39 research outputs found
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Probabilistic concurrent game semantics
This thesis presents a variety of models for probabilistic programming languages in the framework of concurrent games.
Our starting point is the model of concurrent games with symmetry of Castellan, Clairambault and Winskel. We show that they form a symmetric monoidal closed bicategory, and that this can be turned into a cartesian closed bicategory using a linear exponential pseudo-comonad inspired by linear logic.
Then, we enrich this with probability, relying heavily on Winskel's model of probabilistic concurrent strategies. We see that the bicategorical structure is not perturbed by the addition of probability. We apply this model to two probabilistic languages: a probabilistic untyped λ-calculus, and Probabilistic PCF. For the former, we relate the semantics to the probabilistic Nakajima trees of Leventis, thus obtaining a characterisation of observational equivalence for programs in terms of strategies. For the latter, we show a definability result in the spirit of the game semantics tradition. This solves an open problem, as it is notoriously difficult to model Probabilistic PCF with sequential game semantics.
Finally, we introduce a model for measurable game semantics, in which games and strategies come equipped with measure-theoretic structure allowing for an accurate description of computation with continuous data types. The objective of this model is to support computation with arbitrary probability measures on the reals. In the last part of this thesis we see how this can be done by equipping strategies with parametrised families of probability measures (also known as stochastic kernels), and we construct a bicategory of measurable concurrent games and probabilistic measurable strategies
Strong pseudomonads and premonoidal bicategories
Strong monads and premonoidal categories play a central role in clarifying
the denotational semantics of effectful programming languages. Unfortunately,
this theory excludes many modern semantic models in which the associativity and
unit laws only hold up to coherent isomorphism: for instance, because
composition is defined using a universal property. This paper remedies the
situation. We define premonoidal bicategories and a notion of strength for
pseudomonads, and show that the Kleisli bicategory of a strong pseudomonad is
premonoidal. As often in 2-dimensional category theory, the main difficulty is
to find the correct coherence axioms on 2-cells. We therefore justify our
definitions with numerous examples and by proving a correspondence theorem
between actions and strengths, generalizing a well-known category-theoretic
result.Comment: Comments and feedback welcome
Stabilized profunctors and stable species of structures
We introduce a bicategorical model of linear logic which is a novel variation
of the bicategory of groupoids, profunctors, and natural transformations. Our
model is obtained by endowing groupoids with additional structure, called a
kit, to stabilize the profunctors by controlling the freeness of the groupoid
action on profunctor elements.
The theory of generalized species of structures, based on profunctors, is
refined to a new theory of \emph{stable species} of structures between
groupoids with Boolean kits. Generalized species are in correspondence with
analytic functors between presheaf categories; in our refined model, stable
species are shown to be in correspondence with restrictions of analytic
functors, which we characterize as being stable, to full subcategories of
stabilized presheaves. Our motivating example is the class of finitary
polynomial functors between categories of indexed sets, also known as normal
functors, that arises from kits enforcing free actions.
We show that the bicategory of groupoids with Boolean kits, stable species,
and natural transformations is cartesian closed. This makes essential use of
the logical structure of Boolean kits and explains the well-known failure of
cartesian closure for the bicategory of finitary polynomial functors between
categories of set-indexed families and cartesian natural transformations. The
paper additionally develops the model of classical linear logic underlying the
cartesian closed structure and clarifies the connection to stable domain
theory.Comment: FSCD 2022 special issue of Logical Methods in Computer Science, minor
changes (incorporated reviewers comments
Densities of almost-surely terminating probabilistic programs are differentiable almost everywhere
We study the differential properties of higher-order statistical
probabilistic programs with recursion and conditioning. Our starting point is
an open problem posed by Hongseok Yang: what class of statistical probabilistic
programs have densities that are differentiable almost everywhere? To formalise
the problem, we consider Statistical PCF (SPCF), an extension of call-by-value
PCF with real numbers, and constructs for sampling and conditioning. We give
SPCF a sampling-style operational semantics a la Borgstrom et al., and study
the associated weight (commonly referred to as the density) function and value
function on the set of possible execution traces. Our main result is that
almost-surely terminating SPCF programs, generated from a set of primitive
functions (e.g. the set of analytic functions) satisfying mild closure
properties, have weight and value functions that are almost-everywhere
differentiable. We use a stochastic form of symbolic execution to reason about
almost-everywhere differentiability. A by-product of this work is that
almost-surely terminating deterministic (S)PCF programs with real parameters
denote functions that are almost-everywhere differentiable. Our result is of
practical interest, as almost-everywhere differentiability of the density
function is required to hold for the correctness of major gradient-based
inference algorithms
JACO assistive robotic device : empowering people with disabilities through innovative algorithms
JACO is a commercially available robotic assistive device
designed to help people with upper body disabilities gaining
more autonomy in their daily life. The device consists of an
arm and hand (gripper) mounted on a power wheelchair.
