## Line Chart: CIFAR-100 Test Accuracy vs. Alpha ### Overview The image is a line chart comparing the test accuracy of two models, FedProto and FedMRL, on the CIFAR-100 dataset, with respect to the parameter alpha (α). The x-axis represents the value of alpha, ranging from 0.1 to 0.5. The y-axis represents the test accuracy, ranging from 10 to 16. ### Components/Axes * **Title:** CIFAR-100 * **X-axis:** * Label: α * Scale: 0.1, 0.2, 0.3, 0.4, 0.5 * **Y-axis:** * Label: Test Accuracy * Scale: 10, 12, 14 * **Legend:** Located in the top-right corner. * FedProto: Represented by a dashed light green line with circle markers. * FedMRL: Represented by a solid light purple line with star markers. * **Grid:** The chart has a light gray dashed grid. ### Detailed Analysis * **FedProto (light green, dashed line, circle markers):** * Trend: The test accuracy generally decreases as alpha increases. * Data Points: * α = 0.1, Test Accuracy ≈ 12.4 * α = 0.2, Test Accuracy ≈ 11.2 * α = 0.3, Test Accuracy ≈ 10.0 * α = 0.4, Test Accuracy ≈ 9.3 * α = 0.5, Test Accuracy ≈ 9.6 * **FedMRL (light purple, solid line, star markers):** * Trend: The test accuracy decreases from α = 0.1 to α = 0.4, then slightly increases at α = 0.5. * Data Points: * α = 0.1, Test Accuracy ≈ 15.3 * α = 0.2, Test Accuracy ≈ 14.2 * α = 0.3, Test Accuracy ≈ 13.8 * α = 0.4, Test Accuracy ≈ 12.0 * α = 0.5, Test Accuracy ≈ 12.2 ### Key Observations * FedMRL consistently outperforms FedProto across all values of alpha. * The performance of FedProto degrades more significantly with increasing alpha compared to FedMRL. * Both models show a decrease in test accuracy as alpha increases from 0.1 to 0.4, but FedMRL shows a slight increase from 0.4 to 0.5. ### Interpretation The chart suggests that the FedMRL model is more robust to changes in the alpha parameter compared to the FedProto model, as it maintains a higher test accuracy across the range of alpha values. The decreasing trend in test accuracy for both models as alpha increases from 0.1 to 0.4 indicates that a lower alpha value might be preferable for optimal performance. The slight increase in FedMRL's accuracy from alpha 0.4 to 0.5 could indicate a local optimum or a point of diminishing returns. The data implies that FedMRL is a better choice for this particular task and dataset.

\n ## Line Chart: CIFAR-100 Test Accuracy vs. Alpha ### Overview This chart displays the relationship between test accuracy and the parameter alpha (α) for two different federated learning protocols: FedProto and FedMRL, on the CIFAR-100 dataset. The chart uses lines with markers to represent the data for each protocol. ### Components/Axes * **Title:** CIFAR-100 (positioned at the top-center) * **X-axis Label:** α (positioned at the bottom-center) * **Y-axis Label:** Test Accuracy (positioned at the left-center) * **Legend:** Located in the top-right corner. * FedProto (represented by a dashed light-blue line with circular markers) * FedMRL (represented by a solid purple line with star-shaped markers) * **X-axis Markers:** 0.1, 0.2, 0.3, 0.4, 0.5 * **Y-axis Scale:** Ranges from approximately 9 to 16. ### Detailed Analysis **FedProto (Light-Blue Dashed Line with Circles):** The line slopes downward overall. * At α = 0.1, Test Accuracy ≈ 12.1 * At α = 0.2, Test Accuracy ≈ 11.2 * At α = 0.3, Test Accuracy ≈ 10.1 * At α = 0.4, Test Accuracy ≈ 9.4 * At α = 0.5, Test Accuracy ≈ 9.6 **FedMRL (Purple Solid Line with Stars):** The line initially slopes downward, then slightly upward. * At α = 0.1, Test Accuracy ≈ 15.4 * At α = 0.2, Test Accuracy ≈ 14.3 * At α = 0.3, Test Accuracy ≈ 13.2 * At α = 0.4, Test Accuracy ≈ 12.1 * At α = 0.5, Test Accuracy ≈ 12.2 ### Key Observations * FedMRL consistently achieves higher test accuracy than FedProto across all values of α. * FedProto's accuracy decreases steadily as α increases. * FedMRL's accuracy decreases from α = 0.1 to α = 0.4, then shows a slight increase at α = 0.5. * The difference in accuracy between the two protocols is most significant at lower values of α. ### Interpretation The chart suggests that FedMRL is a more effective federated learning protocol than FedProto for the CIFAR-100 dataset, as it consistently yields higher test accuracy. The parameter α appears to have a negative impact on the performance of FedProto, while its effect on FedMRL is more complex, potentially indicating a sweet spot for α within the range tested. The slight increase in FedMRL accuracy at α = 0.5 could be due to the regularization effect of α, preventing overfitting. The data suggests that the choice of α is crucial for optimizing the performance of federated learning algorithms, and that different protocols may respond differently to changes in this parameter. The difference in performance between the two protocols could be attributed to differences in their underlying mechanisms for handling data heterogeneity or communication constraints.

