发表机构
Centro de Modelamiento Matemático (CMM)（数学建模中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究玻尔兹曼机在多数规则下恢复系统的生成能力，通过训练不同配置的深度信念网络，让其根据固定可见单元生成样本并测量偏差，还用离散温度计证实重建处于临界状态，表明DBN能恢复有噪声下仍临界的样本。
AI 中文摘要
我们研究玻尔兹曼机在临界条件下恢复受多数规则支配系统的生成能力。为此，我们训练不同配置的深度信念网络（DBN），其第一层可使用具有两个以上状态的高斯可见单元。然后让DBN根据固定的可见单元‘生成’样本，并测量生成系统与真实系统的偏差。我们还用基于卷积网络的离散温度计证实重建仍处于临界状态。结果表明，尽管问题复杂，DBN能恢复即使在输入噪声下仍保持临界的样本，且物理可观测量相对于原始样本逐渐退化。
英文摘要
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.
