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CATEGORICAL LOGIC

MACHINE LEARNING

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## Derivatives of Turing machines in Linear Logic

Resource type

Authors/contributors

- Murfet, Daniel (Author)
- Clift, James (Author)

Title

Derivatives of Turing machines in Linear Logic

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.

Publication

arXiv:1805.11813 [math]

Date

2019-01-28

Accessed

2019-11-21T20:33:27Z

Library Catalog

Extra

ZSCC: NoCitationData[s0] arXiv: 1805.11813

Notes

Comment: 62 pages, moved the section on naive Bayesian observers earlier (Section 6.2) with slight changes to notation, references added in the introduction to Section 7 and related work in Remark 7.16

Citation

Murfet, D., & Clift, J. (2019). Derivatives of Turing machines in Linear Logic.

*ArXiv:1805.11813 [Math]*. Retrieved from http://arxiv.org/abs/1805.11813
CATEGORICAL LOGIC

DIFFERENTIAL CALCULUS

MACHINE LEARNING

MODEL CHECKING AND STATE MACHINES

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