TY - COMP
TI - dmurfet/2simplicialtransformer
AU - Murfet, Daniel
AB - Code for the 2-simplicial Transformer paper. Contribute to dmurfet/2simplicialtransformer development by creating an account on GitHub.
DA - 2019/10/14/T08:10:47Z
PY - 2019
DP - GitHub
LA - Python
UR - https://github.com/dmurfet/2simplicialtransformer
Y2 - 2019/11/22/16:50:05
KW - Abstract machines
KW - Algebra
KW - Implementation
KW - Machine learning
KW - Semantics
ER -
TY - JOUR
TI - Logic and the $2$-Simplicial Transformer
AU - Murfet, Daniel
AU - Clift, James
AU - Doryn, Dmitry
AU - Wallbridge, James
T2 - arXiv:1909.00668 [cs, stat]
AB - We introduce the $2$-simplicial Transformer, an extension of the Transformer which includes a form of higher-dimensional attention generalising the dot-product attention, and uses this attention to update entity representations with tensor products of value vectors. We show that this architecture is a useful inductive bias for logical reasoning in the context of deep reinforcement learning.
DA - 2019/09/02/
PY - 2019
DP - arXiv.org
UR - http://arxiv.org/abs/1909.00668
Y2 - 2019/11/21/20:31:14
KW - Abstract machines
KW - Algebra
KW - Machine learning
KW - Semantics
ER -
TY - COMP
TI - dmurfet/deeplinearlogic
AU - Murfet, Daniel
AB - Deep learning and linear logic. Contribute to dmurfet/deeplinearlogic development by creating an account on GitHub.
DA - 2018/07/14/T01:08:44Z
PY - 2018
DP - GitHub
LA - Jupyter Notebook
UR - https://github.com/dmurfet/deeplinearlogic
Y2 - 2019/11/22/16:44:43
KW - Categorical ML
KW - Implementation
KW - Linear logic
KW - Machine learning
KW - Semantics
ER -
TY - COMP
TI - dmurfet/polysemantics
AU - Murfet, Daniel
AB - Polynomial semantics of linear logic. Contribute to dmurfet/polysemantics development by creating an account on GitHub.
DA - 2018/04/29/T20:41:43Z
PY - 2018
DP - GitHub
LA - Python
UR - https://github.com/dmurfet/polysemantics
Y2 - 2019/11/22/16:45:35
KW - Categorical ML
KW - Implementation
KW - Linear logic
KW - Machine learning
KW - Semantics
ER -
TY - CHAP
TI - Commutative Semantics for Probabilistic Programming
AU - Staton, Sam
T2 - Programming Languages and Systems
A2 - Yang, Hongseok
AB - We show that a measure-based denotational semantics for probabilistic programming is commutative. The idea underlying probabilistic programming languages (Anglican, Church, Hakaru, ...) is that programs express statistical models as a combination of prior distributions and likelihood of observations. The product of prior and likelihood is an unnormalized posterior distribution, and the inference problem is to ﬁnd the normalizing constant. One common semantic perspective is thus that a probabilistic program is understood as an unnormalized posterior measure, in the sense of measure theory, and the normalizing constant is the measure of the entire semantic domain.
CY - Berlin, Heidelberg
DA - 2017///
PY - 2017
DP - Crossref
VL - 10201
SP - 855
EP - 879
LA - en
PB - Springer Berlin Heidelberg
SN - 978-3-662-54433-4 978-3-662-54434-1
UR - http://link.springer.com/10.1007/978-3-662-54434-1_32
Y2 - 2019/11/23/16:35:50
KW - Bayesianism
KW - Probabilistic programming
KW - Programming language theory
KW - Semantics
ER -
TY - JOUR
TI - A Formal Semantics of Influence in Bayesian Reasoning
AU - Jacobs, Bart
AU - Zanasi, Fabio
T2 - Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany
AB - This paper proposes a formal deﬁnition of inﬂuence in Bayesian reasoning, based on the notions of state (as probability distribution), predicate, validity and conditioning. Our approach highlights how conditioning a joint entwined/entangled state with a predicate on one of its components has ‘crossover’ inﬂuence on the other components. We use the total variation metric on probability distributions to quantitatively measure such inﬂuence. These insights are applied to give a rigorous explanation of the fundamental concept of d-separation in Bayesian networks.
