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    - family: Gillis
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    - family: Horn
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    - family: Rawlings
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    - family: Diehl
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  citation-key: AnderssonCasADi2019
  container-title: Mathematical Programming Computation
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  DOI: 10.1007/s12532-018-0139-4
  ISSN: 1867-2949, 1867-2957
  issue: '1'
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  language: en
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- id: AryaAutomatic2022
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  citation-key: AryaAutomatic2022
  event-title: Advances in Neural Information Processing Systems
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      month: 10
      day: 31
  language: en
  title: Automatic Differentiation of Programs with Discrete Randomness
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- id: BaydinAutomatic2014
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  title: Automatic Differentiation of Algorithms for Machine Learning
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- id: BaydinAutomatic2018
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  issued:
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  title: 'Automatic Differentiation in Machine Learning: a Survey'
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- id: BaydinTricks2016
  author:
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      given: Atılım Güneş
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- id: BlondelEfficient2021
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      day: 8
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      month: 10
      day: 7
  language: en
  title: Efficient and Modular Implicit Differentiation
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- id: BolteMathematical2020
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    - year: 2020
      month: 12
      day: 13
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    - family: Pauwels
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  citation-key: BolteMathematical2020
  container-title: Advances in Neural Information Processing Systems
  issued:
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  language: en
  title: A mathematical model for automatic differentiation in machine learning
  type: paper-conference
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- id: CaoAdjoint2003
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    - family: Li
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    Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The
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- id: CarpenterStan2015
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  citation-key: CarpenterStan2015
  container-title: arXiv preprint arXiv:1509.07164
  issued:
    - year: 2015
  title: 'The Stan Math Library: Reverse-Mode Automatic Differentiation in C++'
  type: article-journal
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- id: CharlierKernel2021
  accessed:
    - year: 2022
      month: 9
      day: 28
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      given: Benjamin
    - family: Feydy
      given: Jean
    - family: Glaunès
      given: Joan Alexis
    - family: Collin
      given: François-David
    - family: Durif
      given: Ghislain
  citation-key: CharlierKernel2021
  container-title: Journal of Machine Learning Research
  ISSN: 1533-7928
  issue: '74'
  issued:
    - year: 2021
  page: 1-6
  title: Kernel Operations on the GPU, with Autodiff, without Memory Overflows
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- id: DangelBackPACK2019
  accessed:
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      month: 8
      day: 5
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      given: Felix
    - family: Kunstner
      given: Frederik
    - family: Hennig
      given: Philipp
  citation-key: DangelBackPACK2019
  container-title: International conference on learning representations
  event-title: International Conference on Learning Representations
  issued:
    - year: 2019
      month: 9
      day: 25
  language: en
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  type: paper-conference
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- id: EatonBelief2022
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      month: 4
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      given: Frederik
  citation-key: EatonBelief2022
  issued:
    - year: 2022
      month: 10
      day: 2
  language: en
  number: arXiv:2210.00610
  publisher: arXiv
  title: Belief propagation generalizes backpropagation
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- id: ErricoWhat1997
  accessed:
    - year: 2019
      month: 8
      day: 31
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      given: Ronald M.
  citation-key: ErricoWhat1997
  container-title: Bulletin of the American Meteorological Society
  container-title-short: Bull. Amer. Meteor. Soc.
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  ISSN: 0003-0007
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      month: 11
      day: 1
  page: 2577-2592
  publisher: American Meteorological Society
  section: Bulletin of the American Meteorological Society
  title: What Is an Adjoint Model?
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- id: FikeDevelopment2011
  accessed:
    - year: 2018
      month: 9
      day: 28
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      given: Jeffrey
    - family: Alonso
      given: Juan
  citation-key: FikeDevelopment2011
  container-title: >-
    49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and
    Aerospace Exposition
  DOI: 10.2514/6.2011-886
  event-place: Orlando, Florida
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    49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and
    Aerospace Exposition
  ISBN: 978-1-60086-950-1
  issued:
    - year: 2011
      month: 1
      day: 4
  language: en
  publisher: American Institute of Aeronautics and Astronautics
  publisher-place: Orlando, Florida
  title: >-
    The Development of Hyper-Dual Numbers for Exact Second-Derivative
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  type: paper-conference
  URL: http://arc.aiaa.org/doi/10.2514/6.2011-886

