Equilibrium propagation is a recently introduced method to use and train
artificial neural networks in which the network is at the minimum (more
generally extremum) of an energy functional. Equilibrium propagation has shown
good performance on a number of benchmark tasks. Here we extend equilibrium
propagation in two directions. First we show that there is a natural quantum
generalization of equilibrium propagation in which a quantum neural network is
taken to be in the ground state (more generally any eigenstate) of the network
Hamiltonian, with a similar training mechanism that exploits the fact that the
mean energy is extremal on eigenstates. Second we extend the analysis of
equilibrium propagation at finite temperature, showing that thermal
fluctuations allow one to naturally train the network without having to clamp
the output layer during training. We also study the low temperature limit of
equilibrium propagation.

均衡传播是最近介绍的一种使用和训练人工神经网络的方法，在该方法中，网络处于能量泛函的极小值（更一般地是极值）状态。均衡传播在许多基准任务上显示出良好的性能。本文将均衡传播在两个方面进行了扩展。首先，我们展示了均衡传播的一个自然量子泛化，其中量子神经网络被认为处于网络哈密顿算子的基态（更一般地说是任意的特征态）状态，并利用了均能量在特征态上的极值训练机制。其次，我们扩展了均衡传播的温度有限的分析，显示了热波动使得在训练过程中无需夹紧输出层的网络自然训练。我们还研究了均衡传播的低温极限。

平衡传播：量子和热力学案例

Equilibrium Propagation: the Quantum and the Thermal Cases

We analyze a sample of optical light curves for 100 quasars, 70 of which have
black hole mass estimates. Our sample is the largest and broadest used yet for
modeling quasar variability. The sources in our sample have z < 2.8 and 10^6 <
M_BH < 10^10. We model the light curves as a continuous time stochastic
process, providing a natural means of estimating the characteristic time scale
and amplitude of quasar variations. We employ a Bayesian approach to estimate
the characteristic time scale and amplitude of flux variations; our approach is
not affected by biases introduced from discrete sampling effects. We find that
the characteristic time scales strongly correlate with black hole mass and
luminosity, and are consistent with disk orbital or thermal time scales. In
addition, the amplitude of short time scale variations is significantly
anti-correlated with black hole mass and luminosity. We interpret the optical
flux fluctuations as resulting from thermal fluctuations that are driven by an
underlying stochastic process, such as a turbulent magnetic field. In addition,
the intranight variations in optical flux implied by our empirical model are <
0.02 mag, consistent with current microvariability observations of radio-quiet
quasars. Our stochastic model is therefore able to unify both long and short
time scale optical variations in radio-quiet quasars as resulting from the same
underlying process, while radio-loud quasars have an additional variability
component that operates on time scales < 1 day.

本文研究了光变曲线在几十个类星体中的特征，并使用贝叶斯方法估算了特征时间尺度与振幅，进一步探讨了短时间尺度变化与黑洞质量和亮度的反相关性以及光学流量波动的成因和机制。

类星体光学流量的变化是否由热波动驱动？

Are the Variations in Quasar Optical Flux Driven by Thermal  Fluctuations?

We present a mechanistic model for a Newtonian fluid called fluid particle
dynamics. By analyzing the concept of ``fluid particle'' from the point of view
of a Voronoi tessellation of a molecular fluid, we propose an heuristic
derivation of a dissipative particle dynamics algorithm that incorporates shear
forces between dissipative particles. The inclusion of these non-central shear
forces requires the consideration of angular velocities of the dissipative
particles in order to comply with the conservation of angular momentum. It is
shown that the equilibrium statistical mechanics requirement that the linear
and angular velocity fields are Gaussian is sufficient to construct the random
thermal forces between dissipative particles. The proposed algorithm is very
similar in structure to the (isothermal) smoothed particle dynamics algorithm.
In this way, this work represents a generalization of smoothed particle
dynamics that incorporates consistently thermal fluctuations and exact angular
momentum conservation. It contains also the dissipative particle dynamics
algorithm as a special case. Finally, the kinetic theory of the dissipative
particles is derived and explicit expressions of the transport coefficients of
the fluid in terms of model parameters are obtained. This allows to discuss
resolution issues for the model.

本文提出了一种基于分子流体的 Voronoi 镶嵌概念的流体粒子动力学机制模型，并推导出具有剪切力的耗散粒子动力学算法，该算法结构类似于标准的平滑粒子动力学算法，并可一般化热力学涨落、精确角动量守恒等；最后，对耗散粒子的动力学理论进行了推导，以参数化的形式提出了流体运输系数的显式表达式。