Fixed points of recurrent neural networks can be leveraged to store and generate information. These fixed points can be captured by the Boltzmann-Gibbs measure, which leads to neural Langevin dynamics that can be used to find them for generative learning of a real dataset. We call this type of generative model a neural Langevin machine, which derives an asymmetric and firing-rate-speed adjusted learning rule requiring only local neural signals, thereby bearing biological relevance in terms of local predictive learning. An interesting out-of-equilibrium regime of the generative process is revealed, together with a memorization-to-generalization transition with increasing training data size. The neuro-inspired machine can also realize a continuous exploration of the phase space for different kinds of generative images and can denoise a corrupted image as well.

翻译：递归神经网络的固定点可用于存储和生成信息。这些固定点可通过玻尔兹曼-吉布斯测度捕获，从而导出能用于寻找这些固定点的神经朗之万动力学，进而实现对真实数据集的生成式学习。我们将此类生成模型称为神经朗之万机，其推导出仅需局部神经信号的非对称且发放速率可调的学习规则，因此在局部预测学习方面具有生物学相关性。该生成过程揭示了一个有趣的非平衡态机制，以及随训练数据量增加而出现的从记忆到泛化的转变。这种神经启发式机器还能实现相空间中的连续探索以生成不同类型的图像，并同样能够对受损图像进行去噪处理。