539 research outputs found
Analysis of structural properties of Petri nets based on product incidence matrix
summary:This paper presents some structural properties of a generalized Petri net (PN) with an algorithm to determine the (partial) conservativeness and (partial) consistency of the net. A product incidence matrix or is defined and used to further improve the relations among PNs, linear inequalities and matrix analysis. Thus, based on Cramer's Rule, a new approach for the study of the solution of a linear system is given in terms of certain sub-determinants of the coefficient matrix and an efficient algorithm is proposed to compute these sub-determinants. The paper extends the common necessary and/or sufficient conditions for conservativeness and consistency in previous papers and some examples are designed to explain the conclusions finally
Learning to Prove Theorems by Learning to Generate Theorems
We consider the task of automated theorem proving, a key AI task. Deep
learning has shown promise for training theorem provers, but there are limited
human-written theorems and proofs available for supervised learning. To address
this limitation, we propose to learn a neural generator that automatically
synthesizes theorems and proofs for the purpose of training a theorem prover.
Experiments on real-world tasks demonstrate that synthetic data from our
approach improves the theorem prover and advances the state of the art of
automated theorem proving in Metamath. Code is available at
https://github.com/princeton-vl/MetaGen
LINE: Large-scale Information Network Embedding
This paper studies the problem of embedding very large information networks
into low-dimensional vector spaces, which is useful in many tasks such as
visualization, node classification, and link prediction. Most existing graph
embedding methods do not scale for real world information networks which
usually contain millions of nodes. In this paper, we propose a novel network
embedding method called the "LINE," which is suitable for arbitrary types of
information networks: undirected, directed, and/or weighted. The method
optimizes a carefully designed objective function that preserves both the local
and global network structures. An edge-sampling algorithm is proposed that
addresses the limitation of the classical stochastic gradient descent and
improves both the effectiveness and the efficiency of the inference. Empirical
experiments prove the effectiveness of the LINE on a variety of real-world
information networks, including language networks, social networks, and
citation networks. The algorithm is very efficient, which is able to learn the
embedding of a network with millions of vertices and billions of edges in a few
hours on a typical single machine. The source code of the LINE is available
online.Comment: WWW 201
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