## Line Chart: Accuracy vs. Attack Ratio for Different Federated Learning Algorithms ### Overview The image is a line chart comparing the accuracy of different federated learning algorithms as the attack ratio increases. The x-axis represents the attack ratio (percentage), and the y-axis represents the accuracy (percentage). Several algorithms are compared: FedAvg, ShieldFL, PBFL, Median, Biscotti, FoolsGold, and "Ours". ### Components/Axes * **X-axis:** Attack ratio (%), with markers at 0, 10, 20, 30, 40, and 50. * **Y-axis:** Accuracy (%), with markers at 10, 20, 30, 40, 50, 60, 70, and 80. * **Legend:** Located on the left side of the chart, listing the algorithms and their corresponding line colors and markers: * FedAvg (blue squares) * ShieldFL (orange diamonds) * PBFL (green triangles) * Median (purple pentagons) * Biscotti (gray stars) * FoolsGold (brown inverted triangles) * Ours (red circles) ### Detailed Analysis * **FedAvg (blue squares):** The accuracy of FedAvg decreases significantly as the attack ratio increases. * At 0% attack ratio, accuracy is approximately 80%. * At 20% attack ratio, accuracy is approximately 50%. * At 30% attack ratio, accuracy is approximately 15%. * At 40% attack ratio, accuracy is approximately 10%. * At 50% attack ratio, accuracy is approximately 10%. * **ShieldFL (orange diamonds):** The accuracy of ShieldFL also decreases with increasing attack ratio, but not as drastically as FedAvg. * At 0% attack ratio, accuracy is approximately 80%. * At 20% attack ratio, accuracy is approximately 75%. * At 30% attack ratio, accuracy is approximately 75%. * At 40% attack ratio, accuracy is approximately 70%. * At 50% attack ratio, accuracy is approximately 15%. * **PBFL (green triangles):** The accuracy of PBFL decreases with increasing attack ratio. * At 0% attack ratio, accuracy is approximately 80%. * At 20% attack ratio, accuracy is approximately 77%. * At 30% attack ratio, accuracy is approximately 70%. * At 40% attack ratio, accuracy is approximately 20%. * At 50% attack ratio, accuracy is approximately 10%. * **Median (purple pentagons):** The accuracy of Median decreases with increasing attack ratio. * At 0% attack ratio, accuracy is approximately 80%. * At 20% attack ratio, accuracy is approximately 78%. * At 30% attack ratio, accuracy is approximately 75%. * At 40% attack ratio, accuracy is approximately 57%. * At 50% attack ratio, accuracy is approximately 15%. * **Biscotti (gray stars):** The accuracy of Biscotti decreases with increasing attack ratio. * At 0% attack ratio, accuracy is approximately 80%. * At 20% attack ratio, accuracy is approximately 78%. * At 30% attack ratio, accuracy is approximately 40%. * At 40% attack ratio, accuracy is approximately 30%. * At 50% attack ratio, accuracy is approximately 15%. * **FoolsGold (brown inverted triangles):** The accuracy of FoolsGold decreases significantly as the attack ratio increases. * At 0% attack ratio, accuracy is approximately 80%. * At 10% attack ratio, accuracy is approximately 68%. * At 20% attack ratio, accuracy is approximately 58%. * At 40% attack ratio, accuracy is approximately 28%. * At 50% attack ratio, accuracy is approximately 10%. * **Ours (red circles):** The accuracy of "Ours" remains relatively constant regardless of the attack ratio. * At 0% attack ratio, accuracy is approximately 80%. * At 50% attack ratio, accuracy is approximately 78%. ### Key Observations * The "Ours" algorithm consistently maintains high accuracy, even with increasing attack ratios. * FedAvg, FoolsGold, PBFL, Median, Biscotti, and ShieldFL are all negatively impacted by increasing attack ratios, with varying degrees of severity. * FedAvg experiences the most significant drop in accuracy as the attack ratio increases. ### Interpretation The chart demonstrates the vulnerability of different federated learning algorithms to attacks. The "Ours" algorithm appears to be the most robust against attacks, maintaining a high level of accuracy even with a high attack ratio. The other algorithms, particularly FedAvg and FoolsGold, are significantly affected by increasing attack ratios, indicating their susceptibility to malicious actors. This suggests that the "Ours" algorithm incorporates mechanisms to mitigate the impact of attacks, making it a more reliable choice in adversarial environments. The data highlights the importance of developing robust federated learning algorithms that can withstand attacks and maintain accuracy.