- id: FischerAutomatic2018
  accessed:
    - year: 2018
      month: 11
      day: 6
  author:
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      given: Keno
    - family: Saba
      given: Elliot
  citation-key: FischerAutomatic2018
  container-title: arXiv:1810.09868 [cs, stat]
  issued:
    - year: 2018
      month: 10
      day: 23
  title: Automatic Full Compilation of Julia Programs and ML Models to Cloud TPUs
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  URL: http://arxiv.org/abs/1810.09868

- id: GallierAlgebra2022
  author:
    - family: Gallier
      given: Jean
    - family: Quaintance
      given: Jocelyn
  citation-key: GallierAlgebra2022
  issued:
    - year: 2022
  language: en
  title: >-
    Algebra, Topology, Diﬀerential Calculus, and Optimization Theory For
    Computer Science and Machine Learning
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- id: GilesCollected2008
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      day: 3
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      given: Mike B.
  citation-key: GilesCollected2008
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      given: Timothy J.
    - family: Griebel
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    - family: Keyes
      given: David E.
    - family: Nieminen
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    - family: Roose
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    - family: Schlick
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  container-title: Advances in Automatic Differentiation
  editor:
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      given: Christian H.
    - family: Bücker
      given: H. Martin
    - family: Hovland
      given: Paul
    - family: Naumann
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    - family: Utke
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  event-place: Berlin, Heidelberg
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  issued:
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  page: 35-44
  publisher: Springer Berlin Heidelberg
  publisher-place: Berlin, Heidelberg
  title: >-
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    Differentiation
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  URL: http://eprints.maths.ox.ac.uk/1079/
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- id: GowerHigherorder2016
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    - year: 2019
      month: 3
      day: 26
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      given: R. M.
    - family: Gower
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  citation-key: GowerHigherorder2016
  container-title: Mathematical Programming
  DOI: 10.1007/s10107-014-0827-4
  ISSN: 0025-5610, 1436-4646
  issue: 1-2
  issued:
    - year: 2016
      month: 1
  language: en
  page: 81-103
  title: >-
    Higher-order reverse automatic differentiation with emphasis on the
    third-order
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  volume: '155'

- id: GriewankEvaluating2008
  author:
    - family: Griewank
      given: Andreas
    - family: Walther
      given: Andrea
  call-number: QA304 .G76 2008
  citation-key: GriewankEvaluating2008
  edition: 2nd ed
  event-place: Philadelphia, PA
  ISBN: 978-0-89871-659-7
  issued:
    - year: 2008
  number-of-pages: '438'
  publisher: Society for Industrial and Applied Mathematics
  publisher-place: Philadelphia, PA
  title: >-
    Evaluating derivatives: principles and techniques of algorithmic
    differentiation
  type: book

- id: GriewankWho2012
  author:
    - family: Griewank
      given: Andreas
  citation-key: GriewankWho2012
  container-title: Documenta Mathematica
  issued:
    - year: 2012
  language: en
  page: '12'
  title: Who Invented the Reverse Mode of Differentiation?
  type: article-journal
  URL: >-
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- id: HaroAutomatic2008
  author:
    - family: Haro
      given: A.
  citation-key: HaroAutomatic2008
  container-title: IMA Note
  issued:
    - year: 2008
  title: >-
    Automatic differentiation methods in computational dynamical systems:
    Invariant manifolds and normal forms of vector fields at fixed points
  type: article-journal
  URL: http://www.maia.ub.es/~alex/admcds/admcds.pdf

- id: HuDiffTaichi2020
  accessed:
    - year: 2020
      month: 4
      day: 25
  author:
    - family: Hu
      given: Yuanming
    - family: Anderson
      given: Luke
    - family: Li
      given: Tzu-Mao
    - family: Sun
      given: Qi
    - family: Carr
      given: Nathan
    - family: Ragan-Kelley
      given: Jonathan
    - family: Durand
      given: Frédo
  citation-key: HuDiffTaichi2020
  container-title: ICLR
  event-title: ICLR
  issued:
    - year: 2020
      month: 2
      day: 14
  title: 'DiffTaichi: Differentiable Programming for Physical Simulation'
  type: paper-conference
  URL: http://arxiv.org/abs/1910.00935

