## Heatmap: Vulnerability and Mitigation Strategies ### Overview The image presents four heatmaps comparing vulnerability and mitigation strategies for backdoor and targeted attacks. The heatmaps visualize the relationship between the number of query paths (2, 3, and 5) and the maximum length of the query path (1-hop, 2-hop, 3-hop, and 4-hop). The color intensity represents the effectiveness of the strategy, with darker green indicating higher effectiveness and lighter yellow indicating lower effectiveness. Each cell contains a numerical value and an arrow indicating the trend (increase or decrease). ### Components/Axes * **Title:** Max Length of Query Path * **Y-axis Title:** Number of Query Paths * **Y-axis Labels:** 2, 3, 5 * **X-axis Labels (Backdoor-Vulnerability):** 1-hop, 2-hop, 3-hop * **X-axis Labels (Backdoor-Mitigation):** 2-hop, 3-hop, 4-hop * **X-axis Labels (Targeted-Vulnerability):** 1-hop, 2-hop, 3-hop * **X-axis Labels (Targeted-Mitigation):** 2-hop, 3-hop, 4-hop * **Color Scale:** Ranges from approximately 0.2 (light yellow) to 1.0 (dark green) on the left side, and from 0.5 to 0.8 on the right side. * **Subplot Titles:** (a) Backdoor-Vulnerability, (b) Backdoor-Mitigation, (c) Targeted-Vulnerability, (d) Targeted-Mitigation * **Trend Indicators:** Upward arrow (↑) indicates an increasing trend, downward arrow (↓) indicates a decreasing trend. ### Detailed Analysis #### (a) Backdoor-Vulnerability | Number of Query Paths | 1-hop | 2-hop | 3-hop | | :-------------------- | :----- | :----- | :----- | | 2 | 0.53 ↑ | 0.70 ↑ | 0.82 ↑ | | 3 | 0.41 ↑ | 0.61 ↑ | 0.74 ↑ | | 5 | 0.30 ↑ | 0.48 ↑ | 0.55 ↑ | * **Trend:** The values increase as the hop length increases for each number of query paths. #### (b) Backdoor-Mitigation | Number of Query Paths | 2-hop | 3-hop | 4-hop | | :-------------------- | :----- | :----- | :----- | | 2 | 0.64 ↑ | 0.79 ↑ | 0.86 ↑ | | 3 | 0.53 ↑ | 0.80 ↑ | 0.85 ↑ | | 5 | 0.38 ↑ | 0.62 ↑ | 0.65 ↑ | * **Trend:** The values increase as the hop length increases for each number of query paths. #### (c) Targeted-Vulnerability | Number of Query Paths | 1-hop | 2-hop | 3-hop | | :-------------------- | :----- | :----- | :----- | | 2 | 0.86 ↓ | 0.89 ↓ | 0.91 ↓ | | 3 | 0.81 ↓ | 0.90 ↓ | 0.90 ↓ | | 5 | 0.78 ↓ | 0.84 ↓ | 0.86 ↓ | * **Trend:** The values are generally high (dark green) and decrease slightly as the number of query paths increases. #### (d) Targeted-Mitigation | Number of Query Paths | 2-hop | 3-hop | 4-hop | | :-------------------- | :----- | :----- | :----- | | 2 | 0.69 ↓ | 0.68 ↓ | 0.70 ↓ | | 3 | 0.62 ↓ | 0.66 ↓ | 0.70 ↓ | | 5 | 0.60 ↓ | 0.63 ↓ | 0.68 ↓ | * **Trend:** The values are relatively consistent across different hop lengths and decrease slightly as the number of query paths increases. ### Key Observations * **Backdoor-Vulnerability:** Vulnerability increases significantly with longer query paths. * **Backdoor-Mitigation:** Mitigation effectiveness also increases with longer query paths. * **Targeted-Vulnerability:** Vulnerability is generally high but decreases slightly with more query paths. * **Targeted-Mitigation:** Mitigation effectiveness is relatively stable and decreases slightly with more query paths. * The color scales are different for the left and right heatmaps. The left heatmaps range from 0.2 to 1.0, while the right heatmaps range from 0.5 to 0.8. ### Interpretation The heatmaps suggest that for backdoor attacks, longer query paths increase both vulnerability and the effectiveness of mitigation strategies. This indicates a trade-off where longer paths might be more susceptible to exploitation but also more amenable to defense. For targeted attacks, vulnerability is generally high, and mitigation strategies show a relatively stable effectiveness, with a slight decrease as the number of query paths increases. This could imply that targeted attacks are inherently more difficult to defend against, and increasing the number of query paths does not significantly improve mitigation. The different color scales between the left and right heatmaps suggest that the range of effectiveness is different for backdoor and targeted attacks, with targeted attacks having a narrower range.