## Line Chart: Accuracy vs. Attack Ratio for Federated Learning Defenses ### Overview This line chart depicts the accuracy of several Federated Learning (FL) defense mechanisms as a function of the attack ratio. The x-axis represents the attack ratio (percentage of compromised clients), and the y-axis represents the accuracy (percentage). The chart compares the performance of FedAvg, ShieldFL, PBFL, Median, Biscotti, FoolsGold, and a method labeled "Ours". ### Components/Axes * **X-axis:** "Attack ratio (%)" - Scale ranges from 0% to 50%, with markers at 0, 10, 20, 30, 40, and 50. * **Y-axis:** "Accuracy (%)" - Scale ranges from 0% to 80%, with markers at 10, 20, 30, 40, 50, 60, 70, and 80. * **Legend:** Located in the bottom-left corner. Contains the following labels and corresponding colors: * FedAvg (Blue) * ShieldFL (Orange) * PBFL (Green) * Median (Purple) * Biscotti (Grey) * FoolsGold (Pink) * Ours (Red) ### Detailed Analysis Here's a breakdown of each line's trend and approximate data points, verified against the legend colors: * **FedAvg (Blue):** Starts at approximately 81% accuracy at 0% attack ratio. The line slopes sharply downward, reaching approximately 52% at 20% attack ratio, 12% at 40% attack ratio, and approximately 8% at 50% attack ratio. * **ShieldFL (Orange):** Starts at approximately 79% accuracy at 0% attack ratio. The line initially decreases slightly, then remains relatively stable until approximately 30% attack ratio (around 70% accuracy). After 30%, it declines rapidly, reaching approximately 18% at 50% attack ratio. * **PBFL (Green):** Starts at approximately 78% accuracy at 0% attack ratio. The line decreases steadily, reaching approximately 68% at 20% attack ratio, 40% at 40% attack ratio, and approximately 10% at 50% attack ratio. * **Median (Purple):** Starts at approximately 80% accuracy at 0% attack ratio. The line decreases gradually, reaching approximately 75% at 20% attack ratio, 56% at 40% attack ratio, and approximately 15% at 50% attack ratio. * **Biscotti (Grey):** Starts at approximately 78% accuracy at 0% attack ratio. The line decreases steadily, reaching approximately 65% at 20% attack ratio, 35% at 40% attack ratio, and approximately 18% at 50% attack ratio. * **FoolsGold (Pink):** Starts at approximately 78% accuracy at 0% attack ratio. The line remains relatively stable until approximately 30% attack ratio (around 76% accuracy). After 30%, it declines, reaching approximately 20% at 50% attack ratio. * **Ours (Red):** Starts at approximately 81% accuracy at 0% attack ratio. The line remains almost flat, maintaining approximately 78-80% accuracy throughout the entire range of attack ratios (0% to 50%). ### Key Observations * The "Ours" method demonstrates significantly higher accuracy compared to all other methods as the attack ratio increases. It maintains a stable accuracy level even at a 50% attack ratio. * FedAvg is the most vulnerable to attacks, experiencing a rapid decline in accuracy with increasing attack ratios. * ShieldFL and FoolsGold show some resilience up to a 30% attack ratio, but their accuracy drops significantly beyond that point. * PBFL, Median, and Biscotti exhibit a more gradual decline in accuracy as the attack ratio increases, but still fall significantly below "Ours". ### Interpretation The data suggests that the proposed "Ours" defense mechanism is substantially more robust against attacks in a Federated Learning environment than the other methods tested. The consistent high accuracy across all attack ratios indicates a strong ability to mitigate the impact of compromised clients. The stark contrast between "Ours" and FedAvg highlights the importance of implementing defense mechanisms in FL systems, as a naive approach (FedAvg) is highly susceptible to attacks. The varying degrees of resilience among ShieldFL, PBFL, Median, Biscotti, and FoolsGold suggest that different defense strategies offer varying levels of protection, and the optimal choice may depend on the specific threat model and system constraints. The fact that most methods degrade in performance as the attack ratio increases is expected, as a higher proportion of malicious clients can exert a greater influence on the global model. This chart provides compelling evidence for the effectiveness of the "Ours" method and underscores the critical need for robust defense mechanisms in Federated Learning.

