## Chart Type: Probability Density Plots of Token Counts for Different Query Types ### Overview The image presents a grid of 12 probability density plots. Each plot visualizes the distribution of the number of tokens for a specific query type across three datasets: NELL, FB15k, and FB15k-237. The x-axis represents the number of tokens, and the y-axis represents the probability density. ### Components/Axes * **Title:** Each plot has a title indicating the "Query Type" (e.g., "Query Type=1p", "Query Type=2p", etc.). * **X-axis:** Labeled "Number of Tokens". The scale varies across plots, ranging from 0 to different maximum values (e.g., 600, 1200, 3500, 25000, 10000). * **Y-axis:** Labeled "Probability Density". The scale varies across plots, ranging from 0 to different maximum values (e.g., 0.012, 0.0035, 0.0010, 0.0004). * **Legend (Key):** Located in the top-right corner of each plot. It identifies the three datasets: * NELL (Blue) * FB15k (Orange) * FB15k-237 (Green) ### Detailed Analysis **Plot 1: Query Type=1p** * X-axis: 0 to 600 tokens * Y-axis: 0 to 0.012 probability density * NELL (Blue): Shows a sharp peak around 100 tokens, then rapidly decreases. * FB15k (Orange): Low probability density, peaking around 200 tokens. * FB15k-237 (Green): Low probability density, peaking around 200 tokens, similar to FB15k. **Plot 2: Query Type=2p** * X-axis: 0 to 1200 tokens * Y-axis: 0 to 0.0035 probability density * NELL (Blue): Peak around 200 tokens, then decreases. * FB15k (Orange): Peak around 600 tokens. * FB15k-237 (Green): Peak around 400 tokens. **Plot 3: Query Type=3p** * X-axis: 0 to 3500 tokens * Y-axis: 0 to 0.0010 probability density * NELL (Blue): Peak around 500 tokens, then decreases. * FB15k (Orange): Peak around 1000 tokens. * FB15k-237 (Green): Peak around 800 tokens. **Plot 4: Query Type=2i** * X-axis: 0 to 6000 tokens * Y-axis: 0 to 0.0010 probability density * NELL (Blue): Peak near 0 tokens, then decreases. * FB15k (Orange): Peak around 1000 tokens. * FB15k-237 (Green): Peak around 500 tokens. **Plot 5: Query Type=3i** * X-axis: 0 to 25000 tokens * Y-axis: 0 to 0.0004 probability density * NELL (Blue): Peak near 0 tokens, then decreases. * FB15k (Orange): Peak around 5000 tokens. * FB15k-237 (Green): Peak around 2500 tokens. **Plot 6: Query Type=ip** * X-axis: 0 to 25000 tokens * Y-axis: 0 to 0.0004 probability density * NELL (Blue): Peak near 0 tokens, then decreases. * FB15k (Orange): Peak around 5000 tokens. * FB15k-237 (Green): Peak around 2500 tokens. **Plot 7: Query Type=pi** * X-axis: 0 to 4000 tokens * Y-axis: 0 to 0.0008 probability density * NELL (Blue): Peak around 200 tokens, then decreases. * FB15k (Orange): Peak around 500 tokens. * FB15k-237 (Green): Peak around 400 tokens. **Plot 8: Query Type=2u** * X-axis: 0 to 10000 tokens * Y-axis: 0 to 0.0006 probability density * NELL (Blue): Peak near 0 tokens, then decreases. * FB15k (Orange): Peak around 1000 tokens. * FB15k-237 (Green): Peak around 500 tokens. **Plot 9: Query Type=up** * X-axis: 0 to 1000 tokens * Y-axis: 0 to 0.200 probability density * NELL (Blue): Peak near 0 tokens, then decreases. * FB15k (Orange): Peak near 0 tokens, then decreases. * FB15k-237 (Green): Peak near 0 tokens, then decreases. **Plot 10: Query Type=2in** * X-axis: 0 to 7000 tokens * Y-axis: 0 to 0.0008 probability density * NELL (Blue): Peak near 0 tokens, then decreases. * FB15k (Orange): Peak around 1000 tokens. * FB15k-237 (Green): Peak around 500 tokens. **Plot 11: Query Type=3in** * X-axis: 0 to 70000 tokens * Y-axis: 0 to 0.00020 probability density * NELL (Blue): Peak near 0 tokens, then decreases. * FB15k (Orange): Peak around 10000 tokens. * FB15k-237 (Green): Peak around 5000 tokens. **Plot 12: Query Type=inp** * X-axis: 0 to 1000 tokens * Y-axis: 0 to 0.0012 probability density * NELL (Blue): Peak around 200 tokens, then decreases. * FB15k (Orange): Peak around 200 tokens. * FB15k-237 (Green): Peak around 