Valente Adrian, Ostojic Srdjan, Pillow Jonathan W
Laboratoire de Neurosciences Cognitives et Computationnelles, INSERM U960, Ecole Normale Superieure-PSL Research University, 75005 Paris, France
Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, U.S.A.
Neural Comput. 2022 Aug 16;34(9):1871-1892. doi: 10.1162/neco_a_01522.
A large body of work has suggested that neural populations exhibit low-dimensional dynamics during behavior. However, there are a variety of different approaches for modeling low-dimensional neural population activity. One approach involves latent linear dynamical system (LDS) models, in which population activity is described by a projection of low-dimensional latent variables with linear dynamics. A second approach involves low-rank recurrent neural networks (RNNs), in which population activity arises directly from a low-dimensional projection of past activity. Although these two modeling approaches have strong similarities, they arise in different contexts and tend to have different domains of application. Here we examine the precise relationship between latent LDS models and linear low-rank RNNs. When can one model class be converted to the other, and vice versa? We show that latent LDS models can only be converted to RNNs in specific limit cases, due to the non-Markovian property of latent LDS models. Conversely, we show that linear RNNs can be mapped onto LDS models, with latent dimensionality at most twice the rank of the RNN. A surprising consequence of our results is that a partially observed RNN is better represented by an LDS model than by an RNN consisting of only observed units.
大量研究表明，神经群体在行为过程中表现出低维动力学。然而，对于低维神经群体活动的建模存在多种不同方法。一种方法涉及潜在线性动力系统（LDS）模型，其中群体活动通过具有线性动力学的低维潜在变量的投影来描述。第二种方法涉及低秩递归神经网络（RNN），其中群体活动直接源于过去活动的低维投影。尽管这两种建模方法有很强的相似性，但它们出现在不同的背景下，并且往往有不同的应用领域。在这里，我们研究潜在LDS模型与线性低秩RNN之间的确切关系。在什么情况下一种模型类别可以转换为另一种，反之亦然？我们表明，由于潜在LDS模型的非马尔可夫性质，潜在LDS模型只能在特定的极限情况下转换为RNN。相反，我们表明线性RNN可以映射到LDS模型上，潜在维度最多为RNN秩的两倍。我们结果的一个惊人结果是，部分观测到的RNN由LDS模型表示比由仅由观测单元组成的RNN更好。