- id: HuTaichi2019
  accessed:
    - year: 2020
      month: 4
      day: 25
  author:
    - family: Hu
      given: Yuanming
    - family: Li
      given: Tzu-Mao
    - family: Anderson
      given: Luke
    - family: Ragan-Kelley
      given: Jonathan
    - family: Durand
      given: Frédo
  citation-key: HuTaichi2019
  container-title: ACM Transactions on Graphics
  container-title-short: ACM Trans. Graph.
  DOI: 10.1145/3355089.3356506
  ISSN: 0730-0301, 1557-7368
  issue: '6'
  issued:
    - year: 2019
      month: 11
      day: 8
  language: en
  page: 1-16
  title: >-
    Taichi: a language for high-performance computation on spatially sparse data
    structures
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  volume: '38'

- id: InnesDon2018
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    - year: 2018
      month: 11
      day: 6
  author:
    - family: Innes
      given: Michael
  citation-key: InnesDon2018
  container-title: arXiv:1810.07951 [cs]
  issued:
    - year: 2018
      month: 10
      day: 18
  title: 'Don''t Unroll Adjoint: Differentiating SSA-Form Programs'
  type: article-journal
  URL: http://arxiv.org/abs/1810.07951

- id: IonescuTraining2016
  accessed:
    - year: 2022
      month: 10
      day: 3
  author:
    - family: Ionescu
      given: Catalin
    - family: Vantzos
      given: Orestis
    - family: Sminchisescu
      given: Cristian
  citation-key: IonescuTraining2016
  DOI: 10.48550/arXiv.1509.07838
  issued:
    - year: 2016
      month: 4
      day: 14
  number: arXiv:1509.07838
  publisher: arXiv
  title: Training Deep Networks with Structured Layers by Matrix Backpropagation
  type: article
  URL: http://arxiv.org/abs/1509.07838

- id: JatavallabhulaSLAM2020
  accessed:
    - year: 2022
      month: 2
      day: 28
  author:
    - family: Jatavallabhula
      given: Krishna Murthy
    - family: Iyer
      given: Ganesh
    - family: Paull
      given: Liam
  citation-key: JatavallabhulaSLAM2020
  container-title: 2020 IEEE International Conference on Robotics and Automation (ICRA)
  DOI: 10.1109/ICRA40945.2020.9197519
  event-place: Paris, France
  event-title: 2020 IEEE International Conference on Robotics and Automation (ICRA)
  ISBN: 978-1-72817-395-5
  issued:
    - year: 2020
      month: 5
  language: en
  page: 2130-2137
  publisher: IEEE
  publisher-place: Paris, France
  title: '∇SLAM: Dense SLAM meets Automatic Differentiation'
  type: paper-conference

- id: JohnsonNotes2012
  author:
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      given: Steven G
  citation-key: JohnsonNotes2012
  issued:
    - year: 2012
  language: en
  page: '6'
  title: Notes on Adjoint Methods for 18.335
  type: article-journal
  URL: https://math.mit.edu/~stevenj/18.336/adjoint.pdf

- id: KavvadiasProper2015
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      day: 14
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      given: I. S.
    - family: Papoutsis-Kiachagias
      given: E. M.
    - family: Giannakoglou
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  container-title-short: Journal of Computational Physics
  DOI: 10.1016/j.jcp.2015.08.012
  ISSN: 0021-9991
  issued:
    - year: 2015
      month: 11
      day: 15
  language: en
  page: 1-18
  title: >-
    On the proper treatment of grid sensitivities in continuous adjoint methods
    for shape optimization
  type: article-journal
  volume: '301'

- id: KidgerHey2021
  accessed:
    - year: 2023
      month: 4
      day: 16
  author:
    - family: Kidger
      given: Patrick
    - family: Chen
      given: Ricky T. Q.
    - family: Lyons
      given: Terry J.
  citation-key: KidgerHey2021
  container-title: Proceedings of the 38th International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  ISSN: 2640-3498
  issued:
    - year: 2021
      month: 7
      day: 1
  language: en
  page: 5443-5452
  publisher: PMLR
  title: '"Hey, that’s not an ODE": Faster ODE Adjoints via Seminorms'
  type: paper-conference
  URL: http://arxiv.org/abs/2009.09457