\n ## Heatmap: Query Path Length vs. Attack Success Rate ### Overview The image presents a comparative heatmap illustrating the success rate of backdoor and targeted attacks based on the maximum length of the query path. The heatmap is divided into four sections, each representing a different attack scenario: Backdoor-Vulnerability, Backdoor-Mitigation, Targeted-Vulnerability, and Targeted-Mitigation. The y-axis represents the number of query paths, ranging from 1 to 5, while the x-axis represents the maximum length of the query path, ranging from 1-hop to 4-hop. The color intensity indicates the attack success rate, with darker shades of green representing higher success rates and lighter shades representing lower success rates. Arrows indicate the trend of success rate as the query path length increases. ### Components/Axes * **Title:** Max Length of Query Path * **Y-axis Title:** Number of Query Paths (1-5) * **X-axis Title:** Max Length of Query Path (1-hop, 2-hop, 3-hop, 4-hop) * **Color Scale:** Ranges from 0.2 (light green) to 1.0 (dark green), representing attack success rate. * **Labels:** * (a) Backdoor-Vulnerability * (b) Backdoor-Mitigation * (c) Targeted-Vulnerability * (d) Targeted-Mitigation * **Trend Indicators:** Upward arrows (↑) indicate an increasing success rate with increasing query path length, while downward arrows (↓) indicate a decreasing success rate. ### Detailed Analysis **Section (a): Backdoor-Vulnerability** * 1 Query Path: 0.53 ↑ * 2 Query Paths: 0.70 ↑ * 3 Query Paths: 0.82 ↑ * 1-hop: 0.53 * 2-hop: 0.70 * 3-hop: 0.82 * 4-hop: Not present **Section (b): Backdoor-Mitigation** * 1 Query Path: 0.38 ↑ * 2 Query Paths: 0.64 ↑ * 3 Query Paths: 0.79 ↑ * 4 Query Paths: 0.86 ↑ * 1-hop: 0.38 * 2-hop: 0.64 * 3-hop: 0.79 * 4-hop: 0.86 **Section (c): Targeted-Vulnerability** * 1 Query Path: 0.86 ↓ * 2 Query Paths: 0.89 ↓ * 3 Query Paths: 0.90 ↓ * 4 Query Paths: 0.68 ↓ * 1-hop: 0.86 * 2-hop: 0.89 * 3-hop: 0.90 * 4-hop: 0.68 **Section (d): Targeted-Mitigation** * 1 Query Path: 0.78 ↓ * 2 Query Paths: 0.81 ↓ * 3 Query Paths: 0.86 ↓ * 4 Query Paths: 0.63 ↓ * 1-hop: 0.78 * 2-hop: 0.81 * 3-hop: 0.86 * 4-hop: 0.63 ### Key Observations * **Backdoor Attacks:** The success rate of backdoor attacks generally *increases* with the length of the query path (Sections a and b). Mitigation strategies (Section b) show lower initial success rates but still exhibit an upward trend. * **Targeted Attacks:** The success rate of targeted attacks generally *decreases* with the length of the query path (Sections c and d). Mitigation strategies (Section d) also show a decreasing trend, but start at a lower success rate than the vulnerability scenario (Section c). * **Mitigation Impact:** Mitigation strategies consistently reduce the success rate of both backdoor and targeted attacks compared to their vulnerable counterparts. * **Peak Success:** Targeted-Vulnerability (Section c) shows the highest success rates, peaking at 0.90 for 3-hop queries. ### Interpretation The data suggests that longer query paths are more effective for exploiting backdoor vulnerabilities, while they