Laboratoire de Neurosciences Cognitives et Computationnelles, Département d'Études Cognitives, INSERM U960, École Normale Supérieure - PSL University, Paris, France.
PLoS Comput Biol. 2022 Aug 9;18(8):e1010426. doi: 10.1371/journal.pcbi.1010426. eCollection 2022 Aug.
Neural population dynamics are often highly coordinated, allowing task-related computations to be understood as neural trajectories through low-dimensional subspaces. How the network connectivity and input structure give rise to such activity can be investigated with the aid of low-rank recurrent neural networks, a recently-developed class of computational models which offer a rich theoretical framework linking the underlying connectivity structure to emergent low-dimensional dynamics. This framework has so far relied on the assumption of all-to-all connectivity, yet cortical networks are known to be highly sparse. Here we investigate the dynamics of low-rank recurrent networks in which the connections are randomly sparsified, which makes the network connectivity formally full-rank. We first analyse the impact of sparsity on the eigenvalue spectrum of low-rank connectivity matrices, and use this to examine the implications for the dynamics. We find that in the presence of sparsity, the eigenspectra in the complex plane consist of a continuous bulk and isolated outliers, a form analogous to the eigenspectra of connectivity matrices composed of a low-rank and a full-rank random component. This analogy allows us to characterise distinct dynamical regimes of the sparsified low-rank network as a function of key network parameters. Altogether, we find that the low-dimensional dynamics induced by low-rank connectivity structure are preserved even at high levels of sparsity, and can therefore support rich and robust computations even in networks sparsified to a biologically-realistic extent.
神经群体动力学通常高度协调，使得与任务相关的计算可以理解为通过低维子空间的神经轨迹。网络连接和输入结构如何产生这种活动，可以借助低秩递归神经网络来研究，这是最近开发的一类计算模型，为将底层连接结构与涌现的低维动力学联系起来提供了丰富的理论框架。该框架迄今为止依赖于全连接的假设，但众所周知，皮质网络是高度稀疏的。在这里，我们研究了连接随机稀疏化的低秩递归网络的动力学，这使得网络连接在形式上是满秩的。我们首先分析了稀疏性对低秩连接矩阵特征谱的影响，并利用这一点来研究其对动力学的影响。我们发现，在存在稀疏性的情况下，复平面中的特征谱由连续的体和孤立的离群值组成，这种形式类似于由低秩和全秩随机分量组成的连接矩阵的特征谱。这种类比使我们能够根据关键网络参数将稀疏化低秩网络的不同动力学状态进行特征化。总的来说，我们发现即使在高稀疏度下，由低秩连接结构诱导的低维动力学也能保持不变，因此即使在以生物现实的程度稀疏化的网络中，也能支持丰富而稳健的计算。