100 tokens. ### Key Observations * The distribution of token counts varies significantly depending on the query type. * NELL tends to have lower token counts compared to FB15k and FB15k-237. * FB15k and FB15k-237 often have similar distributions, but FB15k tends to have slightly higher token counts. * Some query types (e.g., "up") have very low token counts across all datasets. * The x-axis scales vary widely, indicating that some query types involve much larger numbers of tokens than others. ### Interpretation The plots illustrate the probability density of the number of tokens for different query types across three knowledge graph datasets. The data suggests that the complexity and structure of queries, as defined by their type, significantly influence the number of tokens required to represent them. The differences between the datasets (NELL, FB15k, FB15k-237) indicate variations in how these knowledge graphs are structured and queried. NELL generally uses fewer tokens, possibly indicating a simpler or more concise query structure compared to FB15k and FB15k-237. The specific query types (1p, 2p, 3p, etc.) likely correspond to different types of relationships or patterns being queried within the knowledge graphs. The plots can be used to understand the characteristics of different query types and how they relate to the structure of the underlying knowledge graphs. The "up" query type is a notable outlier, suggesting a very simple query structure with minimal token usage.

\n ## Chart: Probability Density vs. Number of Tokens for Different Query Types and Models ### Overview The image presents a 3x3 grid of scatter plots, each visualizing the probability density of text generated by different models (NELL, FB15k, FB15k-237) for various query types (1p, 2p, 3p, 1i, 2i, 3i, 1u, 2u, 3u). The x-axis represents the "Number of Tokens" and the y-axis represents "Probability Density". Each plot displays data points colored according to the model used. ### Components/Axes * **X-axis Label (all plots):** "Number of Tokens" - Scale varies per plot, ranging from 0 to approximately 6000. * **Y-axis Label (all plots):** "Probability Density" - Scale varies per plot, ranging from approximately 0 to 0.012. * **Title (each plot):** Indicates the "Query Type" (1p, 2p, 3p, 1i, 2i, 3i, 1u, 2u, 3u). * **Legend (top-right of each plot):** * NELL (Color: Blue) * FB15k (Color: Green) * FB15k-237 (Color: Red) ### Detailed Analysis or Content Details Here's a breakdown of each plot, noting trends and approximate data points. Due to the scatter plot nature, values are approximate. **Row 1: Query Types 1p, 2p, 3p** * **Query Type=1p:** The blue (NELL) line shows a slight upward trend, starting around (100, 0.002) and ending around (600, 0.010). The green (FB15k) line is relatively flat, hovering around 0.0015. The red (FB15k-237) line is also relatively flat, around 0.0005. * **Query Type=2p:** The blue (NELL) line shows a slight upward trend, starting around (400, 0.001) and ending around (1200, 0.003). The green (FB15k) line is relatively flat, hovering around 0.001. The red (FB15k-237) line is also relatively flat, around 0.0005. * **Query Type=3p:** The blue (NELL) line shows a slight upward trend, starting around (400, 0.0005) and ending around (3500, 0.006). The green (FB15k) line is relatively flat, hovering around 0.0003. The red (FB15k-237) line is also relatively flat, around 0.0002. **Row 2: Query Types 1i, 2i, 3i** * **Query Type=1i:** The blue (NELL) line shows a slight upward trend, starting around (400, 0.0004) and ending around (2000, 0.004). The green (FB15k) line is relatively flat, hovering around 0.0002. The red (FB15k-237) line is also relatively flat, around 0.0001. * **Query Type=2i:** The blue (NELL) line shows a slight upward trend, starting around (400, 0.0002) and ending around (1500, 0.002). The green (FB15k) line is relatively flat, hovering around 0.0001. The red (FB15k-237) line is also relatively flat, around 0.00005. * **Query Type=3i:** The blue (NELL) line shows a slight upward trend, starting around (400, 0.00005) and ending around (2500, 0.00025). The green (FB15k) line is relatively flat, hovering around 0.00002. The red (FB15k-237) line is also relatively flat, around 0.00001. **Row 3: Query Types 1u, 2u, 3u** * **Query Type=1u:** The blue (NELL) line shows a slight upward trend, starting around (400, 0.001) and ending around (2000, 0.004). The green (FB15k) line is relatively flat, hovering around 0.0005. The red (FB15k-237) line is also relatively flat, around 0.0002. * **Query Type=2u:** The blue (NELL) line shows a slight upward trend, starting around (400, 0.0005) and ending around (1500, 0.002). The green (FB15k) line is relatively flat, hovering around 0.0002. The red (FB15k-237) line is also relatively flat, around 0.0001. * **Query Type=3u:** The blue (NELL) line shows a slight upward trend, starting around (400, 0.0002) and ending around (2500, 0.001). The green (FB15k) line is relatively flat, hovering around 0.0001. The red (FB15k-237) line is also relatively flat, around 0.00005. **Footer:** * **Text:** "Fig. 3. Probability density vs. number of tokens for different query types and models." ### Key Observations * NELL consistently exhibits a positive correlation between the number of tokens and probability density across all query types. * FB15k and FB15k-237 show relatively flat probability density curves, indicating a less pronounced relationship with the number of tokens. * The probability density values are generally lower for query types 1i, 2i, 3i, and 1u, 2u, 3u compared to 1p, 2p, and 3p. * FB15k-237 consistently has the lowest probability density across all query types. ### Interpretation The data suggests that the NELL model generates text with a probability density that increases with the number of tokens, implying a greater likelihood of generating longer, more complex sentences or paragraphs. FB15k and FB15k-237, on the other hand, appear to generate text with a more consistent probability density regardless of the number of tokens, potentially indicating a preference for shorter, simpler outputs. The differences in probability density between the query types (1p/2p/3p vs. 1i/2i/3i/1u/2u/3u) could be related to the nature of the queries themselves. The 'p' queries might be more open-ended, allowing for more variation in text length and complexity, while the 'i' and 'u' queries might be more constrained, leading to more uniform outputs. The consistently lower probability density of FB15k-237 suggests that this model may be less capable of generating diverse or complex text compared to NELL and FB15k. This could be due to differences in model architecture, training data, or hyperparameters. The consistent flat lines for FB15k and FB15k-237 suggest a limited capacity to generate text beyond a certain complexity, regardless of the query type.

## Density Plots: Token Count Distributions by Query Type and Dataset ### Overview The image displays a 5x3 grid of 14 individual density plots (the bottom-right cell is empty). Each plot visualizes the probability density distribution of the "Number of Tokens" for a specific query type across three different knowledge graph datasets: NELL, FB15k, and FB15k-237. The overall purpose is to compare the token length characteristics of different query structures across these datasets. ### Components/Axes * **Grid Structure:** 14 subplots arranged in rows and columns. * **Subplot Titles:** Each subplot is titled with a specific "Query Type" (e.g., `Query Type=1p`, `Query Type=2p`, `Query Type=3p`, `Query Type=2i`, `Query Type=3i`, `Query Type=ip`, `Query Type=pi`, `Query Type=2u`, `Query Type=up`, `Query Type=2in`, `Query Type=3in`, `Query Type=inp`, `Query Type=pin`, `Query Type=pni`). * **X-Axis:** Labeled "Number of Tokens" for all plots. The scale varies significantly