are detrimental to targeted attacks. This could be due to the nature of backdoor triggers, which may require a certain sequence or length of queries to activate. Conversely, targeted attacks may become less precise or more detectable with longer, more complex query paths. The mitigation strategies demonstrate a clear benefit in reducing attack success rates, but their effectiveness varies depending on the attack type and query path length. The consistent downward trend in targeted attack success rates with mitigation suggests that these strategies are effective in disrupting precision attacks. The increasing success rate of backdoor attacks with mitigation, despite being lower than the vulnerable scenario, indicates that further refinement of mitigation techniques may be needed to address this threat. The heatmap provides valuable insights into the trade-offs between query path length, attack success rate, and mitigation effectiveness. This information can be used to design more robust security systems and develop targeted mitigation strategies. The anomalies, such as the peak success rate for Targeted-Vulnerability at 3-hop, warrant further investigation to understand the underlying mechanisms driving these results.

## [Heatmap Series]: Vulnerability and Mitigation Analysis Across Query Path Lengths ### Overview The image displays a set of four heatmaps arranged in a 2x2 grid, analyzing the relationship between the "Number of Query Paths" (y-axis) and the "Max Length of Query Path" (x-axis) for different security scenarios. Each heatmap uses a color gradient (light yellow to dark green) to represent a numerical score, with arrows indicating the directional trend of the score as the number of query paths increases. The overall title is "Max Length of Query Path." ### Components/Axes * **Main Title:** "Max Length of Query Path" (centered at the top). * **Y-axis Label (Left):** "Number of Query Paths" (applies to all four subplots). * **Y-axis Categories (Rows):** 2, 3, 5 (for each heatmap). * **X-axis Categories (Columns):** Vary by subplot: * (a) & (c): 1-hop, 2-hop, 3-hop * (b) & (d): 2-hop, 3-hop, 4-hop * **Subplot Titles:** * (a) Backdoor-Vulnerability * (b) Backdoor-Mitigation * (c) Targeted-Vulnerability * (d) Targeted-Mitigation * **Color Bars (Legends):** * **Left Pair (a & b):** Scale from 0.2 (light yellow) to 1.0 (dark green). Positioned to the right of subplot (b). * **Right Pair (c & d):** Scale from 0.5 (light yellow) to 0.8 (dark green). Positioned to the right of subplot (d). * **Data Annotations:** Each cell contains a numerical value (to two decimal places) and an arrow (↑ or ↓). ### Detailed Analysis **Subplot (a) Backdoor-Vulnerability:** * **Trend:** Scores increase with both more query paths and longer path lengths (all arrows ↑). * **Data Points:** * Row "2": 1-hop: 0.53 ↑, 2-hop: 0.70 ↑, 3-hop: 0.82 ↑ * Row "3": 1-hop: 0.41 ↑, 2-hop: 0.61 ↑, 3-hop: 0.74 ↑ * Row "5": 1-hop: 0.30 ↑, 2-hop: 0.48 ↑, 3-hop: 0.55 ↑ **Subplot (b) Backdoor-Mitigation:** * **Trend:** Scores increase with both more query paths and longer path lengths (all arrows ↑). Values are generally higher than in (a). * **Data Points:** * Row "2": 2-hop: 0.64 ↑, 3-hop: 0.79 ↑, 4-hop: 0.86 ↑ * Row "3": 2-hop: 0.53 ↑, 3-hop: 0.80 ↑, 4-hop: 0.85 ↑ * Row "5": 2-hop: 0.38 ↑, 3-hop: 0.62 ↑, 4-hop: 0.65 ↑ **Subplot (c) Targeted-Vulnerability:** * **Trend:** Scores generally decrease as the number of query paths increases (all arrows ↓). Scores are high for 2 and 3 paths but drop for 5 paths. * **Data Points:** * Row "2": 1-hop: 0.86 ↓, 2-hop: 0.89 ↓, 3-hop: 0.91 ↓ * Row "3": 1-hop: 0.81 ↓, 2-hop: 0.90 ↓, 3-hop: 0.90 ↓ * Row "5": 1-hop: 0.78 ↓, 2-hop: 0.84 ↓, 3-hop: 0.86 ↓ **Subplot (d) Targeted-Mitigation:** * **Trend:** Scores decrease as the number of query paths increases (all arrows ↓). Values are lower than in (c). * **Data Points:** * Row "2": 2-hop: 0.69 ↓, 3-hop: 0.68 ↓, 4-hop: 0.70 ↓ * Row "3": 2-hop: 0.62 ↓, 3-hop: 0.66 ↓, 4-hop: 0.70 ↓ * Row "5": 2-hop: 0.60 ↓, 3-hop: 0.63 ↓, 4-hop: 0.68 ↓ ### Key Observations 1. **Opposing Trends:** Backdoor scenarios (a, b) show a positive correlation between score and query path complexity (more paths/longer hops = higher score). Targeted scenarios (c, d) show a negative correlation (more paths = lower score). 2. **Magnitude Differences:** Vulnerability scores (a, c) are generally higher than their corresponding Mitigation scores (b, d) within the same attack type (Backdoor or Targeted). 3. **Scale Discrepancy:** The color scales differ between the left (0.2-1.0) and right (0.5-0.8) pairs, indicating the data for Targeted attacks operates within a narrower, higher baseline range. 4. **Consistent Direction:** Within each subplot, the directional trend (↑ or ↓) is uniform across all cells. ### Interpretation This data suggests a fundamental difference in how backdoor and targeted attacks behave under increasing query complexity. * **For Backdoor Attacks:** Both vulnerability and mitigation effectiveness increase with more and longer query paths. This could imply that backdoor triggers or their detection mechanisms become more pronounced or easier to identify when embedded within more complex query structures. The system's ability to mitigate (b) improves alongside the vulnerability (a), but mitigation scores are consistently higher, suggesting defenses are somewhat effective. * **For Targeted Attacks:** The opposite occurs. Vulnerability and mitigation scores decrease as query paths multiply. This may indicate that targeted attacks become harder to execute successfully (lower vulnerability) or harder to defend against (lower mitigation) when the query structure is more complex and diffuse. The attack's precision might be diluted, but so might the defense's ability to pinpoint it. * **Overall Implication:** The security posture of the system is highly dependent on the attack type. Defenses that work well for backdoor scenarios (where complexity aids detection) may be less effective for targeted scenarios, where complexity appears to hinder both the attack and the defense. The narrower score range for targeted attacks suggests their outcomes are less variable and more consistently challenging to address.

