# Universal Local Attractors on Graphs
## 6 Discussion
### Limitations of Cross-Entropy
\begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline
**Task** & **Eval.** & **MLP** & **GCN**[12] & **APPNP**[8] & **GAT**[13] & **GCNII**[34] & **GCNNRI**[24] & **ULA** \\ \hline \multicolumn{8}{c}{Generalization} \\ \hline Degree & acc \(\uparrow\) & 0.162 (5.6) & 0.293 (2.8) & 0.160 (6.2) & 0.166 (5.6) & 0.174 (4.6) & 0.473 (2.0) & **0.541** (1.2) \\ Triangle & acc \(\uparrow\) & 0.522 (5.2) & 0.523 (3.6) & 0.522 (5.2) & 0.522 (5.2) & 0.522 (5.2) & 0.554 (2.4) & **0.568** (1.2) \\
4 Clique & acc \(\uparrow\) & 0.678 (4.9) & 0.708 (4.1) & 0.677 (6.2) & 0.678 (4.9) & 0.678 (4.9) & 0.846 (2.0) & **0.870** (1.0) \\ LongShort & acc \(\uparrow\) & 0.347 (5.8) & 0.399 (3.0) & 0.344 (6.4) & 0.350 (4.2) & 0.348 (5.6) & 0.597 (2.0) & **0.653** (1.0) \\ Diffuse & mabs \(\downarrow\) & 0.035 (4.0) & 0.032 (2.8) & 0.067 (7.0) & 0.035 (5.0) & 0.037 (6.0) & 0.030 (2.2) & **0.012** (1.0) \\
0.9 Diffuse & mabs \(\downarrow\) & 0.021 (4.6) & 0.015 (3.0) & 0.034 (7.0) & 0.021 (4.4) & 0.021 (6.0) & 0.009 (1.8) & **0.007** (1.2) \\ Propagate & acc \(\uparrow\) & 0.531 (2.6) & 0.501 (4.0) & 0.510 (3.6) & 0.455 (6.1) & 0.443 (6.9) & 0.503 (3.8) & **0.861** (1.0) \\
0.9 Propagate & acc \(\uparrow\) & 0.436 (5.3) & 0.503 (3.0) & 0.452 (4.0) & 0.418 (5.8) & 0.401 (6.7) & 0.546 (2.2) & **0.846** (1.0) \\ Cora & acc \(\uparrow\) & 0.683 (6.6) & 0.855 (4.2) & **0.866** (1.4) & 0.850 (4.1) & 0.863 (2.4) & 0.696 (6.4) & 0.859 (2.9) \\ Citeseer & acc \(\uparrow\) & 0.594 (6.0) & 0.663 (3.9) & 0.676 (2.3) & 0.661 (4.0) & **0.679** (1.8) & 0.443 (7.0) & 0.669 (3.0) \\ Pubmed & acc \(\uparrow\) & 0.778 (6.4) & 0.825 (3.7) & 0.835 (2.0) & 0.821 (4.0) & 0.835 (2.1) & 0.747 (6.6) & 0.829 (3.2) \\ \hline \multicolumn{8}{c}{Average (CD = 1.1)} \\ \hline \multicolumn{8}{c}{Deepness (overtraining capability)} \\ \hline Degree & acc \(\uparrow\) & 0.172 (5.7) & 0.331 (3.0) & 0.170 (6.6) & 0.175 (5.7) & 0.186 (4.0) & **0.632** (1.2) & 0.571 (1.8) \\ Triangle & acc \(\uparrow\) & 0.510 (4.7) & 0.510 (4.2) & 0.510 (4.7) & 0.510 (4.7) & 0.510 (4.7) & 0.536 (3.8) & **0.568** (1.2) \\
4 Clique & acc \(\uparrow\) & 0.665 (5.0) & 0.779 (3.0) & 0.657 (6.4) & 0.665 (5.0) & 0.663 (5.6) & **0.898** (1.4) & 0.894 (1.6) \\ LongShort & acc \(\uparrow\) & 0.347 (6.0) & 0.391 (3.0) & 0.347 (6.0) & 0.351 (4.0) & 0.347 (6.0) & 0.588 (2.0) & **0.688** (1.0) \\ Diffuse & mabs \(\downarrow\) & 0.032 (4.4) & 0.028 (3.0) & 0.061 (7.0) & 0.032 (4.6) & 0.033 (6.0) & 0.026 (2.0) & **0.012** (1.0) \\
0.9 Diffuse & mabs \(\downarrow\) & 0.021 (4.6) & 0.015 (3.0) & 0.034 (7.0) & 0.021 (4.4) & 0.021 (6.0) & 0.009 (1.8) & **0.007** (1.2) \\ Propagate & acc \(\uparrow\) & 0.477 (4.2) & 0.502 (2.4) & 0.454 (4.4) & 0.461 (4.9) & 0.413 (6.6) & 0.503 (4.5) & **0.844** (1.0) \\
0.9 Propagate & acc \(\uparrow\) & 0.493 (4.8) & 0.527 (8.2) & 0.534 (3.2) & 0.444 (6.3) & 0.451 (6.5) & 0.534 (3.4) & **0.873** (1.0) \\ Cora & acc \(\uparrow\) & 0.905 (5.6) & 0.914 (3.2) & 0.905 (5.4) & 0.911 (3.8) & 0.864 (7.0) & 0.930 (2.0) & **0.996** (1.0) \\ Citeseer & acc \(\uparrow\) & 0.865 (2.2) & 0.818 (3.8) & 0.794 (6.0) & 0.808 (5.0) & 0.767 (7.0) & 0.849 (3.0) & **0.959** (1.0) \\ Pubmed & acc \(\uparrow\) & 0.868 (3.8) & 0.871 (2.0) & 0.862 (5.2) & 0.855 (6.8) & 0.859 (6.0) & 0.869 (3.2) & **0.956** (1.0) \\ \hline \multicolumn{8}{c}{Average (CD = 1.1)} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Evaluations of predictive performance and their Nemenyi ranks in parentheses across five repetitions of each task. For each task, best performance is in **bold**. Arrows indicate whether better measure values are larger (\(\uparrow\)) or smaller (\(\downarrow\)). problems could require a lot of data and architecture parameters to train (Section 6.4 includes a more in-depth discussion of this concern). Even when ULA is not the best approach, accuracy differences with the best approach are small and, importantly, we empirically verified that it still finds deeper minima for the optimized loss functions.