Time representation in neural network models trained to perform interval timing tasks

To predict and maximize future rewards in this ever-changing world, animals must be able to discover the temporal structure of stimuli and then take the right action at the right time. However, we still lack a systematic understanding of the neural mechanism of how animals perceive, maintain, and use time intervals ranging from hundreds of milliseconds to multi-seconds in working memory and appropriately combine time information with spatial information processing and decision making. Here, we addressed this problem by training neural network models on four timing tasks: interval production, interval comparison, timed spatial reproduction, and timed decision making. We studied time-coding principles of the network after training, and found them consistent with existing experimental observations. We reveal that neural networks perceive time intervals through the evolution of population state along a stereotypical trajectory, maintain time intervals by line attractors along which the activities of most neurons vary monotonically with the duration of the maintained interval, and adjust the evolution speed of the state trajectory for producing or comparing time intervals. Spatial information or decision choice preserves the profiles of neuronal activities as functions of time intervals maintained in working memory or flow of time, and is coded in the amplitudes of these profiles. Decision making is combined with time perception through two firing sequences with mutual inhibition. Our work discloses fundamental principles of the neuronal coding of time that supports the brain for flexible temporal processing. These principles facilitate generalizable decoding of time and non-time information.