Neural network perturbation theory and its application to the Born series

We evaluate the mutual information between the input and the output of a two layer network in the case of a noisy and nonlinear analogue channel. In the case where the nonlinearity is small with respect to the variability in the noise, we derive an exact expression for the contribution to the mutual information given by the nonlinear term in first order of perturbation theory. Finally we show how the calculation can be simplified by means of a diagrammatic expansion. Our results suggest that the use of perturbation theories applied to neural systems might give an insight on the contribution of nonlinearities to the information transmission and in general to the neuronal dynamics.

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Robust Linear Neural Network for Constrained Quadratic Optimization

Discrete Dynamics in Nature and Society ◽

10.1155/2017/5073640 ◽

2017 ◽

Vol 2017 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Zixin Liu ◽

Yuanan Liu ◽

Lianglin Xiong

Keyword(s):

Neural Network ◽

Numerical Simulation ◽

Perturbation Theory ◽

Optimization Problems ◽

Quadratic Optimization ◽

Linear Matrix ◽

Matrix Inequality ◽

Analysis Method ◽

Linear Neural Network ◽

Constrained Quadratic Optimization

Based on the feature of projection operator under box constraint, by using convex analysis method, this paper proposed three robust linear systems to solve a class of quadratic optimization problems. Utilizing linear matrix inequality (LMI) technique, eigenvalue perturbation theory, Lyapunov-Razumikhin method, and LaSalle’s invariance principle, some stable criteria for the related models are also established. Compared with previous criteria derived in the literature cited herein, the stable criteria established in this paper are less conservative and more practicable. Finally, a numerical simulation example and an application example in compressed sensing problem are also given to illustrate the validity of the criteria established in this paper.

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Quantum Dynamics of Water from Møller-Plesset Perturbation Theory via a Neural Network Potential

10.33774/chemrxiv-2021-n32q8-v2 ◽

2021 ◽

Author(s):

Jinggang Lan ◽

David Wilkins ◽

Vladimir Rybkin ◽

Marcella Iannuzzi ◽

Juerg Hutter

Keyword(s):

Neural Network ◽

Perturbation Theory ◽

Liquid Water ◽

Quantum Dynamics ◽

Diffusion Constant ◽

Distribution Functions ◽

Basis Set ◽

Ambient Conditions ◽

Nuclear Dynamics ◽

Moller Plesset

We report the static and dynamical properties of liquid water at the level of second-order Møller-Plesset per- perturbation theory (MP2) with classical and quantum nuclear dynamics using a neural network potential. We examined the temperature-dependent radial distribution functions, diffusion, and vibrational dynamics. MP2 theory predicts over-structured liquid water as well as a lower diffusion coefficient at ambient conditions compared to experiments, which may be attributed to the incomplete basis set. A better agreement with experimental structural properties and the diffusion constant are observed at an elevated temperature of 340 K from our simulations. Although the high-level electronic structure calculations are expensive, training a neural network potential requires only a few thousand frames. The approach is promising as it involves modest human effort and is straightforwardly extensible to other simple liquids.

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Optical Fiber Nonlinearity Equalizer Based Perturbation Theory on Deep Neural Network Classifier

10.1109/icocn53177.2021.9563641 ◽

2021 ◽

Author(s):

Chao Li ◽

Yongjun Wang ◽

Lu Han

Keyword(s):

Neural Network ◽

Perturbation Theory ◽

Optical Fiber ◽

Deep Neural Network ◽

Neural Network Classifier ◽

Fiber Nonlinearity

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Quantum Dynamics of Water from Møller-Plesset Perturbation Theory via a Neural Network Potential

10.33774/chemrxiv-2021-n32q8 ◽

2021 ◽

Author(s):

Jinggang Lan ◽

David Wilkins ◽

Vladimir Rybkin ◽

Marcella Iannuzzi ◽

Juerg Hutter

Keyword(s):

Neural Network ◽

Perturbation Theory ◽

Liquid Water ◽

Quantum Dynamics ◽

Diffusion Constant ◽

Basis Set ◽

Ambient Conditions ◽

Moller Plesset ◽

Dynamics Simulations ◽

Plesset Perturbation Theory

We report the static and dynamical properties of liquid water at second-order Møller-Plesset perturbation theory level (MP2) with classical and quantum dynamics simulations using a neural network potential. We examined the temperature-dependent radial distribution function, diffusion and vibrational dynamics. MP2 theory predicts an over-structured liquid water at ambient conditions, which may be attributed to the incomplete basis set. The excellent agreement with experimental structural properties as well as the diffusion constant is observed at an elevated temperature of 340K.

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Visualizing a neural network that develops quantum perturbation theory

Physical Review A ◽

10.1103/physreva.98.010701 ◽

2018 ◽

Vol 98 (1) ◽

Cited By ~ 5

Author(s):

Yadong Wu ◽

Pengfei Zhang ◽

Huitao Shen ◽

Hui Zhai

Keyword(s):

Neural Network ◽

Perturbation Theory ◽

Quantum Perturbation Theory

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A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

International Astronomical Union Colloquium ◽

10.1017/s025292110010805x ◽

1988 ◽

Vol 102 ◽

pp. 343-347

Author(s):

M. Klapisch

Keyword(s):

Perturbation Theory ◽

Small Parameter ◽

Classification Scheme ◽

Sum Rules ◽

Energy Levels ◽

Natural Classification ◽

Quantum Numbers ◽

Formal Expansion ◽

Atomic Energy Levels ◽

As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

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