinuous2021
  accessed:
    - year: 2024
      month: 7
      day: 22
  author:
    - family: Zhang
      given: Jing
    - family: Zhang
      given: Peng
    - family: Kong
      given: Baiwen
    - family: Wei
      given: Junqiu
    - family: Jiang
      given: Xin
  citation-key: ZhangContinuous2021
  container-title: Proceedings of the AAAI Conference on Artificial Intelligence
  DOI: 10.1609/aaai.v35i16.17692
  ISSN: 2374-3468
  issue: '16'
  issued:
    - year: 2021
      month: 5
      day: 18
  language: en
  number: '16'
  page: 14393-14401
  title: Continuous Self-Attention Models with Neural ODE Networks
  type: article-journal
  URL: https://ojs.aaai.org/index.php/AAAI/article/view/17692
  volume: '35'

- id: ZinkevichOnline2003
  accessed:
    - year: 2018
      month: 3
      day: 17
  author:
    - family: Zinkevich
      given: Martin
  citation-key: ZinkevichOnline2003
  collection-title: ICML'03
  container-title: >-
    Proceedings of the Twentieth International Conference on International
    Conference on Machine Learning
  event-place: Washington, DC, USA
  ISBN: 978-1-57735-189-4
  issued:
    - year: 2003
  page: 928–935
  publisher: AAAI Press
  publisher-place: Washington, DC, USA
  title: Online Convex Programming and Generalized Infinitesimal Gradient Ascent
  type: paper-conference
  URL: http://dl.acm.org/citation.cfm?id=3041838.3041955
...
