scholarly journals An Awkward Symmetry: The Tension between Particle Ontologies and Permutation Invariance

2011 ◽  
Vol 78 (1) ◽  
pp. 39-59 ◽  
Author(s):  
Benjamin Jantzen
Keyword(s):  
Permutation Invariance

scholarly journals Extracting Entity Synonymous Relations via Context-Aware Permutation Invariance

2022 ◽  
Vol 17 (1) ◽  
pp. 1-17
Author(s):  
Nan Yan ◽  
Subin Huang ◽  
Chao Kong
Keyword(s):  
Real World ◽  
Relation Extraction ◽  
The Other ◽  
Context Aware ◽  
Important Work ◽  
Relational Context ◽  
Permutation Invariance ◽  
Level Statistics ◽  
Real World Datasets ◽  
Better Than

Discovering entity synonymous relations is an important work for many entity-based applications. Existing entity synonymous relation extraction approaches are mainly based on lexical patterns or distributional corpus-level statistics, ignoring the context semantics between entities. For example, the contexts around ''apple'' determine whether ''apple'' is a kind of fruit or Apple Inc. In this paper, an entity synonymous relation extraction approach is proposed using context-aware permutation invariance. Specifically, a triplet network is used to obtain the permutation invariance between the entities to learn whether two given entities possess synonymous relation. To track more synonymous features, the relational context semantics and entity representations are integrated into the triplet network, which can improve the performance of extracting entity synonymous relations. The proposed approach is implemented on three real-world datasets. Experimental results demonstrate that the approach performs better than the other compared approaches on entity synonymous relation extraction task.

scholarly journals Mixed ƒ-divergence for Multiple Pairs of Measures

2017 ◽  
Vol 60 (3) ◽  
pp. 641-654 ◽  
Author(s):  
Elisabeth Werner ◽  
Deping Ye
Keyword(s):  
Isoperimetric Inequality ◽  
Type Inequality ◽  
Probability Measures ◽  
Permutation Invariance

AbstractIn this paper, the concept of the classical ƒ-divergence for a pair of measures is extended to the mixed ƒ-divergence formultiple pairs ofmeasures. The mixed ƒ-divergence provides a way to measure the diòerence between multiple pairs of (probability) measures. Properties for the mixed ƒ-divergence are established, such as permutation invariance and symmetry in distributions. An Alexandrov–Fenchel type inequality and an isoperimetric inequality for the mixed ƒ-divergence are proved.

scholarly journals On permutation-invariance of limit theorems

2015 ◽  
Vol 31 (3) ◽  
pp. 372-379 ◽  
Author(s):  
I. Berkes ◽  
R. Tichy
Keyword(s):  
Limit Theorems ◽  
Permutation Invariance
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