@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}
}