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Nonlocal neural networks [25] have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of diffusion and damping effect of nonlocal networks by doing spectrum analysis on the weight matrices of the well-trained networks, and then propose a new formulation of the nonlocal block. The new block not only learns the nonlocal interactions but also has stable dynamics, thus allowing deeper nonlocal structures. Moreover, we interpret our formulation from the general nonlocal modeling perspective, where we make connections between the proposed nonlocal network and other nonlocal models, such as nonlocal diffusion process and Markov jump process.
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A new nonlocal calculus framework. Helmholtz decompositions, properties, and convergence for nonlocal operators in the limit of the vanishing horizon
- Award ID(s):
- 2109149
- PAR ID:
- 10344682
- Date Published:
- Journal Name:
- SN Partial Differential Equations and Applications
- Volume:
- 3
- ISSN:
- 2662-2963
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Asymptotically nonlocal field theories approximate ghost-free nonlocal theories at low energies, yet are theories of finite order in the number of derivatives. These theories have an emergent nonlocal scale that regulates loop diagrams and can provide a solution to the hierarchy problem. Asymptotic nonlocality has been studied previously in scalar theories, Abelian and non-Abelian gauge theories with complex scalars, and linearized gravity. Here we extend that work by considering an asymptotically nonlocal generalization of QCD, which can be used for realistic phenomenological investigations. In particular, we derive Feynman rules relevant for the study of the production of dijets at hadron colliders and compute the parton-level cross sections at leading order. We use these to determine a bound on the scale of new physics from Large Hadron Collider data, both for a typical choice of model parameters, and in the nonlocal limit.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s42985-022-00178-z