## Line Chart: CIFAR-100 Test Accuracy vs. Alpha (α) ### Overview The image is a line chart comparing the test accuracy of two federated learning methods, FedProto and FedMRL, on the CIFAR-100 dataset as a function of the parameter alpha (α). The chart demonstrates that both methods experience a decline in accuracy as α increases, but FedMRL consistently achieves higher accuracy than FedProto across all tested values. ### Components/Axes * **Title:** "CIFAR-100" (centered at the top). * **Y-Axis:** Labeled "Test Accuracy". The scale runs from 10 to 14, with major tick marks at 10, 12, and 14. The axis extends slightly below 10 and above 14. * **X-Axis:** Labeled "α" (the Greek letter alpha). The scale shows discrete values: 0.1, 0.2, 0.3, 0.4, and 0.5. * **Legend:** Positioned in the top-right quadrant of the chart area. * **FedProto:** Represented by a green circle (○) connected by a dashed green line. * **FedMRL:** Represented by a purple star (☆) connected by a solid purple line. * **Grid:** A light gray, dashed grid is present for both major x and y ticks. ### Detailed Analysis **Data Series & Trends:** 1. **FedProto (Green Circles, Dashed Line):** * **Trend:** The line shows a consistent downward slope from left to right, indicating decreasing accuracy with increasing α. The rate of decrease slows slightly between α=0.4 and α=0.5. * **Data Points (Approximate):** * α = 0.1: ~12.3 * α = 0.2: ~11.2 * α = 0.3: ~10.0 * α = 0.4: ~9.2 * α = 0.5: ~9.5 2. **FedMRL (Purple Stars, Solid Line):** * **Trend:** The line also slopes downward overall. It shows a steeper initial decline from α=0.1 to α=0.4, followed by a near-plateau or very slight increase between α=0.4 and α=0.5. * **Data Points (Approximate):** * α = 0.1: ~15.5 * α = 0.2: ~14.2 * α = 0.3: ~13.5 * α = 0.4: ~12.1 * α = 0.5: ~12.2 **Spatial & Visual Confirmation:** * The FedMRL line (purple stars) is positioned vertically above the FedProto line (green circles) at every corresponding α value on the x-axis. * The gap between the two lines is largest at α=0.1 (~3.2 difference) and narrows as α increases, being smallest at α=0.5 (~2.7 difference). ### Key Observations 1. **Performance Hierarchy:** FedMRL outperforms FedProto at every measured point of α. 2. **Negative Correlation:** For both methods, test accuracy is negatively correlated with the parameter α within the range [0.1, 0.5]. 3. **Convergence of Performance:** The performance gap between the two methods decreases as α increases. 4. **Inflection Point:** Both methods show a change in trend slope at α=0.4. FedProto's decline halts and slightly reverses, while FedMRL's decline nearly stops. ### Interpretation The chart presents a comparative analysis of two algorithms' sensitivity to a hyperparameter (α) on a standard image classification benchmark (CIFAR-100). The data suggests that: * **Methodological Robustness:** FedMRL is a more robust method than FedProto for this task, as it maintains a higher accuracy under the same conditions (same α value). This could imply better feature representation or more effective model aggregation in the federated learning setting. * **Hyperparameter Sensitivity:** The parameter α has a significant detrimental effect on the final model performance for both approaches. Without additional context, α could represent a factor like data heterogeneity, client drift, or a regularization term. The negative trend indicates that increasing this factor makes the learning task harder. * **Diminishing Returns of Mitigation:** The narrowing performance gap suggests that as the problem becomes more challenging (higher α), the relative advantage of the more sophisticated FedMRL method over FedProto diminishes, though it remains superior. * **Potential Optimal Range:** The data implies that lower values of α (closer to 0.1) are preferable for achieving higher test accuracy with either method. The slight upturn for both at α=0.5 is an interesting anomaly that might warrant further investigation to determine if it's a consistent pattern or noise.

## Line Chart: CIFAR-100 Test Accuracy vs. α ### Overview The chart compares the test accuracy of two machine learning methods (FedProto and FedMRL) across varying values of α (0.1 to 0.5) on the CIFAR-100 dataset. Test accuracy is measured on the y-axis (10–14), while α is plotted on the x-axis. Two distinct trends are observed: FedProto shows a steady decline, while FedMRL exhibits a sharp initial drop followed by stabilization. ### Components/Axes - **X-axis (α)**: Labeled "α" with values 0.1, 0.2, 0.3, 0.4, 0.5. - **Y-axis (Test Accuracy)**: Labeled "Test Accuracy" with values 10, 12, 14. - **Legend**: Located in the top-right corner, with: - **FedProto**: Dashed teal line with hollow circles. - **FedMRL**: Solid purple line with star markers. ### Detailed Analysis 1. **FedProto (Teal Line)**: - Starts at **~12.2** when α = 0.1. - Declines steadily to **~9.8** at α = 0.5. - Intermediate points: ~11.0 (α=0.2), ~10.0 (α=0.3), ~9.5 (α=0.4). 2. **FedMRL (Purple Line)**: - Begins at **~15.0** when α = 0.1. - Drops sharply to **~13.5** at α = 0.3. - Stabilizes with a slight increase to **~12.5** at α = 0.5. - Intermediate points: ~14.0 (α=0.2), ~13.5 (α=0.3), ~12.5 (α=0.5). ### Key Observations - FedMRL consistently outperforms FedProto across all α values. - FedProto’s decline is linear, while FedMRL’s performance plateaus after α = 0.3. - The largest gap between methods occurs at α = 0.1 (~2.8 accuracy difference). ### Interpretation The data suggests that FedMRL is more robust to changes in α, maintaining higher accuracy even as α increases. FedProto’s performance degrades linearly, indicating sensitivity to α. The stabilization of FedMRL at higher α values implies potential adaptability to model complexity or noise in the CIFAR-100 dataset. The sharp drop in FedMRL’s accuracy between α = 0.1 and 0.3 may reflect a threshold where model assumptions become less valid. These trends highlight the importance of tuning α for federated learning frameworks on non-IID datasets like CIFAR-100.