Fig. 4.

Decoding generalizability. (A) A schematic that explains Decoder 1 and Decoder 2. The decoders read the value of $a$ through state ${\mathbf{f}}_0$ in iso-$b$ line $\mathbf{f}\left(a;b_{test}\right)$ (green) after being trained by another iso-$b$ line $\mathbf{f}\left(a;b_{train}\right)$ (orange). Decoder 1 reads $a$ to be the same as that of ${\mathbf{f}}_1$ because ${\mathbf{f}}_0$ and ${\mathbf{f}}_1$ project to the same point on PC1 (black horizontal line) of $\mathbf{f}\left(a;b_{train}\right)$. Decoder 2 first translationally moves $\mathbf{f}\left(a;b_{test}\right)$ so that its mass center $\mathcal{T}\left(O\right)$ after translational movement $\mathcal{T}$ projects to the same point as the mass center $O_{train}$ of $\mathbf{f}\left(a;b_{train}\right)$ on PC1 and then reads $a$ according to $\mathcal{T}\left({\mathbf{f}}_0\right)$, which is the $a$ value of ${\mathbf{f}}_2$. (B) Two error sources of Decoder 1. (B, Upper) The mass centers $O$ and $O_{train}$ do not project to the same point on PC1. (B, Lower) The projections of $\mathbf{f}\left(a;b_{train}\right)$ and $\mathbf{f}\left(a;b_{test}\right)$ on PC1 (lines $A_{train}{B}_{train}$ and $A_{test}{B}_{test}$) do not have the same length. (C) The error of Decoder 1 (indicated by dot color) to read temporal flow across different spatial locations as a function of the angle (AG) and mixed variance (MV) between the temporal flow and spatial subspaces in the production epoch of t-SR task. (D) Correlations between decoding error (DE) and AG and between DE and MV. (E and F) The same as C and D except for Decoder 2. (G) DE as a function of $|x_{train}-x_{test}|$ after Decoder 1 (solid line) or Decoder 2 (dashed line) is trained to read the temporal flow using the isospace line at spatial location $x_{train}$ and then tested at spatial location $x_{test}$. The horizontal dashed line indicates chance level, supposing that the decoder works by random guess. Error bars represent mean $\pm$ SEM across simulation trials. C–F analyze the data averaging over $|x_{train}-x_{test}|$ in individual training configurations. $T=\mathrm{1,200}$ ms. Decoding generalizability in other epochs of the t-SR task and the t-DM task is shown in SI Appendix, Figs. S7 and S8.