Brain-inspired recurrent spiking neural networks for multiscale dynamic representation with manifolds.

Understanding how network structure shapes neural population dynamics and representation of external inputs is a key issue in neuroscience. This study proposes a modeling framework for recurrent spiking neural networks (RSNN) and elucidates dynamical computation mechanism of RSNN by linking input dimensionality, network structure and dynamic representation. Inspired by biological neural systems, the RSNN leverages the low-rank connectivity and small-world topology for robust dynamics and efficient computation. The proposed framework is applied in behavior and recognition tasks with multiscale inputs to evaluate the representation capability of RSNN. It is found that neural computation is accomplished by high-dimensional network responses to external inputs, that can be represented by nonlinear dynamics embedded in low-dimensional manifolds. Based on computational and dynamical analysis, we show that high-dimensional neural activity can be decomposed into a steady-state component and a transient component residing in the orthogonal subspace. The steady-state component is jointly regulated by network connectivity vector and input vector, whereas the transient component is determined by topological structure. Interestingly, representation reliability is optimized when the rank of RSNN is aligned with the intrinsic dimensionality of the external input. Compared with regular and random networks, small-world topology of RSNN can largely improve the accuracy of dynamic representations. This work provides a guidance for designing brain-inspired network models with optimized structures and dynamics for efficient computation.