520 research outputs found
Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
A class of generative models that unifies flow-based and diffusion-based
methods is introduced. These models extend the framework proposed in Albergo &
Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time
stochastic processes called `stochastic interpolants' to bridge any two
arbitrary probability density functions exactly in finite time. These
interpolants are built by combining data from the two prescribed densities with
an additional latent variable that shapes the bridge in a flexible way. The
time-dependent probability density function of the stochastic interpolant is
shown to satisfy a first-order transport equation as well as a family of
forward and backward Fokker-Planck equations with tunable diffusion. Upon
consideration of the time evolution of an individual sample, this viewpoint
immediately leads to both deterministic and stochastic generative models based
on probability flow equations or stochastic differential equations with an
adjustable level of noise. The drift coefficients entering these models are
time-dependent velocity fields characterized as the unique minimizers of simple
quadratic objective functions, one of which is a new objective for the score of
the interpolant density. Remarkably, we show that minimization of these
quadratic objectives leads to control of the likelihood for any of our
generative models built upon stochastic dynamics. By contrast, we establish
that generative models based upon a deterministic dynamics must, in addition,
control the Fisher divergence between the target and the model. We also
construct estimators for the likelihood and the cross-entropy of
interpolant-based generative models, discuss connections with other stochastic
bridges, and demonstrate that such models recover the Schr\"odinger bridge
between the two target densities when explicitly optimizing over the
interpolant
Stochastic interpolants with data-dependent couplings
Generative models inspired by dynamical transport of measure -- such as flows
and diffusions -- construct a continuous-time map between two probability
densities. Conventionally, one of these is the target density, only accessible
through samples, while the other is taken as a simple base density that is
data-agnostic. In this work, using the framework of stochastic interpolants, we
formalize how to \textit{couple} the base and the target densities, whereby
samples from the base are computed conditionally given samples from the target
in a way that is different from (but does preclude) incorporating information
about class labels or continuous embeddings. This enables us to construct
dynamical transport maps that serve as conditional generative models. We show
that these transport maps can be learned by solving a simple square loss
regression problem analogous to the standard independent setting. We
demonstrate the usefulness of constructing dependent couplings in practice
through experiments in super-resolution and in-painting
Equivariant flow-based sampling for lattice gauge theory
We define a class of machine-learned flow-based sampling algorithms for
lattice gauge theories that are gauge-invariant by construction. We demonstrate
the application of this framework to U(1) gauge theory in two spacetime
dimensions, and find that near critical points in parameter space the approach
is orders of magnitude more efficient at sampling topological quantities than
more traditional sampling procedures such as Hybrid Monte Carlo and Heat Bath.Comment: 6 pages, 4 figure
Sampling QCD field configurations with gauge-equivariant flow models
Machine learning methods based on normalizing flows have been shown to address important challenges, such as critical slowing-down and topological freezing, in the sampling of gauge field configurations in simple lattice field theories. A critical question is whether this success will translate to studies of QCD. This Proceedings presents a status update on advances in this area. In particular, it is illustrated how recently developed algorithmic components may be combined to construct flow-based sampling algorithms for QCD in four dimensions. The prospects and challenges for future use of this approach in at-scale applications are summarized
Tracker Operation and Performance at the Magnet Test and Cosmic Challenge
During summer 2006 a fraction of the CMS silicon strip tracker was operated in a comprehensive slice test called the Magnet Test and Cosmic Challenge (MTCC). At the MTCC, cosmic rays detected in the muon chambers were used to trigger the readout of all CMS sub-detectors in the general data acquisition system and in the presence of the 4 T magnetic field produced by the CMS superconducting solenoid. This document describes the operation of the Tracker hardware and software prior, during and after data taking. The performance of the detector as resulting from the MTCC data analysis is also presented
Measurement of the underlying event activity in pp collisions at √s = 0.9 and 7 TeV with the novel jet-area/median approach
Open Access: This article is distributed under the terms of the Creative Commons Attribution License.-- Chatrchyan, S. et al.The first measurement of the charged component of the underlying event using the novel >jet-area/median> approach is presented for proton-proton collisions at centre-of-mass energies of 0.9 and 7 TeV. The data were recorded in 2010 with the CMS experiment at the LHC. A new observable, sensitive to soft particle production, is introduced and investigated inclusively and as a function of the event scale defined by the transverse momentum of the leading jet. Various phenomenological models are compared to data, with and without corrections for detector effects. None of the examined models describe the data satisfactorily. © 2012 SISSA.Acknowledge support from BMWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES (Croatia); RPF (Cyprus); MoER, SF0690030s09 and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France);BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NKTH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); NRF and WCU (Korea); LAS (Lithuania); CINVESTAV, CONACYT, SEP, and UASLP-FAI (Mexico); MSI (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Armenia, Belarus, Georgia, Ukraine, Uzbekistan); MON, RosAtom, RAS and RFBR (Russia); MSTD (Serbia); SEIDI and CPAN (Spain); Swiss Funding Agencies (Switzerland); NSC (Taipei); ThEP, IPST and NECTEC (Thailand); TUBITAK and TAEK (Turkey); NASU (Ukraine); STFC (United Kingdom); DOE and NSF (USA). Individuals have received support from the Marie-Curie program and the European Research Council (European Union); the Leventis Foundation; the A. P. Sloan Foundation; the Alexander von Humboldt Foundation; the Austrian Science Fund (FWF); the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWTBelgium); the Ministry of Education, Youth and Sports (MEYS) of Czech Republic; the Council of Science and Industrial Research, India; the Compagnia di San Paolo (Torino); and the HOMING PLUS program of Foundation for Polish Science, cofinanced from European Union, Regional Development Fund.Peer Reviewe
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