Abstract We studyℓ∞norms ofℓ2-normalized eigenfunctions of quantum cat maps. For maps with short quantum periods (constructed by Bonechi and de Biévre in F Bonechi and S De Bièvre (2000,Communications in Mathematical Physics,211, 659–686)) we show that there exists a sequence of eigenfunctionsuwith . For general eigenfunctions we show the upper bound . Here the semiclassical parameter is . Our upper bound is analogous to the one proved by Bérard in P Bérard (1977,Mathematische Zeitschrift,155, 249-276) for compact Riemannian manifolds without conjugate points.
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Bit Blasting Probabilistic Programs
Probabilistic programming languages (PPLs) are an expressive means for creating and reasoning about probabilistic models. Unfortunatelyhybridprobabilistic programs that involve both continuous and discrete structures are not well supported by today’s PPLs. In this paper we develop a new approximate inference algorithm for hybrid probabilistic programs that first discretizes the continuous distributions and then performs discrete inference on the resulting program. The key novelty is a form of discretization that we callbit blasting, which uses a binary representation of numbers such that a domain of discretized points can be succinctly represented as a discrete probabilistic program overpoly Boolean random variables. Surprisingly, we prove that many common continuous distributions can be bit blasted in a manner that incurs no loss of accuracy over an explicit discretization and supports efficient probabilistic inference. We have built a probabilistic programming system for hybrid programs calledHyBit, which employs bit blasting followed by discrete probabilistic inference. We empirically demonstrate the benefits of our approach over existing sampling-based and symbolic inference approaches
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- Award ID(s):
- 2220408
- PAR ID:
- 10625337
- Publisher / Repository:
- Proceedings of the ACM on Programming Languages, Volume 8, Issue PLDI
- Date Published:
- Journal Name:
- Proceedings of the ACM on Programming Languages
- Volume:
- 8
- Issue:
- PLDI
- ISSN:
- 2475-1421
- Page Range / eLocation ID:
- 865 to 888
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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