@article{baydin_automatic_2018,
title = {Automatic differentiation in machine learning: a survey},
shorttitle = {Automatic differentiation in machine learning},
url = {http://arxiv.org/abs/1502.05767},
abstract = {Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "autodiff", is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational fluid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names "dynamic computational graphs" and "differentiable programming". We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.},
urldate = {2019-11-22},
journal = {arXiv:1502.05767 [cs, stat]},
author = {Baydin, Atilim Gunes and Pearlmutter, Barak A. and Radul, Alexey Andreyevich and Siskind, Jeffrey Mark},
month = feb,
year = {2018},
note = {ZSCC: 0000318
arXiv: 1502.05767},
keywords = {Automatic differentiation, Classical ML, Differentiation, Machine learning}
}
@article{murfet_derivatives_2019,
title = {Derivatives of {Turing} machines in {Linear} {Logic}},
url = {http://arxiv.org/abs/1805.11813},
abstract = {We calculate denotations under the Sweedler semantics of the Ehrhard-Regnier derivatives of various encodings of Turing machines into linear logic. We show that these derivatives calculate the rate of change of probabilities naturally arising in the Sweedler semantics of linear logic proofs. The resulting theory is applied to the problem of synthesising Turing machines by gradient descent.},
urldate = {2019-11-21},
journal = {arXiv:1805.11813 [math]},
author = {Murfet, Daniel and Clift, James},
month = jan,
year = {2019},
note = {ZSCC: NoCitationData[s0]
arXiv: 1805.11813},
keywords = {Abstract machines, Categorical ML, Differentiation, Linear logic, Machine learning}
}
@inproceedings{sprunger_differentiable_2019,
address = {Vancouver, BC, Canada},
title = {Differentiable {Causal} {Computations} via {Delayed} {Trace}},
isbn = {978-1-72813-608-0},
url = {https://ieeexplore.ieee.org/document/8785670/},
doi = {10/ggdf98},
abstract = {We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the ﬁrst n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called “delayed trace”, which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee.},
language = {en},
urldate = {2019-11-23},
booktitle = {2019 34th {Annual} {ACM}/{IEEE} {Symposium} on {Logic} in {Computer} {Science} ({LICS})},
publisher = {IEEE},
author = {Sprunger, David and Katsumata, Shin-ya},
month = jun,
year = {2019},
note = {ZSCC: 0000002},
keywords = {Categorical ML, Differentiation},
pages = {1--12}
}