arXiv subjects

Simone Rossi

Publications and source records attributed to Simone Rossi.

24 records · Page 2Linked to original sources

arXiv2020

Walsh-Hadamard Variational Inference for Bayesian Deep Learning

Over-parameterized models, such as DeepNets and ConvNets, form a class of models that are routinely adopted in a wide variety of applications, and for which Bayesian inference is desirable but extremely challenging. Variational inference offers the tools to tackle this challenge in a scalable way and with some degree of flexibility on the approximation, but for over-parameterized models this is challenging due to the over-regularization property of the variational objective. Inspired by the literature on kernel methods, and in particular on structured approximations of distributions of random matrices, this paper proposes Walsh-Hadamard Variational Inference (WHVI), which uses Walsh-Hadamard-based factorization strategies to reduce the parameterization and accelerate computations, thus avoiding over-regularization issues with the variational objective. Extensive theoretical and empirical analyses demonstrate that WHVI yields considerable speedups and model reductions compared to other techniques to carry out approximate inference for over-parameterized models, and ultimately show how advances in kernel methods can be translated into advances in approximate Bayesian inference.

stat.ML↗

arXiv2020

Magneto-optical determination of the carrier lifetime in coherent Ge(1-x)Sn(x)/Ge heterostructures

We present a magneto-optical study of the carrier dynamics in compressively strained Ge(1-x)Sn(x) films having Sn compositions up to 10% epitaxially grown on blanket Ge on Si (001) virtual substrates. We leverage the Hanle effect under steady-state excitation to study the spin-dependent optical transitions in presence of an external magnetic field. This allowed us to obtain direct access to the dynamics of the optically-induced carrier population. Our approach singled out that at cryogenic temperatures the effective lifetime of the photogenerated carriers in coherent Ge(1-x)Sn(x) occurs in the sub-ns time scale. Supported by a model estimate of the radiative lifetime, our measurements indicate that carrier recombination is dominated by non-radiative processes. Our results thus provide central information to advance the fundamental understanding of carrier kinetics in this novel direct-gap group-IV material system. Such knowledge can be a stepping stone in the quest for the implementation of Ge(1-x)Sn(x)-based functional devices.

physics.optics↗

arXiv2020

Stabilization approaches for the hyperelastic immersed boundary method for problems of large-deformation incompressible elasticity

The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses Lagrangian coordinates to describe the structural deformations, stresses, and resultant forces. Integral transforms with Dirac delta function kernels connect the Eulerian and Lagrangian frames. The fluid and the structure are both typically treated as incompressible materials. Upon discretization, however, the incompressibility of the structure is only maintained approximately. To obtain an immersed method for incompressible hyperelastic structures that is robust under large structural deformations, we introduce a volumetric energy in the solid region that stabilizes the formulation and improves the accuracy of the numerical scheme. This formulation augments the discrete Lagrange multiplier for the incompressibility constraint, thereby improving the original method's accuracy. This volumetric energy is incorporated by decomposing the strain energy into isochoric and dilatational components, as in standard solid mechanics formulations of nearly incompressible elasticity. We study the performance of the stabilized method using several quasi-static solid mechanics benchmarks, a dynamic fluid-structure interaction benchmark, and a detailed three-dimensional model of esophageal transport. The accuracy achieved by the stabilized immersed formulation is comparable to that of a stabilized finite element method for incompressible elasticity using similar numbers of structural degrees of freedom.

math.NA↗

arXiv2019

Efficient Approximate Inference with Walsh-Hadamard Variational Inference

Variational inference offers scalable and flexible tools to tackle intractable Bayesian inference of modern statistical models like Bayesian neural networks and Gaussian processes. For largely over-parameterized models, however, the over-regularization property of the variational objective makes the application of variational inference challenging. Inspired by the literature on kernel methods, and in particular on structured approximations of distributions of random matrices, this paper proposes Walsh-Hadamard Variational Inference, which uses Walsh-Hadamard-based factorization strategies to reduce model parameterization, accelerate computations, and increase the expressiveness of the approximate posterior beyond fully factorized ones.

stat.ML↗

arXiv2019

Good Initializations of Variational Bayes for Deep Models

Stochastic variational inference is an established way to carry out approximate Bayesian inference for deep models. While there have been effective proposals for good initializations for loss minimization in deep learning, far less attention has been devoted to the issue of initialization of stochastic variational inference. We address this by proposing a novel layer-wise initialization strategy based on Bayesian linear models. The proposed method is extensively validated on regression and classification tasks, including Bayesian DeepNets and ConvNets, showing faster and better convergence compared to alternatives inspired by the literature on initializations for loss minimization.

stat.ML↗

arXiv2017

Incorporating Inductances in Tissue-Scale Models of Cardiac Electrophysiology

In standard models of cardiac electrophysiology, including the bidomain and monodomain models, local perturbations can propagate at infinite speed. We address this unrealistic property by developing a hyperbolic bidomain model that is based on a generalization of Ohm's law with a Cattaneo-type model for the fluxes. Further, we obtain a hyperbolic monodomain model in the case that the intracellular and extracellular conductivity tensors have the same anisotropy ratio. In one spatial dimension, the hyperbolic monodomain model is equivalent to a cable model that includes axial inductances, and the relaxation times of the Cattaneo fluxes are strictly related to these inductances. A purely linear analysis shows that the inductances are negligible, but models of cardiac electrophysiology are highly nonlinear, and linear predictions may not capture the fully nonlinear dynamics. In fact, contrary to the linear analysis, we show that for simple nonlinear ionic models, an increase in conduction velocity is obtained for small and moderate values of the relaxation time. A similar behavior is also demonstrated with biophysically detailed ionic models. Using the Fenton-Karma model along with a low-order finite element spatial discretization, we numerically analyze differences between the standard monodomain model and the hyperbolic monodomain model. In a simple benchmark test, we show that the propagation of the action potential is strongly influenced by the alignment of the fibers with respect to the mesh in both the parabolic and hyperbolic models when using relatively coarse spatial discretizations. Accurate predictions of the conduction velocity require computational mesh spacings on the order of a single cardiac cell. We also compare the two formulations in the case of spiral break up and atrial fibrillation in an anatomically detailed model of the left atrium, and [...].

math.NA↗