\n ## Line Chart: Accuracy vs. Attack Ratio for Federated Learning Methods ### Overview The image is a line chart comparing the performance of seven different federated learning methods under varying levels of adversarial attack. The chart plots model accuracy against the percentage of malicious participants (attack ratio) in the system. The primary trend shows that as the attack ratio increases, the accuracy of most methods degrades, but at significantly different rates. ### Components/Axes * **Chart Type:** Multi-line chart. * **X-Axis:** Labeled **"Attack ratio (%)"**. It has major tick marks at 0, 10, 20, 30, 40, and 50. * **Y-Axis:** Labeled **"Accuracy (%)"**. It has major tick marks at 10, 20, 30, 40, 50, 60, 70, and 80. * **Legend:** Located in the **top-left corner** of the plot area. It lists seven data series with corresponding line colors and marker styles: 1. **FedAvg** - Blue line with square markers. 2. **ShieldFL** - Orange line with diamond markers. 3. **PBFL** - Green line with upward-pointing triangle markers. 4. **Median** - Purple line with circle markers. 5. **Biscotti** - Gray line with star (asterisk) markers. 6. **FoolsGold** - Brown line with downward-pointing triangle markers. 7. **Ours** - Red line with circle markers. ### Detailed Analysis The following table reconstructs the approximate data points for each method at the specified attack ratios. Values are estimated from the chart's grid lines, with an uncertainty of ±2%. | Method (Color) | Attack Ratio: 0% | 10% | 20% | 30% | 40% | 50% | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | **FedAvg (Blue)** | ~80% | ~78% | ~50% | ~16% | ~10% | ~10% | | **ShieldFL (Orange)** | ~80% | ~78% | ~76% | ~72% | ~38% | ~10% | | **PBFL (Green)** | ~80% | ~78% | ~76% | ~66% | ~22% | ~10% | | **Median (Purple)** | ~80% | ~80% | ~78% | ~76% | ~56% | ~10% | | **Biscotti (Gray)** | ~80% | ~78% | ~76% | ~76% | ~30% | ~19% | | **FoolsGold (Brown)** | ~80% | ~66% | ~58% | ~37% | ~28% | ~10% | | **Ours (Red)** | ~80% | ~81% | ~80% | ~79% | ~79% | ~78% | **Trend Verification per Series:** * **FedAvg (Blue):** Slopes downward sharply after 10% attack ratio, reaching a low plateau at 40-50%. * **ShieldFL (Orange):** Maintains high accuracy until 30%, then drops steeply. * **PBFL (Green):** Follows a similar but slightly steeper decline than ShieldFL after 30%. * **Median (Purple):** Shows the most resilience among baseline methods, with a gradual decline until 30% and a steeper drop afterward. * **Biscotti (Gray):** Performs similarly to Median until 30%, then declines more sharply but ends higher than most at 50%. * **FoolsGold (Brown):** Begins degrading immediately, showing the poorest early resilience. * **Ours (Red):** Exhibits a nearly flat, horizontal trend, maintaining accuracy above 78% across the entire range. ### Key Observations 1. **Universal Starting Point:** All methods begin at approximately 80% accuracy with 0% attack ratio, establishing a common baseline. 2. **Critical Threshold:** For most methods (except "Ours"), a significant performance drop occurs between 30% and 40% attack ratio. 3. **Outlier Performance:** The method labeled **"Ours"** is a clear outlier, demonstrating exceptional robustness with negligible accuracy loss even at 50% attack ratio. 4. **Convergence at Failure:** At the maximum attack ratio of 50%, six of the seven methods converge to a very low accuracy range of 10-19%, indicating system failure. "Ours" and "Biscotti" are the only methods not at the absolute bottom. 5. **Early Degradation:** "FoolsGold" is the only method that shows substantial accuracy loss at a low (10%) attack ratio. ### Interpretation This chart presents a comparative evaluation of Byzantine-robust or secure aggregation algorithms in federated learning. The data suggests that the proposed method ("Ours") significantly outperforms the other six baseline methods in maintaining model accuracy as the proportion of malicious clients increases. The **"Attack ratio (%)"** represents the fraction of total participants sending poisoned or manipulated updates. The **"Accuracy (%)"** measures the global model's performance on a clean test dataset. The stark contrast between the flat red line ("Ours") and the declining trajectories of the others indicates that the underlying technique of "Ours" is highly effective at filtering out or neutralizing malicious contributions without harming the aggregation of legitimate updates. The **Peircean investigative reading** reveals a narrative of resilience versus vulnerability. The chart doesn't just show numbers; it tells a story of system integrity under siege. The baselines represent established defenses that hold until a tipping point (around 30-40% attack ratio), after which they collapse. "Ours" represents a paradigm shift, maintaining integrity well beyond the failure point of its competitors. The anomaly of "Biscotti" performing slightly better than others at 50% but worse at 40% may indicate a different failure mode or a non-monotonic response to attack strength, warranting further investigation. The immediate decline of "FoolsGold" suggests its defense mechanism is either too sensitive or fundamentally misaligned with the attack model used in this evaluation.

