## Line Chart: Pass@1 Performance vs. Number of Alternative Tokens
### Overview
This line chart compares the Pass@1 performance of two models, GSM8K and SVAMP, as the number of alternative tokens increases from 3 to 10. The y-axis represents the Pass@1 accuracy (in percentage), and the x-axis represents the number of alternative tokens considered.
### Components/Axes
* **X-axis Title:** "number of alternative tokens"
* Scale: 3 to 10, with increments of 1.
* **Y-axis Title:** "pass@1 (%)"
* Scale: 80 to 94, with increments of 2.
* **Legend:** Located in the top-right corner.
* GSM8K: Represented by a yellow line with square markers.
* SVAMP: Represented by a teal line with circular markers.
* **Gridlines:** Present in both horizontal and vertical directions, aiding in value estimation.
### Detailed Analysis
**GSM8K (Yellow Line):**
The line representing GSM8K shows a slight upward trend, but plateaus after 7 alternative tokens.
* At 3 alternative tokens: Approximately 84.5% Pass@1.
* At 4 alternative tokens: Approximately 85.5% Pass@1.
* At 5 alternative tokens: Approximately 87% Pass@1.
* At 6 alternative tokens: Approximately 87.5% Pass@1.
* At 7 alternative tokens: Approximately 88% Pass@1.
* At 8 alternative tokens: Approximately 88% Pass@1.
* At 9 alternative tokens: Approximately 88% Pass@1.
* At 10 alternative tokens: Approximately 88% Pass@1.
**SVAMP (Teal Line):**
The line representing SVAMP shows a more consistent upward trend throughout the range of alternative tokens.
* At 3 alternative tokens: Approximately 87% Pass@1.
* At 4 alternative tokens: Approximately 87.5% Pass@1.
* At 5 alternative tokens: Approximately 88% Pass@1.
* At 6 alternative tokens: Approximately 88.5% Pass@1.
* At 7 alternative tokens: Approximately 88.5% Pass@1.
* At 8 alternative tokens: Approximately 89% Pass@1.
* At 9 alternative tokens: Approximately 89.5% Pass@1.
* At 10 alternative tokens: Approximately 90% Pass@1.
### Key Observations
* SVAMP consistently outperforms GSM8K across all tested numbers of alternative tokens.
* The performance gain for GSM8K diminishes significantly after 7 alternative tokens, suggesting a saturation point.
* SVAMP shows a more sustained improvement in Pass@1 as the number of alternative tokens increases.
* The difference in performance between the two models is relatively small, but noticeable.
### Interpretation
The chart demonstrates the impact of increasing the number of alternative tokens on the Pass@1 accuracy of two language models, GSM8K and SVAMP. The results suggest that while both models benefit from considering more alternatives, SVAMP is more effectively utilizing this increased search space. The plateauing performance of GSM8K indicates that its ability to leverage additional tokens is limited, potentially due to architectural constraints or training data characteristics. The consistent improvement of SVAMP suggests a more robust mechanism for exploring and selecting optimal solutions from a larger set of possibilities. This could be due to differences in model size, training methodology, or the specific tasks they were trained on. The data suggests that for maximizing Pass@1 accuracy, increasing the number of alternative tokens is a beneficial strategy, particularly for models like SVAMP that can effectively exploit this expanded search space.
