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Relaxing Bijectivity Constraints with Continuously Indexed Normalising Flows [article]

Rob Cornish, Anthony L. Caterini, George Deligiannidis, Arnaud Doucet
2021 arXiv   pre-print
To address this, we propose Continuously Indexed Flows (CIFs), which replace the single bijection used by normalising flows with a continuously indexed family of bijections, and which can intuitively "  ...  We show that normalising flows become pathological when used to model targets whose supports have complicated topologies.  ...  Continuously Indexed Flows In this section we propose continuously indexed flows (CIFs) for relaxing the bijectivity of standard normalising flows.  ... 
arXiv:1909.13833v5 fatcat:4njrgtpwfnhoxj2zbk3hdftypi

On Purely Mechanical Simple Kinematic Internal Constraints

Adam Zdunek
2019 Journal of elasticity  
The involved relaxation of internal constraints is briefly illustrated herein.  ...  The classic purely mechanical approach to materials with simple kinematic internal constraints is supplemented.  ...  It is assumed to be bijective and continuously differentiable with respect to the time parameter t as many times as needed. The tangent map is the linear transformation F := Grad ϕ : T X P 0 → T x P.  ... 
doi:10.1007/s10659-019-09747-7 fatcat:y634zfjpaveptcgkzs4kq7ixe4

Reliable Categorical Variational Inference with Mixture of Discrete Normalizing Flows [article]

Tomasz Kuśmierczyk, Arto Klami
2021 arXiv   pre-print
In practice, selecting the amount of relaxation is difficult and one needs to optimize an objective that does not align with the desired one, causing problems especially with models having strong meaningful  ...  Continuous relaxations, such as the Gumbel-Softmax for categorical distribution, enable gradient-based optimization, but do not define a valid probability mass for discrete observations.  ...  Relaxing bijectivity constraints with continuously indexed normalising flows. arXiv:1909.13833, 2019.  ... 
arXiv:2006.15568v2 fatcat:delvtnvefrflno5tyt7bzpd2ei

Dissipative structures in magnetorotational turbulence

Johnathan Ross, Henrik N Latter
2018 Monthly notices of the Royal Astronomical Society  
Q and cooling by Λ, a simple relaxation law Λ = θ(P − P * )/[(γ − 1)τc], where, γ is the adiabatic index, τc is a relaxation timescale, and P * is the pressure the system wants to cool to, chosen so that  ...  In Figure 8a we plot the probability distribution of D for znf256 along with a curve with the critical index.  ... 
doi:10.1093/mnras/sty791 fatcat:p2vukx7mwnhk5nsqmaye6bhnxi

and the triplet model

David Ridout
2010 Nuclear Physics B  
Conformal field theories with sl(2)_-1/2 symmetry are studied with a view to investigating logarithmic structures.  ...  constraints).  ...  To summarise, we have a bijective correspondence between modules and characters with a given region of convergence.  ... 
doi:10.1016/j.nuclphysb.2010.03.018 fatcat:y6urdqji7be2rgfkpoa2rtvl4y

Vocabulary Alignment in Openly Specified Interactions

Paula Daniela Chocron, Marco Schorlemmer
2020 The Journal of Artificial Intelligence Research  
In states with index 0 ≤ j < len(i), let the propositional variable for the j-th message in i be true, and all other propositional variables be false.  ...  We created pairs of compatible protocols P1, P2, with vocabular- ies V1 and V2 respectively by building a bijective alignment α : V2 → V1 and then using it to translate the constraints in a protocol P2  ... 
doi:10.1613/jair.1.11497 fatcat:mk2ipnokpjgy3fqpfkzcluksxi

Approximation of the relaxed perimeter functional under a connectedness constraint by phase-fields [article]

Patrick Dondl, Matteo Novaga, Benedikt Wirth, Stephan Wojtowytsch
2018 arXiv   pre-print
We develop a phase-field approximation of the relaxation of the perimeter functional in the plane under a connectedness constraint based on the classical Modica-Mortola functional and the connectedness  ...  constraint of (Dondl, Lemenant, Wojtowytsch 2017).  ...  Therefore, the L 1 -lower semi-continuous envelope of the perimeter functional without any additional constraints agrees with the functional itself, independently of whether the approximating sets in the  ... 
arXiv:1810.05787v1 fatcat:4xzduvoecfe7tjmcowvlnruwpu

Regularising Inverse Problems with Generative Machine Learning Models [article]

Margaret Duff, Neill D. F. Campbell, Matthias J. Ehrhardt
2022 arXiv   pre-print
Normalising flows and, more generally, invertible neural networks [45] are designed to be bijective, with forward or inverse mappings efficiently computable with a tractable Jacobian.  ...  Invertible neural networks and normalising flows are a growing field of generative modelling [49] .  ...  For P, Q, probability distributions on X , with probability density functions p and q, where P is absolutely continuous with respect to Q, the KL divergence from Q to P is defined as Parametrising the  ... 
arXiv:2107.11191v2 fatcat:xno43ggolfbclk6chsq4aiivam

