用深度信念网络模拟符合多数规则的临界社会系统，可稳定生成临界态样本。
Exploration of the generative capabilities of Boltzmann machines applied to social systems under the majority rule
- 采用含非二元可见单元的DBN建模，通过条件“梦境”生成新样本。
- 生成样本在输入噪声下仍保持临界态，物理可观测量缓慢退化。
- 适合研究临界相变与复杂系统建模的科研人员参考。
我们研究了玻尔兹曼机在临界条件下恢复受多数规则支配的社会系统的生成能力。为此，训练了具有不同配置的深度信念网络（DBNs），其中第一层使用超过两个状态的高斯可见单元（即非二元单元）。随后，让DBN在固定可见单元条件下“做梦”，生成样本，并测量其与真实系统的偏差。同时，利用基于卷积网络的离散温度计验证重建样本仍处于临界态。在多次不同架构的训练中，尽管问题复杂，DBN仍能恢复保持临界性的样本，即使在输入噪声下也表现出渐进式的物理可观测量退化，表明其具备良好的鲁棒性与生成稳定性。
原文摘要 · Abstract (English)
We study the generative capabilities of Boltzmann machines to recover systems governed by the majority rule under critical conditions. To this end, we train deep belief networks (DBNs) with different configurations, where the first layer can use Gaussian visible units with more than two states (i.e., non-binary units). We then allow the DBN to "dream" samples conditioned on visible units that we keep fixed, and we measure the deviation of this dreamed system from the real one. We also corroborate, using a discrete thermometer based on a convolutional network, that the reconstructions remain in a critical state. Across several training sessions with different architectures, we show that, despite the complexity of the problem, the DBN can recover samples that remain critical even under input noise, with a gradual degradation of physical observables relative to the original sample.
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