We consider the problem of encoding pairwise correlations between coupled dynamical systems in a low-dimensional latent space based on few distinct observations. We use variational autoencoders (VAEs) to embed temporal correlations between coupled nonlinear oscillators that model brain states in the wake-sleep cycle into a two-dimensional manifold. Training a VAE with samples generated using two different parameter combinations results in an embedding that encodes the repertoire of collective dynamics, as well as the topology of the underlying connectivity network. We first follow this approach to infer the trajectory of brain states measured from wakefulness to deep sleep from the two end points of this trajectory; then, we show that the same architecture was capable of representing the pairwise correlations of generic Landau-Stuart oscillators coupled by complex network topology.

中文翻译：

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使用变分自动编码器的大脑集体动力学的生成嵌入

我们基于几个不同的观察结果，考虑了在低维潜在空间中耦合动力系统之间成对关联编码的问题。我们使用变分自动编码器（VAE）将耦合的非线性振荡器之间的时间相关性嵌入到二维流形中，该耦合的非线性振荡器对唤醒睡眠周期中的大脑状态进行建模。用使用两种不同参数组合生成的样本训练VAE会导致嵌入，该嵌入对集体动力学的组成部分以及基础连接网络的拓扑进行编码。我们首先遵循这种方法，从该轨迹的两个端点推断从觉醒到深度睡眠的大脑状态轨迹。然后，