## Line Charts: F1 Score vs. Hypervector Dimension for WebQSP, CWQ, and GrailQA ### Overview The image presents three line charts side-by-side, each displaying the relationship between the F1 score (in percentage) and the hypervector dimension for different datasets: WebQSP, CWQ, and GrailQA. The x-axis represents the hypervector dimension, with values ranging from 512 to 8192. The y-axis represents the F1 score, with different ranges for each dataset. ### Components/Axes * **Titles:** * Left Chart: WebQSP * Middle Chart: CWQ * Right Chart: GrailQA * **X-Axis (Horizontal):** * Label: Hypervector Dimension * Values: 512, 1024, 2048, 3072, 4096, 6144, 8192 * **Y-Axis (Vertical):** * Label: F1 (%) * Left Chart (WebQSP): Range approximately 77% to 79% * Ticks: 77, 78, 79 * Middle Chart (CWQ): Range approximately 64% to 66% * Ticks: 64, 65, 66 * Right Chart (GrailQA): Range approximately 86.0% to 87.0% * Ticks: 86.0, 86.5, 87.0 * **Data Series:** Each chart contains a single data series represented by a blue line with circular markers at each data point. ### Detailed Analysis **WebQSP (Left Chart):** * Trend: The F1 score increases sharply from 512 to 2048, then plateaus around 78.7% until 4096, and then decreases slightly towards 8192. * Data Points: * 512: Approximately 77.3% * 1024: Approximately 78.1% * 2048: Approximately 78.6% * 3072: Approximately 78.7% * 4096: Approximately 78.7% * 6144: Approximately 78.5% * 8192: Approximately 78.2% **CWQ (Middle Chart):** * Trend: The F1 score increases sharply from 512 to 2048, continues to increase at a slower rate until 6144, and then decreases slightly towards 8192. * Data Points: * 512: Approximately 64.2% * 1024: Approximately 65.0% * 2048: Approximately 65.5% * 3072: Approximately 65.7% * 4096: Approximately 65.8% * 6144: Approximately 65.9% * 8192: Approximately 65.7% **GrailQA (Right Chart):** * Trend: The F1 score increases sharply from 512 to 3072, plateaus around 86.7% until 4096, and then decreases towards 8192. * Data Points: * 512: Approximately 86.1% * 1024: Approximately 86.4% * 2048: Approximately 86.6% * 3072: Approximately 86.7% * 4096: Approximately 86.7% * 6144: Approximately 86.6% * 8192: Approximately 86.4% ### Key Observations * All three datasets show a similar trend: a rapid increase in F1 score with increasing hypervector dimension up to a certain point, followed by a plateau or slight decrease. * The optimal hypervector dimension appears to be around 3072-4096 for WebQSP and GrailQA, and around 6144 for CWQ, beyond which increasing the dimension does not significantly improve the F1 score and may even slightly reduce it. * GrailQA has the highest F1 scores, followed by WebQSP, and then CWQ. ### Interpretation The charts suggest that increasing the hypervector dimension initially improves the performance (F1 score) of the models on these datasets. However, there is a point of diminishing returns, beyond which increasing the dimension does not lead to significant improvements and may even lead to a slight decrease in performance. This could be due to overfitting or increased noise in the higher-dimensional space. The optimal hypervector dimension varies slightly depending on the dataset. The higher F1 scores for GrailQA indicate that the model performs better on this dataset compared to WebQSP and CWQ, potentially due to the nature of the questions or the structure of the knowledge graph.

