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## 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.