- id: KidgerNeural2020
  accessed:
    - year: 2021
      month: 9
      day: 28
  author:
    - family: Kidger
      given: Patrick
    - family: Morrill
      given: James
    - family: Foster
      given: James
    - family: Lyons
      given: Terry
  citation-key: KidgerNeural2020
  container-title: arXiv:2005.08926 [cs, stat]
  issued:
    - year: 2020
      month: 11
      day: 5
  title: Neural Controlled Differential Equations for Irregular Time Series
  type: article-journal
  URL: http://arxiv.org/abs/2005.08926

- id: LaueComputing2018
  accessed:
    - year: 2019
      month: 3
      day: 18
  author:
    - family: Laue
      given: Soeren
    - family: Mitterreiter
      given: Matthias
    - family: Giesen
      given: Joachim
  citation-key: LaueComputing2018
  container-title: Advances in Neural Information Processing Systems 31
  editor:
    - family: Bengio
      given: S.
    - family: Wallach
      given: H.
    - family: Larochelle
      given: H.
    - family: Grauman
      given: K.
    - family: Cesa-Bianchi
      given: N.
    - family: Garnett
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  issued:
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  page: 2750–2759
  publisher: Curran Associates, Inc.
  title: Computing Higher Order Derivatives of Matrix and Tensor Expressions
  type: paper-conference
  URL: >-
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- id: LaunayDirect2020
  author:
    - family: Launay
      given: Julien
    - family: Poli
      given: Iacopo
    - family: Boniface
      given: François
    - family: Krzakala
      given: Florent
  citation-key: LaunayDirect2020
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2020
  language: en
  page: '15'
  title: >-
    Direct Feedback Alignment Scales to Modern Deep Learning Tasks and
    Architectures
  type: paper-conference
  URL: http://arxiv.org/abs/2006.12878
  volume: '33'

- id: LiaoDifferentiable2019
  accessed:
    - year: 2024
      month: 4
      day: 4
  author:
    - family: Liao
      given: Hai-Jun
    - family: Liu
      given: Jin-Guo
    - family: Wang
      given: Lei
    - family: Xiang
      given: Tao
  citation-key: LiaoDifferentiable2019
  container-title: Physical Review X
  container-title-short: Phys. Rev. X
  DOI: 10.1103/PhysRevX.9.031041
  ISSN: 2160-3308
  issue: '3'
  issued:
    - year: 2019
      month: 9
      day: 5
  language: en
  page: '031041'
  title: Differentiable Programming Tensor Networks
  type: article-journal
  URL: https://link.aps.org/doi/10.1103/PhysRevX.9.031041
  volume: '9'

- id: LiScalable2020
  accessed:
    - year: 2020
      month: 8
      day: 23
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      given: Xuechen
    - family: Wong
      given: Ting-Kam Leonard
    - family: Chen
      given: Ricky T. Q.
    - family: Duvenaud
      given: David
  citation-key: LiScalable2020
  container-title: International Conference on Artificial Intelligence and Statistics
  event-title: International Conference on Artificial Intelligence and Statistics
  ISSN: 2640-3498
  issued:
    - year: 2020
      month: 6
      day: 3
  language: en
  page: 3870-3882
  publisher: PMLR
  title: Scalable Gradients for Stochastic Differential Equations
  type: paper-conference
  URL: http://proceedings.mlr.press/v108/li20i.html

- id: MaclaurinGradientbased2015
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      month: 4
      day: 23
  author:
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      given: Dougal
    - family: Duvenaud
      given: David
    - family: Adams
      given: Ryan
  citation-key: MaclaurinGradientbased2015
  container-title: Proceedings of the 32nd International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  ISSN: 1938-7228
  issued:
    - year: 2015
      month: 6
      day: 1
  language: en
  page: 2113-2122
  publisher: PMLR
  title: Gradient-based Hyperparameter Optimization through Reversible Learning
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  URL: https://proceedings.mlr.press/v37/maclaurin15.html

- id: MargossianReview2019
  accessed:
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      month: 4
      day: 15
  author:
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      given: Charles C.
  citation-key: MargossianReview2019
  container-title: WIREs Data Mining and Knowledge Discovery
  container-title-short: WIREs Data Min & Knowl
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  issued:
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  page: e1305
  title: A Review of automatic differentiation and its efficient implementation
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- id: MogensenOptim2018
  accessed:
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      month: 7
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...