## Chart: Hypervector Dimension vs. F1 Score for Different Datasets ### Overview This image presents three line charts, each displaying the relationship between Hypervector Dimension and F1 Score (%) for three different datasets: WebQSP, CWQ, and GrailQA. Each chart shows how the F1 score changes as the hypervector dimension increases. ### Components/Axes * **X-axis (all charts):** Hypervector Dimension, with markers at 3/512, 1024, 2048, 3072, 4096, 6144, and 8192. * **Y-axis (all charts):** F1 Score (%), ranging from approximately 76.5% to 87.0%. * **Chart 1 (left):** WebQSP dataset. * **Chart 2 (center):** CWQ dataset. * **Chart 3 (right):** GrailQA dataset. * **Line Color (all charts):** Blue. ### Detailed Analysis **Chart 1: WebQSP** The line representing WebQSP slopes upward from a value of approximately 76.5% at a hypervector dimension of 3/512 to a peak of approximately 78.8% at 4096. It then declines slightly to approximately 77.8% at 8192. * 3/512: ~76.5% * 1024: ~77.8% * 2048: ~78.4% * 3072: ~78.7% * 4096: ~78.8% * 6144: ~78.2% * 8192: ~77.8% **Chart 2: CWQ** The line representing CWQ starts at approximately 64.2% at a hypervector dimension of 3/512, increases to a peak of approximately 66.3% at 6144, and then decreases to approximately 65.8% at 8192. * 3/512: ~64.2% * 1024: ~65.0% * 2048: ~65.5% * 3072: ~65.9% * 4096: ~66.1% * 6144: ~66.3% * 8192: ~65.8% **Chart 3: GrailQA** The line representing GrailQA begins at approximately 85.8% at a hypervector dimension of 3/512, rises to a peak of approximately 86.7% at 4096, and then declines to approximately 86.3% at 8192. * 3/512: ~85.8% * 1024: ~86.1% * 2048: ~86.3% * 3072: ~86.5% * 4096: ~86.7% * 6144: ~86.5% * 8192: ~86.3% ### Key Observations * All three datasets show an initial increase in F1 score as the hypervector dimension increases. * The F1 scores generally plateau or slightly decrease after reaching a certain hypervector dimension. * GrailQA consistently exhibits the highest F1 scores across all hypervector dimensions. * CWQ consistently exhibits the lowest F1 scores across all hypervector dimensions. * The peak F1 score for each dataset occurs at different hypervector dimensions (WebQSP: 4096, CWQ: 6144, GrailQA: 4096). ### Interpretation The charts demonstrate the impact of hypervector dimension on the performance (measured by F1 score) of models trained on different datasets. The initial increase in F1 score suggests that increasing the hypervector dimension allows the model to capture more complex relationships within the data. However, the plateau or decline in F1 score at higher dimensions indicates that there is a point of diminishing returns, and potentially overfitting, where adding more dimensions does not further improve performance. The differences in peak F1 scores and optimal hypervector dimensions across the datasets suggest that the optimal model configuration is dataset-dependent. GrailQA, with its consistently high F1 scores, may be a simpler or more structured dataset compared to WebQSP and CWQ. The fact that the optimal dimension varies suggests that the complexity of the relationships within each dataset differs. The diminishing returns observed in all three charts suggest that there is a trade-off between model complexity (hypervector dimension) and generalization performance.

## Line Charts: F1 Score vs. Hypervector Dimension for Three Datasets ### Overview The image displays three separate line charts arranged horizontally. Each chart plots the F1 score (a performance metric) as a percentage against the "Hypervector Dimension" for a different dataset: WebQSP, CWQ, and GrailQA. The charts collectively illustrate how model performance, measured by F1 score, changes as the dimensionality of the hypervector representation is varied. ### Components/Axes * **Chart Titles (Top Center of each plot):** "WebQSP", "CWQ", "GrailQA". * **X-Axis (All Charts):** Label: "Hypervector Dimension". The axis is categorical with the following tick marks: 512, 1024, 2048, 3072, 4096, 6144, 8192. * **Y-Axis (All Charts):** Label: "F1 (%)". The scale and range differ for each chart: * **WebQSP:** Range approximately 77% to 79%. Major ticks at 77, 78, 79. * **CWQ:** Range approximately 64% to 66%. Major ticks at 64, 65, 66. * **GrailQA:** Range approximately 86.0% to 87.0%. Major ticks at 86.0, 86.5, 87.0. * **Data Series:** Each chart contains a single blue line with circular markers at each data point. There is no separate legend, as each plot represents one dataset. ### Detailed Analysis **1. WebQSP Chart (Left)** * **Trend:** The line shows an initial steep increase, peaks in the middle range of dimensions, and then gradually declines. * **Data Points (Approximate F1 %):** * Dimension 512: ~77.4% * Dimension 1024: ~78.1% * Dimension 2048: ~78.5% * Dimension 3072: ~78.6% (Appears to be the peak) * Dimension 4096: ~78.6% (Similar to 3072) * Dimension 6144: ~78.4% * Dimension 8192: ~78.1% **2. CWQ Chart (Center)** * **Trend:** The line shows a consistent upward trend that begins to plateau and then slightly dips at the highest dimension. * **Data Points (Approximate F1 %):** * Dimension 512: ~64.3% * Dimension 1024: ~65.0% * Dimension 2048: ~65.5% * Dimension 3072: ~65.7% * Dimension 4096: ~65.8% * Dimension 6144: ~66.0% (Appears to be the peak) * Dimension 8192: ~65.8% **3. GrailQA Chart (Right)** * **Trend:** The line rises sharply to a peak and then follows a steady, gradual decline. * **Data Points (Approximate F1 %):** * Dimension 512: ~86.2% * Dimension 1024: ~86.5% * Dimension 2048: ~86.7% * Dimension 3072: ~86.8% (Appears to be the peak) * Dimension 4096: ~86.8% (Similar to 3072) * Dimension 6144: ~86.7% * Dimension 8192: ~86.5% ### Key Observations 1. **Common Pattern:** All three datasets exhibit a similar inverted-U or "rise-then-fall" pattern. Performance improves as the hypervector dimension increases from 512, reaches an optimal point, and then degrades as the dimension increases further. 