Benchmarking Quantum(-inspired) Annealing Hardware on Practical Use Cases [article]

Tian Huang, Jun Xu, Tao Luo, Xiaozhe Gu, Rick Goh, Weng-Fai Wong
2022 arXiv   pre-print
Experiments suggest that both annealers are effective on problems with small size and simple settings, but lose their utility when facing problems in practical size and settings.  ...  In this paper, we benchmark quantum(-inspired) annealers with three combinatorial optimisation problems ranging from generic scientific problems to complex problems in practical use.  ...  (b) Normalised energy. All energy is normalised to that of Gurobi's. (c) The energy distribution of solutions of the problem with 5430 nodes. X axis represents normalised energy.  ... 
arXiv:2203.02325v1 fatcat:fvpg5zdu3nh3nmvvmytptpal5y

A Graph Symmetrisation Bound on Channel Information Leakage under Blowfish Privacy [article]

Tobias Edwards, Benjamin I. P. Rubinstein, Zuhe Zhang, Sanming Zhou
2021 arXiv   pre-print
A construction meeting our bound with asymptotic equality demonstrates tightness.  ...  Blowfish privacy is a recent generalisation of differential privacy that enables improved utility while maintaining privacy policies with semantic guarantees, a factor that has driven the popularity of  ...  These secrets and constraints together induce the adjacency relation on which response distribution smoothness is (relaxed) to hold on.  ... 
arXiv:2007.05975v3 fatcat:ufhhiwecnbc5xlqqklaryws34q

Dynamical Phase Transitions for Flows on Finite Graphs [article]

Davide Gabrielli, D.R. Michiel Renger
2020 arXiv   pre-print
paths of the density and flow.  ...  We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph.  ...  On the continuous torus, [0, 1] with periodic boundary conditions, we consider smooth non-negative flows and densities q(x, t), ρ(x, t) ≥ 0 such that the continuous version of the continuity equation is  ... 
arXiv:2005.03262v3 fatcat:xsz5q32p7bdv7ftg3xxvxywwrq

Quasiconformal model with CNN features for large deformation image registration [article]

Ho Law, Gary P. T. Choi, Ka Chun Lam, Lok Ming Lui
2021 arXiv   pre-print
Moreover, unlike many prior image registration methods, the bijectivity of our method is guaranteed by quasiconformal theory.  ...  Image registration has been widely studied over the past several decades, with numerous applications in science, engineering and medicine.  ...  In [22] , Horn and Schunck presented a method for registering images using optical flow.  ... 
arXiv:2011.00731v3 fatcat:xftudnfgrbbi5ggsqzv5qre73i

An objective function for order preserving hierarchical clustering [article]

Daniel Bakkelund
2022 arXiv   pre-print
We provide a demonstration on a benchmark dataset, showing that our method outperforms existing methods for order preserving hierarchical clustering with significant margin.  ...  Finding an optimal solution is NP-hard, so we provide a polynomial time approximation algorithm, with a relative performance guarantee of O(log^3/2 n ), based on successive applications of directed sparsest  ...  Element wise adjusted order Rand index.  ... 
arXiv:2109.04266v3 fatcat:7g36k4tb4jfttlnz73qo3ezkru

Symmetries and phase diagrams with real-space mutual information neural estimation [article]

Doruk Efe Gökmen, Zohar Ringel, Sebastian D. Huber, Maciej Koch-Janusz
2021 arXiv   pre-print
Here we describe in detail how these results can be combined with differentiable coarse-graining operations to develop a single unsupervised neural-network based algorithm, the RSMI-NE, efficiently extracting  ...  We acknowledge insights into the physics of the chipping and aggregation model coming from an earlier study of this system together with R. Thomale. D.E.G., S.D.H., and M.K.  ...  continuously changing with T .  ... 
arXiv:2103.16887v3 fatcat:lsmq7q6lzzbndhyjimnnrhwxlm

Iterative Bregman Projections for Regularized Transportation Problems [article]

Jean-David Benamou, Guillaume Carlier, Gabriel Peyré
2014 arXiv   pre-print
solutions of in-compressible Euler equations, partial un-balanced optimal transport and optimal transport with capacity constraints.  ...  variational problems related to optimal transport: barycenters for the optimal trans-port metric, tomographic reconstruction, multi-marginal optimal trans-port and in particular its application to Brenier's relaxed  ...  Generalized Euler Flows Brenier proposed in a series of papers [13, 14, 15] a relaxation of the Euler equation of incompressible fluids with constrained initial and final data.  ... 
arXiv:1412.5154v1 fatcat:mcvk7nsi7vhoxcbd235vmyau3i
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