SlowGuess/NeurIPS_2023_OCR huggingface dataset:
(b) GNN  $\psi_{\mathfrak{G}}^{\mathcal{F}'}$
Figure 31:  $\mathcal{NC}_1(\mathbf{H}),\widetilde{\mathcal{NC}}_1(\mathbf{H})$  metrics (top) and traces of covariance matrices (bottom) across 64 layers for  $\psi_{\Theta}^{\mathcal{F}}$  and  $\psi_{\Theta}^{\mathcal{F}'}$  (a,b) on D2:  $C = 2, N = 1000, p = 0.0017, q = 0.025, K(test) = 100.$
(b) GNN  $\psi_{\Theta}^{\mathcal{F}'}$
Figure 32: Ratio of traces of covariance matrices across 64 layers for GNNs  $\psi_{\Theta}^{\mathcal{F}}$  and  $\psi_{\Theta}^{\mathcal{F}'}$  (a,b) on D2:  $C = 2, N = 1000, p = 0.0017, q = 0.025, K(test) = 100$ .
(a) GNN  $\psi_{\mathcal{O}}^{\mathcal{F}}$
(b) GNN  $\psi_{\mathfrak{G}}^{\mathcal{F}'}$
Figure 33:  $\mathcal{NC}_1(\mathbf{H})$ ,  $\widetilde{\mathcal{NC}}_1(\mathbf{H})$  metrics (top) and traces of covariance matrices (bottom) across 128 layers for  $\psi_{\Theta}^{\mathcal{F}}$  and  $\psi_{\Theta}^{\mathcal{F}'}$  (a,b) on D2:  $C = 2$ ,  $N = 1000$ ,  $p = 0.0017$ ,  $q = 0.025$ ,  $K(test) = 100$ .
(a) GNN  $\psi_{\mathcal{O}}^{\mathcal{F}}$
(b) GNN  $\psi_{\Theta}^{\mathcal{F}'}$
Figure 34: Ratio of traces of covariance matrices across 128 layers for GNNs  $\psi_{\Theta}^{\mathcal{F}}$  and  $\psi_{\Theta}^{\mathcal{F}'}$  (a,b) on D2:  $C = 2, N = 1000, p = 0.0017, q = 0.025, K(test) = 100.$