TY - JOUR
TI - Derivatives of Turing machines in Linear Logic
AU - Murfet, Daniel
AU - Clift, James
T2 - arXiv:1805.11813 [math]
AB - 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.
DA - 2019/01/28/
PY - 2019
DP - arXiv.org
UR - http://arxiv.org/abs/1805.11813
Y2 - 2019/11/21/20:33:27
KW - Abstract machines
KW - Categorical ML
KW - Differentiation
KW - Linear logic
KW - Machine learning
ER -
TY - CONF
TI - Differentiable Causal Computations via Delayed Trace
AU - Sprunger, David
AU - Katsumata, Shin-ya
T2 - 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
AB - 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.
C1 - Vancouver, BC, Canada
C3 - 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
DA - 2019/06//
PY - 2019
DO - 10/ggdf98
DP - Crossref
SP - 1
EP - 12
LA - en
PB - IEEE
SN - 978-1-72813-608-0
UR - https://ieeexplore.ieee.org/document/8785670/
Y2 - 2019/11/23/16:57:38
KW - Categorical ML
KW - Differentiation
ER -