## Line Graph: Accuracy vs. Attack Ratio ### Overview The image is a line graph comparing the accuracy of various methods (FedAvg, ShieldFL, PBFL, Median, Biscotti, FoolsGold, and "Ours") as the attack ratio increases from 0% to 50%. Accuracy is measured on the y-axis (10–80%), and attack ratio on the x-axis (0–50%). The graph highlights how each method's performance degrades under increasing adversarial pressure. ### Components/Axes - **Y-axis**: Accuracy (%) with ticks at 10, 20, 30, 40, 50, 60, 70, 80. - **X-axis**: Attack ratio (%) with ticks at 0, 10, 20, 30, 40, 50. - **Legend**: Located in the bottom-left corner, mapping colors and markers to methods: - **Blue squares**: FedAvg - **Orange diamonds**: ShieldFL - **Green triangles**: PBFL - **Purple diamonds**: Median - **Gray stars**: Biscotti - **Brown triangles**: FoolsGold - **Red circles**: Ours ### Detailed Analysis 1. **FedAvg (Blue squares)**: - Starts at ~80% accuracy at 0% attack ratio. - Drops sharply to ~75% at 10%, ~50% at 20%, ~15% at 30%, ~10% at 40%, and stabilizes at ~10% at 50%. 2. **ShieldFL (Orange diamonds)**: - Begins at ~80% at 0%, declines to ~78% at 10%, ~75% at 20%, ~65% at 30%, ~35% at 40%, and ~10% at 50%. 3. **PBFL (Green triangles)**: - Starts at ~80% at 0%, drops to ~77% at 10%, ~75% at 20%, ~65% at 30%, ~25% at 40%, and ~10% at 50%. 4. **Median (Purple diamonds)**: - Remains near ~80% at 0%, declines to ~75% at 10%, ~70% at 20%, ~55% at 30%, ~55% at 40%, and ~10% at 50%. 5. **Biscotti (Gray stars)**: - Starts at ~80% at 0%, declines to ~78% at 10%, ~75% at 20%, ~70% at 30%, ~25% at 40%, and ~10% at 50%. 6. **FoolsGold (Brown triangles)**: - Begins at ~80% at 0%, drops to ~65% at 10%, ~55% at 20%, ~35% at 30%, ~20% at 40%, and ~10% at 50%. 7. **"Ours" (Red circles)**: - Maintains ~80% accuracy across all attack ratios (0–50%), with minimal deviation. ### Key Observations - **"Ours" (Red circles)** consistently outperforms all other methods, maintaining near-80% accuracy even at 50% attack ratio. - **FedAvg (Blue squares)** and **FoolsGold (Brown triangles)** exhibit the steepest declines, dropping to ~10% accuracy by 40% attack ratio. - **ShieldFL (Orange diamonds)** and **PBFL (Green triangles)** show moderate resilience but still degrade significantly under high attack ratios. - **Median (Purple diamonds)** and **Biscotti (Gray stars)** perform better than FedAvg and FoolsGold but worse than "Ours." ### Interpretation The graph demonstrates that the method labeled "Ours" is exceptionally robust against adversarial attacks, maintaining high accuracy regardless of attack ratio. This suggests it employs a more effective defense mechanism or model architecture compared to the other methods. In contrast, FedAvg and FoolsGold are highly vulnerable, indicating potential flaws in their design or training processes. ShieldFL and PBFL offer mid-tier performance, while Median and Biscotti provide moderate resilience. The stark contrast between "Ours" and other methods underscores its superiority in adversarial environments, making it a critical candidate for applications requiring high security and reliability.