Modeling Interval Timing by Recurrent Neural Nets - Raphan, Theodore; Dorokhin, Eugene; Delamater, Andrew R. (Frontiers in Integrative Neuroscience, 2019)
We studied how recurrent neural nets (RNN), which utilize delayed feedback weights, could model the encoding of time at the supra-second level. Recurrent “Go” and “No-Go” neural processing units with different dynamics were identified whose outputs were summated to generate a pulse that drives a fixed integrator unit. This system was used to model empirical data from rodents performing in an instrumental “peak interval timing” task for Tone and Flash inputs. Reward availability was signaled after different times from stimulus onset during training. Rodent performance was assessed on non-rewarded trials, following training, with each stimulus tested individually and simultaneously in a stimulus compound. The weights in the Go/No-Go network were trained using experimentally obtained mean distribution of bar press rates across an 80 s period. The rewards for tone and flash were given 5 s and 30 s from stimulus onset, respectively. Different Go/No-Go systems were used for each stimulus, but the weighted output of each fed into a final common recurrent integrator unit, whose weights were unmodifiable. The RNN was implemented and trained in Matlab using the data from non-rewarded trials. The neural net output accurately fit the temporal distribution of tone and flash-initiated bar press data. A “Temporal Averaging” effect was obtained when the flash and tone stimuli were combined. Average auto-correlation functions for the tone, flash and compound responses and cross-correlations between their pairwise combinations confirmed that the peaks and variances of the three response functions significantly differed, with the compound being intermediate between tone and flash but somewhat more similar to flash than tone. Combining tone and flash responses were not superposed as in a linear system. Rather, implementation of nonlinear “saliency functions” that limited the output signal of each stimulus to the final integrator when the other was co-present better fit the data. The model suggests that the brain encodes timing through connection weights of a dynamic RNN. Thus, event timing is coded similar to the way other sensory-motor systems, such as the vestibulo-ocular and optokinetic systems combine sensory inputs from the vestibular and visual systems to generate the temporal aspects of compensatory eye movements.