between plots, ranging from a maximum of ~600 (for `1p`) to ~70,000 (for `3in`). * **Y-Axis:** Labeled "Probability Density" for all plots. The scale also varies, with peak densities ranging from ~0.0002 to ~0.20. * **Legend:** Present in the top-right corner of each subplot. It contains three entries: * `NELL` (represented by a blue filled area/line) * `FB15k` (represented by an orange filled area/line) * `FB15k-237` (represented by a green filled area/line) ### Detailed Analysis The following describes each subplot, noting the approximate x-axis range, the visual trend for each dataset, and key density peaks. **Row 1:** 1. **Query Type=1p:** X-axis: 0-600. **NELL (blue):** Extremely sharp, high peak (density ~0.012) near 100 tokens, then drops to near zero. **FB15k (orange) & FB15k-237 (green):** Very low, broad distributions peaking gently around 150-200 tokens. 2. **Query Type=2p:** X-axis: 0-1200. **NELL:** Sharp peak (density ~0.0035) near 150 tokens. **FB15k & FB15k-237:** Broader, lower distributions. FB15k-237 (green) has a slightly higher and later peak (~400 tokens) than FB15k. 3. **Query Type=3p:** X-axis: 0-3500. **NELL:** Sharp peak (density ~0.0010) near 250 tokens. **FB15k & FB15k-237:** Very broad, low distributions extending past 3000 tokens, with FB15k-237 peaking slightly higher and earlier than FB15k. **Row 2:** 4. **Query Type=2i:** X-axis: 0-6000. **NELL:** Sharp peak (density ~0.0010) near 200 tokens. **FB15k & FB15k-237:** Broad distributions with peaks around 500-1000 tokens, extending to 6000. 5. **Query Type=3i:** X-axis: 0-25000. **NELL:** Sharp peak (density ~0.0004) near 500 tokens. **FB15k & FB15k-237:** Very broad, low distributions with multiple small humps, extending to 25,000 tokens. 6. **Query Type=ip:** X-axis: 0-25000. **NELL:** Sharp peak (density ~0.0004) near 1000 tokens. **FB15k & FB15k-237:** Broad distributions with a notable secondary hump for FB15k around 5000 tokens. **Row 3:** 7. **Query Type=pi:** X-axis: 0-4000. **NELL:** Sharp peak (density ~0.0008) near 250 tokens. **FB15k & FB15k-237:** Broader distributions with peaks around 500 tokens, extending to 4000. 8. **Query Type=2u:** X-axis: 0-10000. **NELL:** Sharp peak (density ~0.0006) near 500 tokens. **FB15k & FB15k-237:** Broad distributions with peaks around 1000-2000 tokens. 9. **Query Type=up:** X-axis: 0-1000. **NELL:** Extremely sharp, very high peak (density ~0.20) near 100 tokens. **FB15k & FB15k-237:** Very low, flat distributions barely visible on this scale. **Row 4:** 10. **Query Type=2in:** X-axis: 0-7000. **NELL:** Sharp peak (density ~0.0008) near 500 tokens. **FB15k & FB15k-237:** Broader distributions with peaks around 1000-1500 tokens. 11. **Query Type=3in:** X-axis: 0-70000. **NELL:** Sharp peak (density ~0.0002) near 2000 tokens. **FB15k & FB15k-237:** Very broad, low distributions with multiple small humps, extending to 70,000 tokens. 12. **Query Type=inp:** X-axis: 0-1000. **NELL:** Broad peak (density ~0.0012) centered around 200 tokens. **FB15k & FB15k-237:** Broader, lower distributions. FB15k-237 (green) is notably higher than FB15k (orange) across most of the range. **Row 5:** 13. **Query Type=pin:** X-axis: 0-1200. **NELL:** Sharp peak (density ~0.0030) near 200 tokens. **FB15k & FB15k-237:** Broader distributions with peaks around 300-400 tokens. 14. **Query Type=pni:** X-axis: 0-1200. **NELL:** Sharp peak (density ~0.0035) near 150 tokens. **FB15k & FB15k-237:** Broader distributions with peaks around 200-300 tokens. ### Key Observations 1. **Consistent Dataset Behavior:** Across nearly all query types, the **NELL** dataset (blue) exhibits a distribution with a much sharper, higher peak at a lower token count compared to the other two datasets. This indicates NELL queries are consistently more concise. 