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. 2015 Jul 28;9:108. doi: 10.3389/fnsys.2015.00108

Figure 3.

Figure 3

Multi-dimensional population vector selectively encoding two pairs of variables at different times. Each of 20 neurons is represented by a colored arrow pointing in its preferred direction. The length of each arrow represents that neuron's firing rate. The two planes, x⊥y (tan) and u⊥v (blue), each show the individual neuron's firing rates and preferred directions projected into the two pairs of dimensions. The population vector sum (heavy black line) projected into each plane represents the population's estimate of the two pairs of variables: x and y, u and v. The black cardioid curve represents the predicted firing rates given the population vector if each neuron was ideally cosine-tuned to a given pair of variables (x and y, or u and v). The two panels (A,B) represent two different points in time. At the first time point (A), the individual neuron firing rates are related most closely to x and y, matching the idealized cosine tuning to those two variables, as represented by the cardioid in that plane. But at the second time point (B), the firing rates of the same 20 neurons are related most closely to u and v. The firing rates of these neurons may not be representing both pairs of variables equally at all points in time, but rather selectively encoding one pair of variables at each time. At either time point, if a single linear decoder were used to estimate all four dimensions—x, y, u, and v—simultaneously from the population, one pair would be estimated accurately and the other pair inaccurately. But using two different decoders—one to estimate x and y, the other to estimate u and v—and then selecting the currently decoded output by assessing which idealized model is better fit at the time, would enable more accurate decoding overall. The Supplemental Video provides an animated version of this Figure. (N.B. To illustrate a 4-dimensional space in 3-dimensions, we have made u linearly dependent on x and y in these images; but in the actual high-dimensional neural space, all four variables can be linearly independent).