How short decoding times, stimulus dimensionality and spontaneous activity constrain the shape of tuning curves: A speed-accuracy trade-off
According to the efficient coding hypothesis, sensory neurons are adapted to provide maximal information about the environment given some biophysical constraints. Early sensory neurons modulate their average firing rates in response to some features of the external stimulus, creating tuned responses. In early visual areas, these modulations (or tunings) are predominantly single-peaked. However, periodic tuning, as exhibited by grid cells, has been linked to a significant increase in decoding performance. Does this imply that the tuning curves in early visual areas are sub-optimal? We argue that the time scale at which neurons encode information is imperative to understanding the relative advantages of single-peaked and periodic tuning curves. Because, if decoding ability scales differently with time for the different shapes of tuning curves, the time scale at which the neurons operate becomes critical. Here, we show that the possibility of catastrophic (large) errors due to overlapping neural responses for distinct stimulus conditions creates a trade-off between decoding time and decoding ability. Unfortunately, standard theoretical measures such as Fisher information do not capture these errors. We investigate how (very) short decoding times and stimulus dimensionality affect the optimal shape of tuning curves for stimuli with finite domains. In particular, we focus on the spatial periods of the tuning curves (or the number of "peaks") for a class of circular tuning curves. We show a general trend for minimal decoding time, i.e., the shortest decoding time required to produce a statistically reliable signal, to increase with increasing Fisher information implying a trade-off between accuracy and speed. This trade-off is reinforced whenever the stimulus dimensionality is high or there is ongoing activity. Thus, given constraints on processing speed, we present normative arguments for the existence of single-peaked, rather than a periodic, tuning organization observed in early visual areas.