2. **Optimal Dimension Range:** The peak performance for all datasets occurs in the mid-range of dimensions tested, specifically between 3072 and 6144. 3. **Dataset Sensitivity:** The magnitude of performance change varies. The CWQ dataset shows the most dramatic relative improvement (from ~64.3% to ~66.0%), while the GrailQA dataset operates in a higher, narrower performance band (86.2% to 86.8%). 4. **Performance Degradation:** For WebQSP and GrailQA, the decline after the peak is more pronounced and begins at a lower dimension (after 4096) compared to CWQ, which peaks later (at 6144) and shows a very slight drop. ### Interpretation This data demonstrates a critical hyperparameter tuning insight for models using hypervector representations. The relationship between hypervector dimension and task performance (F1 score) is not linear; there is a clear point of diminishing returns followed by negative returns. * **The "Sweet Spot":** The charts suggest that simply increasing dimensionality does not guarantee better performance. There is an optimal complexity (dimension) for representing the knowledge required by each dataset. Dimensions that are too low may lack the capacity to encode necessary information, while dimensions that are too high may introduce noise, overfit, or make the representation less efficient, leading to performance degradation. * **Dataset-Dependent Optimum:** The exact optimal dimension varies by dataset (e.g., ~3072-4096 for WebQSP/GrailQA vs. ~6144 for CWQ). This implies that the ideal model configuration is dependent on the specific characteristics and complexity of the target data. * **Practical Implication:** For practitioners, this underscores the importance of empirical validation across a range of dimensions when designing hypervector-based systems. The charts provide a clear guide that testing dimensions from 512 to 8192 is necessary to identify the peak, and that the optimal value likely lies between 2048 and 6144 for similar question-answering tasks.

## Line Charts: F1 Score vs. Hypervector Dimension for WebQSP, CWQ, and GrailQA ### Overview The image contains three line charts comparing the F1 score (a metric for evaluating classification models) across varying hypervector dimensions (512 to 8192) for three datasets: **WebQSP**, **CWQ**, and **GrailQA**. Each chart shows a trendline with data points at specific hypervector dimensions, illustrating how model performance changes with increasing dimensionality. --- ### Components/Axes - **X-axis (Hypervector Dimension)**: Logarithmically spaced values: 512, 1024, 2048, 3072, 4096, 6144, 8192. - **Y-axis (F1 Score %)**: Ranges from ~64% to ~87% across the datasets. - **Legends**: Positioned at the top of each chart, labeled with dataset names (**WebQSP**, **CWQ**, **GrailQA**). All lines are blue, with no additional color differentiation. - **Markers**: Data points are marked with blue circles. --- ### Detailed Analysis #### WebQSP - **Trend**: The F1 score increases steadily from 512 to 3072 dimensions, peaking at **78.6%**, then declines slightly. - **Data Points**: - 512: 77.5% - 1024: 78.2% - 2048: 78.5% - 3072: 78.6% - 4096: 78.4% - 6144: 78.2% - 8192: 77.8% #### CWQ - **Trend**: The F1 score rises from 64.5% at 512 dimensions, peaks at **65.8%** at 6144 dimensions, then drops. - **Data Points**: - 512: 64.5% - 1024: 65.1% - 2048: 65.5% - 3072: 65.7% - 4096: 65.6% - 6144: 65.8% - 8192: 65.4% #### GrailQA - **Trend**: The F1 score starts at 86.0% at 512 dimensions, peaks at **87.0%** at 3072 dimensions, then declines. - **Data Points**: - 512: 86.0% - 1024: 86.3% - 2048: 86.5% - 3072: 87.0% - 4096: 86.7% - 6144: 86.5% - 8192: 86.2% --- ### Key Observations 1. **Optimal Dimensionality**: All datasets show a peak F1 score at intermediate dimensions (2048–6144), suggesting diminishing returns or overfitting at extreme dimensions. 2. **Performance Gaps**: - **WebQSP** consistently outperforms the others, with the highest F1 score (78.6%). - **CWQ** has the lowest performance (65.8% peak). 3. **Plateaus and Declines**: All charts exhibit a decline after the peak, indicating potential overfitting or noise amplification at higher dimensions. --- ### Interpretation The data suggests that hypervector dimensionality significantly impacts model performance, with an optimal range for each dataset. The peak F1 scores align with mid-range dimensions (2048–6144), implying that excessively large dimensions may introduce redundancy or noise. The performance disparity between datasets (e.g., WebQSP vs. CWQ) could reflect differences in data complexity, task difficulty, or model architecture suitability. These trends highlight the importance of hyperparameter tuning in natural language processing tasks, where balancing model capacity and generalization is critical.