Many deep neural networks have been used to solve Ising models, including
autoregressive neural networks, convolutional neural networks, recurrent neural
networks, and graph neural networks. Learning a probability distribution of
energy configuration or finding the ground states of a disordered, fully
connected Ising model is essential for statistical mechanics and NP-hard
problems. Despite tremendous efforts, a neural network architecture with the
ability to high-accurately solve these fully connected and extremely
intractable problems on larger systems is still lacking. Here we propose a
variational autoregressive architecture with a message passing mechanism, which
can effectively utilize the interactions between spin variables. The new
network trained under an annealing framework outperforms existing methods in
solving several prototypical Ising spin Hamiltonians, especially for larger
spin systems at low temperatures. The advantages also come from the great
mitigation of mode collapse during the training process of deep neural
networks. Considering these extremely difficult problems to be solved, our
method extends the current computational limits of unsupervised neural networks
to solve combinatorial optimization problems.

我们提出了一种具有消息传递机制的变分自回归体系结构，在一个退火框架下进行训练。该网络在解决几个典型的伊辛自旋哈密顿量方面表现优于现有方法，尤其是在低温下的更大自旋系统。我们的方法将无监督神经网络在解决组合优化问题方面推广到了当前的计算限制的范围内。

消息传递变分自回归网络求解棘手伊辛模型

Message Passing Variational Autoregressive Network for Solving  Intractable Ising Models

By investigating iterative methods for a constrained linear model, we propose
a new class of fully connected V-cycle MgNet for long-term time series
forecasting, which is one of the most difficult tasks in forecasting. MgNet is
a CNN model that was proposed for image classification based on the multigrid
(MG) methods for solving discretized partial differential equations (PDEs). We
replace the convolutional operations with fully connected operations in the
existing MgNet and then apply them to forecasting problems. Motivated by the
V-cycle structure in MG, we further propose the FV-MgNet, a V-cycle version of
the fully connected MgNet, to extract features hierarchically. By evaluating
the performance of FV-MgNet on popular data sets and comparing it with
state-of-the-art models, we show that the FV-MgNet achieves better results with
less memory usage and faster inference speed. In addition, we develop ablation
experiments to demonstrate that the structure of FV-MgNet is the best choice
among the many variants.

该论文提出了一种新型的全连接 V-cycle MgNet，它是用于长期时间序列预测的迭代方法，并取得了比现有最先进模型更好的预测结果。

FV-MgNet: 可解释时间序列预测的全连接 V 循环 MgNet

FV-MgNet: Fully Connected V-cycle MgNet for Interpretable Time Series Forecasting

Deep Neural Networks are robust to minor perturbations of the learned network
parameters and their minor modifications do not change the overall network
response significantly. This allows space for model stealing, where a
malevolent attacker can steal an already trained network, modify the weights
and claim the new network his own intellectual property. In certain cases this
can prevent the free distribution and application of networks in the embedded
domain. In this paper, we propose a method for creating an equivalent version
of an already trained fully connected deep neural network that can prevent
network stealing: namely, it produces the same responses and classification
accuracy, but it is extremely sensitive to weight changes.

本文提出了一种方法，通过使深度神经网络对权重变化非常敏感，创建一个等效的神经网络模型，从而防止模型盗窃，这个等效模型具有与原来模型相同的响应和分类准确性。