2. **FB15k vs. FB15k-237:** The **FB15k** (orange) and **FB15k-237** (green) distributions are generally broader and shifted to higher token counts. In many plots (e.g., `2p`, `3p`, `inp`), the FB15k-237 distribution is slightly higher or peaks earlier than the standard FB15k distribution. 3. **Query Type Complexity:** The x-axis scale (max token count) increases with apparent query complexity. Simple queries like `1p` and `up` have ranges <1000, while complex queries like `3i`, `3in`, and `ip` have ranges extending to 25,000-70,000 tokens. 4. **Extreme Outlier:** The `Query Type=up` plot is a major outlier. The NELL distribution here is an exceptionally sharp spike (density ~0.20), suggesting this specific query type in NELL has an extremely consistent and very short token length. The FB15k distributions are negligible on this scale. ### Interpretation This visualization provides a technical analysis of query structure complexity across different knowledge graph benchmarks. The data suggests: * **Structural Differences in Datasets:** The stark contrast between NELL and the FB15k variants implies fundamental differences in how queries are formulated or what they represent in these datasets. NELL queries appear to be templated or constrained to be very short, while FB15k queries allow for much greater variability and length. * **Impact of Dataset Version:** The subtle but consistent differences between FB15k and FB15k-237 (a filtered version of FB15k) suggest that the filtering process may slightly alter the distribution of query lengths, often making them marginally shorter or more concentrated. * **Query Type Taxonomy:** The varying x-axis scales serve as a proxy for the inherent complexity of the query types. The `u` (union) and `n` (negation) operators, especially in combination (`3in`), appear to generate the most verbose queries. The `p` (projection) and `i` (intersection) operators also lead to longer queries. * **Practical Implication:** For researchers using these datasets, this analysis highlights that models processing FB15k queries must handle significantly longer and more variable input sequences than those processing NELL. The `up` query type in NELL is a special case of extreme consistency. This information is crucial for designing model architectures, setting maximum sequence lengths, and understanding benchmark difficulty.

## Line Graphs: Probability Density Distributions Across Query Types and Models ### Overview The image displays 14 line graphs arranged in a grid, each representing the probability density distribution of token counts for different query types (e.g., `1p`, `2p`, `3p`, `ip`, `pi`, `up`, `in`, `inp`, `pin`, `2i`, `3i`, `2u`, `3u`). Three models are compared: `key` (blue), `NELL` (orange), and `FB15k-237` (green). Each graph shows how token counts are probabilistically distributed for a specific query type across these models. --- ### Components/Axes - **X-Axis**: "Number of Tokens" (ranges vary per graph, e.g., 0–600 for `1p`, 0–1200 for `2p`, up to 10,000 for `2u`). - **Y-Axis**: "Probability Density" (consistent scale: 0.0000 to 0.0012). - **Legend**: Located in the top-right corner of each graph, with labels: - `key` (blue) - `NELL` (orange) - `FB15k-237` (green) - **Graph Titles**: Positioned at the top of each subplot, labeled with query types (e.g., `Query Type=1p`, `Query Type=2p`). --- ### Detailed Analysis #### Query Type `1p` - **Key (blue)**: Sharp peak at ~100 tokens (probability density ~0.0012). - **NELL (orange)**: Broader distribution, peaking at ~150 tokens (density ~0.0008). - **FB15k-237 (green)**: Flattest distribution, peaking at ~200 tokens (density ~0.0005). #### Query Type `2p` - **Key (blue)**: Peak at ~200 tokens (density ~0.0035). - **NELL (orange)**: Broader peak at ~300 tokens (density ~0.0025). - **FB15k-237 (green)**: Gradual decline from ~400 tokens (density ~0.0015). #### Query Type `3p` - **Key (blue)**: Peak at ~500 tokens (density ~0.0010). - **NELL (orange)**: Broader peak at ~700 tokens (density ~0.0008). - **FB15k-237 (green)**: Flattest