## Heatmap: Query Path Effectiveness Across Backdoor and Targeted Scenarios ### Overview The image presents a comparative heatmap analysis of query path effectiveness in four scenarios: Backdoor-Vulnerability, Backdoor-Mitigation, Targeted-Vulnerability, and Targeted-Mitigation. The data is organized into 3x4 grids (rows = number of query paths [2, 3, 5]; columns = max query path length [1-hop to 4-hop]). Color intensity (green gradient) and numerical values indicate effectiveness, with arrows showing directional trends. --- ### Components/Axes - **Y-Axis (Left)**: "Number of Query Paths" (values: 2, 3, 5) - **X-Axis (Top)**: "Max Length of Query Path" (values: 1-hop, 2-hop, 3-hop, 4-hop) - **Legend (Right)**: Color scale from 0.2 (light yellow) to 1.0 (dark green), representing effectiveness magnitude. - **Sub-Figures**: - (a) Backdoor-Vulnerability - (b) Backdoor-Mitigation - (c) Targeted-Vulnerability - (d) Targeted-Mitigation --- ### Detailed Analysis #### (a) Backdoor-Vulnerability - **Trend**: Effectiveness increases with both query paths and hop length. - Example: 5-query paths, 4-hop = **0.55** (↑) - **Key Values**: - 2-query paths: 0.53 (1-hop), 0.70 (2-hop), 0.82 (3-hop), 0.64 (4-hop) - 3-query paths: 0.41 (1-hop), 0.61 (2-hop), 0.74 (3-hop), 0.53 (4-hop) - 5-query paths: 0.30 (1-hop), 0.48 (2-hop), 0.55 (3-hop), 0.38 (4-hop) #### (b) Backdoor-Mitigation - **Trend**: Effectiveness decreases with longer hop lengths but improves with more query paths. - Example: 5-query paths, 4-hop = **0.65** (↑) - **Key Values**: - 2-query paths: 0.64 (1-hop), 0.79 (2-hop), 0.86 (3-hop), 0.86 (4-hop) - 3-query paths: 0.53 (1-hop), 0.80 (2-hop), 0.85 (3-hop), 0.85 (4-hop) - 5-query paths: 0.38 (1-hop), 0.62 (2-hop), 0.65 (3-hop), 0.65 (4-hop) #### (c) Targeted-Vulnerability - **Trend**: Effectiveness decreases with longer hop lengths but stabilizes at higher query paths. - Example: 5-query paths, 4-hop = **0.68** (↓) - **Key Values**: - 2-query paths: 0.86 (1-hop), 0.89 (2-hop), 0.91 (3-hop), 0.69 (4-hop) - 3-query paths: 0.81 (1-hop), 0.90 (2-hop), 0.90 (3-hop), 0.62 (4-hop) - 5-query paths: 0.78 (1-hop), 0.84 (2-hop), 0.86 (3-hop), 0.60 (4-hop) #### (d) Targeted-Mitigation - **Trend**: Effectiveness decreases with longer hop lengths and fewer query paths. - Example: 2-query paths, 4-hop = **0.70** (↓) - **Key Values**: - 2-query paths: 0.86 (1-hop), 0.89 (2-hop), 0.91 (3-hop), 0.69 (4-hop) - 3-query paths: 0.81 (1-hop), 0.90 (2-hop), 0.90 (3-hop), 0.62 (4-hop) - 5-query paths: 0.78 (1-hop), 0.84 (2-hop), 0.86 (3-hop), 0.60 (4-hop) --- ### Key Observations 1. **Backdoor Scenarios**: - Vulnerability peaks at 3-hop for 2-query paths (0.82 in (a)). - Mitigation improves with more query paths (e.g., 5-query paths, 4-hop = 0.65 in (b)). 2. **Targeted Scenarios**: - Vulnerability remains high even at 4-hop (0.68–0.91 in (c)). - Mitigation effectiveness drops sharply at 4-hop (0.60–0.70 in (d)). 3. **Color Consistency**: - Darker greens (closer to 1.0) dominate Backdoor-Mitigation (b) and Targeted-Vulnerability (c). - Lighter greens (closer to 0.5) appear in Backdoor-Vulnerability (a) and Targeted-Mitigation (d). --- ### Interpretation - **Query Path Trade-offs**: Increasing query paths generally improves mitigation (e.g., 5-query paths in (b) vs. 2-query paths) but may reduce vulnerability in targeted scenarios (e.g., 5-query paths in (c) vs. 2-query paths). - **Hop Length Impact**: Longer hop lengths (4-hop) correlate with reduced mitigation effectiveness across all scenarios, suggesting complexity limits defensive strategies. - **Targeted vs. Backdoor**: Targeted scenarios show higher vulnerability (0.78–0.91 in (c)) but also stronger mitigation (0.60–0.91 in (d)) compared to backdoor cases, indicating tailored attacks exploit system weaknesses more effectively. The data underscores the importance of balancing query path complexity and length to optimize security outcomes, with targeted attacks demanding more nuanced mitigation strategies.