This assistance is possible through basic functions such as
tri-dimensional displacement of the gripper in space, finger
opening and closing and orientation of the wrist. Although
these basic functionalities allow the user to perform many
tasks, advanced functionalities were required to further
empower the users. This paper presents advanced
functionalities that were implemented in JACO in order to
increase the users’ safety and to enhance their autonomy by
increasing the number of achievable tasks and diminishing
the time and effort needed to achieve them
Associations between resident perceptions of the local residential environment and metabolic syndrome
Extent: 11p.A substantial body of research has arisen concerning the relationships between objective residential area features, particularly area-level socioeconomic status and cardiometabolic outcomes. Little research has explored residents’ perceptions of such features and how these might relate to cardiometabolic outcomes. Perceptions of environments are influenced by individual and societal factors, and may not correspond to objective reality. Understanding relations between environmental perceptions and health is important for the development of environment interventions. This study evaluated associations between perceptions of local built and social environmental attributes and metabolic syndrome, and tested whether walking behaviour mediated these associations. Individual-level data were drawn from a population-based biomedical cohort study of adults in Adelaide, South Australia (North West Adelaide Health Study). Participants’ local-area perceptions were analysed in cross-sectional associations with metabolic syndrome using multilevel regression models (n = 1,324). A nonparametric bootstrapping procedure evaluated whether walking mediated these associations. Metabolic syndrome was negatively associated with greater local land-use mix, positive aesthetics, and greater infrastructure for walking, and was positively associated with greater perceived crime and barriers to walking. Walking partially mediated associations between metabolic syndrome and perceived environmental features. Initiatives targeting residents’ perceptions of local areas may enhance the utility of environmental interventions to improve population health.Katherine Baldock, Catherine Paquet, Natasha Howard, Neil Coffee, Graeme Hugo, Anne Taylor, Robert Adams, and Mark Danie
The Quantitative Collapse of Concurrent Games with Symmetry
We explore links between the thin concurrent games of Castellan, Clairambault and Winskel, and the weighted relational models of linear logic studied by Laird, Manzonetto, McCusker and Pagani. More precisely, we show that there is an interpretationpreserving "collapse" functor from the former to the latter. On objects, the functor defines for each game a set of possible execution states. Defining the action on morphisms is more subtle, and this is the main contribution of the paper. Given a strategy and an execution state, our functor needs to count the witnesses for this state within the strategy. Strategies in thin concurrent games describe non-linear behaviour explicitly, so in general each witness exists in countably many symmetric copies. The challenge is to define the right notion of witnesses, factoring out this infinity while matching the weighted relational model. Understanding how witnesses compose is particularly subtle and requires a delve into the combinatorics of witnesses and their symmetries. In its basic form, this functor connects thin concurrent games and a relational model weighted by N ∪ {+∞}. We will additionally consider a generalised setting where both models are weighted by elements of an arbitrary continuous semiring; this covers the probabilistic case, among others. Witnesses now additionally carry a value from the semiring, and our interpretation-preserving collapse functor extends to this setting