Figure 7. Distribution of preferred directions and invariance of representation across workspaces.

(A) Adopted from Prud’homme and Kalaska, 1994; distribution of preferred directions in primate S1. (B) Distribution of preferred directions for spindle input. (C) Distribution of preferred directions for one spatial-temporal model instantiation (all units with ${\displaystyle R^2>0.2}$ are included). Bottom: the corresponding untrained model. For visibility, all histograms are scaled to the same size and the colors indicate the number of tuned neurons. (D) For quantifying uniformity, we calculated the total absolute deviation from the corresponding uniform distribution over the bins in the histogram (red line in inset) for the spatial-temporal model (left), the spatiotemporal model (middle), and the long short-term memory (LSTM) model (right). Normalized absolute deviation from uniform distribution for preferred directions per instantiation is shown ($N=5$, faint lines) for trained and untrained models as well as mean and 95% confidence intervals over instantiations (solid line; $N=5$). Note that there is no data for layers 7 and 8 of the trained spatial-temporal model, layer 8 of the untrained spatial-temporal model, and layer 4 of the spatiotemporal model as they have no direction-selective units (${\displaystyle R^2>0.2}$). (E) For quantifying invariance, we calculated mean absolute deviation in preferred orientation for units from the central plane to each other vertical plane (for units with ${\displaystyle R^2>0.2}$). Results are shown for each instantiation ($N=5$, faint lines) for trained and untrained models plus mean (solid) and 95% confidence intervals over instantiations ($N=5$). Note that there is no data for layer 4 of the trained spatiotemporal model, as it has no direction-selective units (${\displaystyle R^2>0.2}$).

Figure 7—figure supplement 1. Invariance of preferred orientations.

(A) To quantify invariance, we calculated mean absolute deviation in preferred orientation for units from a central plane at $z=0$ to each other horizontal plane (for units with ${\displaystyle R^2>0.2}$). Results are shown for each instantiation ($N=5$, faint lines) for trained and untrained models plus mean (solid) and 95% confidence intervals over instantiations ($N=5$) for the spatial-temporal (left), spatiotemporal (right), and long short-term memory (LSTM) (right) networks. Note that there is no data for layer 4 of the trained spatiotemporal model, as it has no direction-selective units (${\displaystyle R^2>0.2}$). (B) Deviation in preferred direction for individual spindles (N=25). The preferred directions are fit for each plane and displayed in relation to a central horizontal (left) and vertical plane (right). Individual gray lines are for all units (spindles) with ${\displaystyle R^2>0.2}$, the thick red line marks the mean. (C) Same as (B), but for direction tuning in vertical planes for units in layer 5 of one instantiation of the best spatial-temporal model for the trained (left) and untrained model (right). Individual gray lines are for units with ${\displaystyle R^2>0.2}$, and the red line is the plane-wise mean. (D) Same as in (B) but for layer 5 of the trained spatial-temporal network. (E) Same as in (D) but for layer 5 of the corresponding untrained network.