distribution, peaking at ~1,000 tokens (density ~0.0005). #### Query Type `ip` - **Key (blue)**: Sharp peak at ~200 tokens (density ~0.0004). - **NELL (orange)**: Broader peak at ~300 tokens (density ~0.0002). - **FB15k-237 (green)**: Flattest distribution, peaking at ~500 tokens (density ~0.0001). #### Query Type `pi` - **Key (blue)**: Sharp peak at ~1,000 tokens (density ~0.0008). - **NELL (orange)**: Broader peak at ~1,500 tokens (density ~0.0005). - **FB15k-237 (green)**: Flattest distribution, peaking at ~2,000 tokens (density ~0.0003). #### Query Type `up` - **Key (blue)**: Single sharp peak at ~200 tokens (density ~0.20). - **NELL (orange)**: Minimal presence, negligible density. - **FB15k-237 (green)**: Minimal presence, negligible density. #### Query Type `in` - **Key (blue)**: Sharp peak at ~1,000 tokens (density ~0.0020). - **NELL (orange)**: Broader peak at ~2,000 tokens (density ~0.0010). - **FB15k-237 (green)**: Flattest distribution, peaking at ~3,000 tokens (density ~0.0005). #### Query Type `inp` - **Key (blue)**: Sharp peak at ~500 tokens (density ~0.0012). - **NELL (orange)**: Broader peak at ~800 tokens (density ~0.0008). - **FB15k-237 (green)**: Flattest distribution, peaking at ~1,200 tokens (density ~0.0005). #### Query Type `pin` - **Key (blue)**: Sharp peak at ~300 tokens (density ~0.0030). - **NELL (orange)**: Broader peak at ~500 tokens (density ~0.0020). - **FB15k-237 (green)**: Flattest distribution, peaking at ~700 tokens (density ~0.0010). #### Query Type `pi` (Repeated) - Same as earlier `pi` analysis. #### Query Type `2i` - **Key (blue)**: Sharp peak at ~1,000 tokens (density ~0.0008). - **NELL (orange)**: Broader peak at ~2,000 tokens (density ~0.0005). - **FB15k-237 (green)**: Flattest distribution, peaking at ~3,000 tokens (density ~0.0003). #### Query Type `3i` - **Key (blue)**: Sharp peak at ~5,000 tokens (density ~0.0004). - **NELL (orange)**: Broader peak at ~7,000 tokens (density ~0.0003). - **FB15k-237 (green)**: Flattest distribution, peaking at ~9,000 tokens (density ~0.0002). #### Query Type `2u` - **Key (blue)**: Sharp peak at ~5,000 tokens (density ~0.0006). - **NELL (orange)**: Broader peak at ~7,000 tokens (density ~0.0004). - **FB15k-237 (green)**: Flattest distribution, peaking at ~9,000 tokens (density ~0.0002). #### Query Type `3u` - **Key (blue)**: Sharp peak at ~10,000 tokens (density ~0.0003). - **NELL (orange)**: Broader peak at ~12,000 tokens (density ~0.0002). - **FB15k-237 (green)**: Flattest distribution, peaking at ~14,000 tokens (density ~0.0001). --- ### Key Observations 1. **Model Differences**: - `key` consistently shows sharp, narrow peaks, indicating precise token usage. - `NELL` exhibits broader distributions, suggesting variability in token requirements. - `FB15k-237` has the flattest distributions, implying uniform token usage across ranges. 2. **Query Type Trends**: - Complex query types (e.g., `3p`, `2u`, `3u`) require higher token counts. - Simpler query types (e.g., `1p`, `up`) cluster around lower token counts. 3. **Anomalies**: - The `up` query type (`Query Type=up`) has an extreme outlier: `key` dominates with a single sharp peak, while `NELL` and `FB15k-237` are negligible. --- ### Interpretation The data suggests that: - The `key` model is optimized for specific token counts, likely due to its precision in handling structured queries. - `NELL` and `FB15k-237` models exhibit trade-offs between flexibility and uniformity, with `NELL` being more variable and `FB15k-237` more consistent. - Query types with higher token counts (e.g., `3p`, `2u`) may involve more complex or ambiguous tasks, requiring models to explore wider token ranges. - The `up` query type’s dominance by `key` highlights its unique suitability for this specific task, possibly due to its simplicity or structured nature. This analysis underscores the importance of model selection based on query complexity and token efficiency requirements.