\n ## Bar Chart: NMSE Comparison of Different Models ### Overview The image presents a bar chart comparing the Normalized Mean Squared Error (NMSE) on a logarithmic scale for three different model configurations: "w/o Phy", "w/o TokenReg", and "PIT-PO". The chart distinguishes between "In-Distribution" (ID) and "Out-of-Distribution" (OOD) data. ### Components/Axes * **X-axis:** Model Configuration - "w/o Phy", "w/o TokenReg", "PIT-PO" * **Y-axis:** NMSE (log scale) - ranging from 10^-29 to 10^-10. The scale is logarithmic. * **Legend:** * ID (White bars with light gray diagonal pattern) * OOD (Orange bars with darker orange diagonal pattern) ### Detailed Analysis The chart displays NMSE values for both In-Distribution (ID) and Out-of-Distribution (OOD) data for each model. * **w/o Phy:** * ID: The blue bar representing ID data has a value of approximately 7.60e-21. * OOD: The blue bar representing OOD data has a value of approximately 2.06e-10. * **w/o TokenReg:** * ID: The blue bar representing ID data has a value of approximately 2.77e-19. * OOD: The blue bar representing OOD data has a value of approximately 9.97e-11. * **PIT-PO:** * ID: The orange bar representing ID data has a value of approximately 6.40e-31. * OOD: The orange bar representing OOD data has a value of approximately 1.63e-30. The bars for "w/o Phy" and "w/o TokenReg" are blue, indicating the ID and OOD data. The bars for "PIT-PO" are orange, indicating the ID and OOD data. ### Key Observations * The PIT-PO model consistently exhibits the lowest NMSE values for both ID and OOD data, by several orders of magnitude. * The NMSE values are significantly higher for OOD data compared to ID data for the "w/o Phy" and "w/o TokenReg" models. * The difference in NMSE between ID and OOD data is less pronounced for the PIT-PO model. ### Interpretation The data suggests that the PIT-PO model performs significantly better than the other two configurations ("w/o Phy" and "w/o TokenReg") in terms of minimizing NMSE for both in-distribution and out-of-distribution data. This indicates that the PIT-PO model is more robust and generalizes better to unseen data. The large difference in NMSE between ID and OOD data for the "w/o Phy" and "w/o TokenReg" models suggests that these models are more prone to overfitting or are less capable of handling data that deviates from the training distribution. The smaller difference for PIT-PO suggests better generalization capabilities. The logarithmic scale emphasizes the substantial differences in error rates, particularly the very low errors achieved by PIT-PO. The chart demonstrates the effectiveness of the PIT-PO approach in reducing prediction error, especially when dealing with out-of-distribution data.