Recurrent neural networks (RNNs) have been widely used to model sequential neural dynamics (“neural sequences”) of cortical circuits in cognitive and motor tasks. Efforts to incorporate biological constraints and Dale's principle will help elucidate the neural representations and mechanisms of underlying circuits. We trained an excitatory-inhibitory RNN to learn neural sequences in a supervised manner and studied the representations and dynamic attractors of the trained network. The trained RNN was robust to trigger the sequence in response to various input signals and interpolated a time-warped input for sequence representation. Interestingly, a learned sequence can repeat periodically when the RNN evolved beyond the duration of a single sequence. The eigenspectrum of the learned recurrent connectivity matrix with growing or damping modes, together with the RNN's nonlinearity, were adequate to generate a limit cycle attractor. We further examined the stability of dynamic attractors while training the RNN to learn two sequences. Together, our results provide a general framework for understanding neural sequence representation in the excitatory-inhibitory RNN.

Large-scale fluorescence calcium imaging methods have become widely adopted for studies of long-term hippocampal and cortical neuronal dynamics. Pyramidal neurons of the rodent hippocampus show spatial tuning in freely foraging or head-fixed navigation tasks. Development of efficient neural decoding methods for reconstructing the animal's position in real or virtual environments can provide a fast readout of spatial representations in closed-loop neuroscience experiments. Here, we develop an efficient strategy to extract features from fluorescence calcium imaging traces and further decode the animal's position. We validate our spike inference-free decoding methods in multiple in vivo calcium imaging recordings of the mouse hippocampus based on both supervised and unsupervised decoding analyses. We systematically investigate the decoding performance of our proposed methods with respect to the number of neurons, imaging frame rate, and signal-to-noise ratio. Our proposed supervised decoding analysis is ultrafast and robust, and thereby appealing for real-time position decoding applications based on calcium imaging.