A Neurocomputational Account of Ecologically Plausible, Flexible Timing with Legendre Memory

2nd Annual Conference of the Timing Research Forum, 2019

Joost de Jong, Aaron R. Voelker, Hedderik van Rijn, Terrence C. Stewart, Chris Eliasmith


Most computational models of timing rely on well-defined start- and stop-signals, however, these are quite rare in our natural environments. Moreover, theories typically propose different mechanisms to account for retrospective and prospective timing, an assumption that is difficult to align with naturalistic, continuative types of timing. Here we propose a spiking recurrent neural network model of flexible human timing behavior: Legendre Memory Timing (LMT). Our model continually and optimally represents the history of its input by compressing the input into a q-dimensional state, consisting of Legendre polynomials. At any point in time, the network represents a rolling window of its input history that spans from the current time to θ seconds in the past and uses this window to assess time (Voelker & Eliasmith, 2018). Where previous models require constrained ramping, decaying, or oscillating neural activity, our model is not restricted to a single firing pattern, but - consistent with available experimental data from monkeys (Wang, Narain, Hosseini, and Jazayeri, 2018) - utilizes heterogeneous firing patterns in individual spiking neurons that temporally scale with the timed interval. Without an explicit clock, or any specific clock-focussed assumptions, this model accounts for a number of key timing phenomena. For example, the scalar property naturally arises from our model and is functionally linked to the numbers of dimensions that are used to represent input history. Moreover, the model explains why constant standard deviation may be observed for well-trained subjects (e.g., Fetterman & Killeen, 1992). The model suggests that the scalar property and neural scaling are tightly linked: inter-trial variability in timing responses are correlated with inter-trial variability in neural scaling. In doing so, the model explains how accurate timing performance, both prospective and retrospective, may be accomplished in more ecological settings without relying on clear start- and stop-signals (van Rijn, 2018).

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2nd Annual Conference of the Timing Research Forum
Querétaro, México


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