Figure 6:

Universal mechanisms across architectures and datasets (see Appendix A for all other architecture-dataset combinations). Top row: comparison of left eigenvector (blue) against instantaneous effect of word input J^inpx by valence (green and red dots are positive and negative words, compare to Fig. 4a) for an example fixed point. Second row: Histogram of input projections summarizing the effect of input across fixed points (average of ${\ell }_1^{\top }{\text{J}}^{\text{inp}}\text{x}$, compare to Fig. 4c). Third row: Example fixed point (blue) shown on top of the manifold of fixed points (gray) projected into the principal components of hidden state activity, along with the corresponding top right eigenvector (compare to Fig. 4b). Bottom row: Distribution of projections of the top right eigenvector onto the manifold across fixed points (distribution of ${\mathbf{r}}_1^{\top }\mathbf{m}$, compare to Fig. 4d).