A geometric interpretation of indoor MIMO systems using a deterministic model

This paper is a step towards developing a geometric understanding of a popular algorithm for training deep neural networks named stochastic gradient descent (SGD). We built upon a recent result which observed that the noise in SGD while training typical networks is highly non-isotropic. That motivated a deterministic model in which the trajectories of our dynamical systems are described via geodesics of a family of metrics arising from a certain diffusion matrix; namely, the covariance of the stochastic gradients in SGD. Our model is analogous to models in general relativity: the role of the electromagnetic field in the latter is played by the gradient of the loss function of a deep network in the former.

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Analysis of array geometries for indoor MIMO systems using a deterministic model

2012 Loughborough Antennas & Propagation Conference (LAPC) ◽

10.1109/lapc.2012.6403014 ◽

2012 ◽

Cited By ~ 1

Author(s):

A. Grennan ◽

M. Davis ◽

C. Downing

Keyword(s):

Deterministic Model ◽

Mimo Systems

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Mathematical simulation of error functions of decision-making at tolerance control of measuring techniques availability

Metrologiya ◽

10.32446/0132-4713.2020-3-3-15 ◽

2020 ◽

pp. 3-15

Author(s):

Rustam Z. Khayrullin ◽

Alexey S. Kornev ◽

Andrew A. Kostoglotov ◽

Sergey V. Lazarenko

Keyword(s):

Measurement Error ◽

Geometric Interpretation ◽

Measuring Instruments ◽

Measured Quantity ◽

Metrological Examination ◽

Technical Documentation ◽

Error Functions ◽

Measuring Techniques ◽

Tolerance Control ◽

Laws Of Distribution

Analytical and computer models of false failure and undetected failure (error functions) were developed with tolerance control of the parameters of the components of the measuring technique. A geometric interpretation of the error functions as two-dimensional surfaces is given, which depend on the tolerance on the controlled parameter and the measurement error. The developed models are applicable both to theoretical laws of distribution, and to arbitrary laws of distribution of the measured quantity and measurement error. The results can be used in the development of metrological support of measuring equipment, the verification of measuring instruments, the metrological examination of technical documentation and the certification of measurement methods.

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Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2005.10.4.15116 ◽

2005 ◽

Vol 10 (4) ◽

pp. 365-381 ◽

Cited By ~ 1

Author(s):

Š. Repšys ◽

V. Skakauskas

Keyword(s):

Population Dynamics ◽

Numerical Analysis ◽

Population Model ◽

Local Stability ◽

Deterministic Model ◽

Random Mating ◽

Spatial Diffusion ◽

Neumann Problems ◽

Structured Population ◽

Structured Population Dynamics

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.

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