DA - 2017///
PY - 2017
DO - 10/ggdgbc
DP - DataCite
LA - en
UR - http://drops.dagstuhl.de/opus/volltexte/2017/8089/
Y2 - 2019/11/24/12:11:15
KW - Bayesianism
KW - Categorical probability theory
KW - Programming language theory
KW - Semantics
ER -
TY - JOUR
TI - A Predicate/State Transformer Semantics for Bayesian Learning
AU - Jacobs, Bart
AU - Zanasi, Fabio
T2 - Electronic Notes in Theoretical Computer Science
T3 - The Thirty-second Conference on the Mathematical Foundations of Programming Semantics (MFPS XXXII)
AB - This paper establishes a link between Bayesian inference (learning) and predicate and state transformer operations from programming semantics and logic. Specifically, a very general definition of backward inference is given via first applying a predicate transformer and then conditioning. Analogously, forward inference involves first conditioning and then applying a state transformer. These definitions are illustrated in many examples in discrete and continuous probability theory and also in quantum theory.
DA - 2016/10/05/
PY - 2016
DO - 10/ggdgbb
DP - ScienceDirect
VL - 325
SP - 185
EP - 200
J2 - Electronic Notes in Theoretical Computer Science
LA - en
SN - 1571-0661
UR - http://www.sciencedirect.com/science/article/pii/S1571066116300883
Y2 - 2019/11/24/12:04:12
KW - Bayesianism
KW - Categorical ML
KW - Categorical probability theory
KW - Effectus theory
KW - Programming language theory
KW - Semantics
ER -
TY - JOUR
TI - Semantics for probabilistic programming: higher-order functions, continuous distributions, and soft constraints
AU - Staton, Sam
AU - Yang, Hongseok
AU - Heunen, Chris
AU - Kammar, Ohad
AU - Wood, Frank
T2 - Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16
AB - We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an idealised version of Anglican) for probabilistic computation with the above features, develop both operational and denotational semantics, and prove soundness, adequacy, and termination. They involve measure theory, stochastic labelled transition systems, and functor categories, but admit intuitive computational readings, one of which views sampled random variables as dynamically allocated read-only variables. We apply our semantics to validate nontrivial equations underlying the correctness of certain compiler optimisations and inference algorithms such as sequential Monte Carlo simulation. The language enables defining probability distributions on higher-order functions, and we study their properties.
DA - 2016///
PY - 2016
DO - 10/ggdf97
DP - arXiv.org
SP - 525
EP - 534
ST - Semantics for probabilistic programming
UR - http://arxiv.org/abs/1601.04943
Y2 - 2019/11/23/16:36:30
KW - Bayesianism
KW - Probabilistic programming
KW - Programming language theory
KW - Semantics
ER -
TY - CONF
TI - Probabilistic coherence spaces are fully abstract for probabilistic PCF
AU - Ehrhard, Thomas
AU - Tasson, Christine
AU - Pagani, Michele
T2 - the 41st ACM SIGPLAN-SIGACT Symposium
AB - Probabilistic coherence spaces (PCoh) yield a semantics of higherorder probabilistic computation, interpreting types as convex sets and programs as power series. We prove that the equality of interpretations in PCoh characterizes the operational indistinguishability of programs in PCF with a random primitive.
C1 - San Diego, California, USA
C3 - Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '14
DA - 2014///
PY - 2014
DO - 10/ggdf9x
DP - Crossref
SP - 309
EP - 320
LA - en
PB - ACM Press
SN - 978-1-4503-2544-8
UR - http://dl.acm.org/citation.cfm?doid=2535838.2535865
Y2 - 2019/11/22/17:00:49
KW - Coherence spaces
KW - Probabilistic programming
KW - Programming language theory
KW - Semantics
ER -
TY - JOUR
TI - Probabilistic coherence spaces as a model of higher-order probabilistic computation
AU - Ehrhard, Thomas
AU - Danos, Vincent
T2 - Information and Computation
AB - We study a probabilistic version of coherence spaces and show that these objects provide a model of linear logic. We build a model of the pure lambda-calculus in this setting and show how to interpret a probabilistic version of the functional language PCF. We give a probabilistic interpretation of the semantics of probabilistic PCF closed terms of ground type. Last we suggest a generalization of this approach, using Banach spaces.
DA - 2011/06/01/
PY - 2011
DO - 10/ctfch6
DP - ScienceDirect
VL - 209
IS - 6
SP - 966
EP - 991
J2 - Information and Computation
LA - en
SN - 0890-5401
UR - http://www.sciencedirect.com/science/article/pii/S0890540111000411
Y2 - 2019/11/22/17:01:53
KW - Coherence spaces
KW - Probabilistic programming
KW - Programming language theory
KW - Semantics
ER -
TY - SLIDE
TI - Linear logic and deep learning
A2 - Murfet, Daniel
A2 - Hu, Huiyi
LA - en
KW - Categorical ML
KW - Linear logic
KW - Machine learning
KW - Semantics
ER -