Figure 1.

Theory of scale-invariant temporal context and neurophysiological evidence. A. A method for constructing a scale-invariant timeline. Top: an input function through time. Middle: a set of units retains the Laplace transform of the input function up to that point. Different lines are units with different time constants, corresponding to different values of the (real) Laplace domain variable. Bottom: By approximating the inverse Laplace transform a set of cells constructs an estimate of the history of the input function up to that point. Three units corresponding to different parts of a compressed timeline are shown. These units respond a characteristic time after the input was presented. Because the timeline decreases in accuracy as it recedes into the past, the “time fields” of these cells grow wider and the number of cells with time fields decreases as the delay goes on. After [48]. B. Neurophysiological observation of time cells with the qualitative properties predicted by theoretical work. Left: Firing rate properties of neurons in rodent CA1. These cells fire sequentially during the delay of a memory experiment, with increasing width of the time fields as the sequence goes on. After [49]. Right: Width of time fields as a function of the center location in various brain regions in rat. The theoretical framework in [50] predicts a linear increase. Clockwise from top left, rodent hippocampus (different colors for CA1 vs CA3) [51], rodent medial entorhinal cortex (different colors show grid cells vs non-grid cells [52], medial prefrontal cortex [53], and striatum (different colors are different delay durations) [54].