45,118 research outputs found
Labelled Lambda-calculi with Explicit Copy and Erase
We present two rewriting systems that define labelled explicit substitution
lambda-calculi. Our work is motivated by the close correspondence between
Levy's labelled lambda-calculus and paths in proof-nets, which played an
important role in the understanding of the Geometry of Interaction. The
structure of the labels in Levy's labelled lambda-calculus relates to the
multiplicative information of paths; the novelty of our work is that we design
labelled explicit substitution calculi that also keep track of exponential
information present in call-by-value and call-by-name translations of the
lambda-calculus into linear logic proof-nets
Catalytic and communicating Petri nets are Turing complete
In most studies about the expressiveness of Petri nets, the focus has been put either on adding suitable arcs or on assuring that a complete snapshot of the system can be obtained. While the former still complies with the intuition on Petri nets, the second is somehow an orthogonal approach, as Petri nets are distributed in nature. Here, inspired by membrane computing, we study some classes of Petri nets where the distribution is partially kept and which are still Turing complete
Generalization and Equilibrium in Generative Adversarial Nets (GANs)
We show that training of generative adversarial network (GAN) may not have
good generalization properties; e.g., training may appear successful but the
trained distribution may be far from target distribution in standard metrics.
However, generalization does occur for a weaker metric called neural net
distance. It is also shown that an approximate pure equilibrium exists in the
discriminator/generator game for a special class of generators with natural
training objectives when generator capacity and training set sizes are
moderate.
This existence of equilibrium inspires MIX+GAN protocol, which can be
combined with any existing GAN training, and empirically shown to improve some
of them.Comment: This is an updated version of an ICML'17 paper with the same title.
The main difference is that in the ICML'17 version the pure equilibrium
result was only proved for Wasserstein GAN. In the current version the result
applies to most reasonable training objectives. In particular, Theorem 4.3
now applies to both original GAN and Wasserstein GA
Sequentiality vs. Concurrency in Games and Logic
Connections between the sequentiality/concurrency distinction and the
semantics of proofs are investigated, with particular reference to games and
Linear Logic.Comment: 35 pages, appeared in Mathematical Structures in Computer Scienc
Introduction to linear logic and ludics, part II
This paper is the second part of an introduction to linear logic and ludics,
both due to Girard. It is devoted to proof nets, in the limited, yet central,
framework of multiplicative linear logic and to ludics, which has been recently
developped in an aim of further unveiling the fundamental interactive nature of
computation and logic. We hope to offer a few computer science insights into
this new theory
The Geometry of Concurrent Interaction: Handling Multiple Ports by Way of Multiple Tokens (Long Version)
We introduce a geometry of interaction model for Mazza's multiport
interaction combinators, a graph-theoretic formalism which is able to
faithfully capture concurrent computation as embodied by process algebras like
the -calculus. The introduced model is based on token machines in which
not one but multiple tokens are allowed to traverse the underlying net at the
same time. We prove soundness and adequacy of the introduced model. The former
is proved as a simulation result between the token machines one obtains along
any reduction sequence. The latter is obtained by a fine analysis of
convergence, both in nets and in token machines
Local antithetic sampling with scrambled nets
We consider the problem of computing an approximation to the integral
. Monte Carlo (MC) sampling typically attains a root
mean squared error (RMSE) of from independent random function
evaluations. By contrast, quasi-Monte Carlo (QMC) sampling using carefully
equispaced evaluation points can attain the rate for
any and randomized QMC (RQMC) can attain the RMSE
, both under mild conditions on . Classical
variance reduction methods for MC can be adapted to QMC. Published results
combining QMC with importance sampling and with control variates have found
worthwhile improvements, but no change in the error rate. This paper extends
the classical variance reduction method of antithetic sampling and combines it
with RQMC. One such method is shown to bring a modest improvement in the RMSE
rate, attaining for any , for
smooth enough .Comment: Published in at http://dx.doi.org/10.1214/07-AOS548 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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