## Bar Chart: Model Performance on Math Problems
### Overview
The image is a series of bar charts comparing the performance of different language models on various math problem sets. The charts show the "Pass@1 accuracy (%)" for each model on the MATH, AIME 2024, AMC 2023, Olympiad Bench, and College Math datasets. The performance is broken down into "Policy model" and "PPM improvement" for rStar models, and "Policy model" and "ORM improvement" for Qwen models.
### Components/Axes
* **Title:** Model Performance on Math Problems
* **X-axis:** Pass@1 accuracy (%), with scales from 0 to 50 for MATH, AMC 2023, Olympiad Bench, and College Math; and 0 to 40 for AIME 2024.
* **Y-axis:** Language models:
* rStar-Math (Qwen7B)
* rStar-Math (Qwen1.5B)
* rStar-Math (Phi3.8B)
* Qwen2.5-Math-72B
* **Chart Categories:** MATH, AIME 2024, AMC 2023, Olympiad Bench, College Math
* **Legend:** Located at the top of the image.
* rStar Policy model (light green)
* rStar 7B PPM improvement (dark green)
* Qwen 72B Policy model (light blue)
* Qwen 72B ORM improvement (light purple)
### Detailed Analysis
#### MATH
* **rStar-Math (Qwen7B):**
* rStar Policy model: 78.4%
* rStar 7B PPM improvement: 89.4%
* **rStar-Math (Qwen1.5B):**
* rStar Policy model: 74.8%
* rStar 7B PPM improvement: 87.8%
* **rStar-Math (Phi3.8B):**
* rStar Policy model: 68%
* rStar 7B PPM improvement: 85.4%
* **Qwen2.5-Math-72B:**
* Qwen 72B Policy model: 85.6%
* Qwen 72B ORM improvement: 85.8%
#### AIME 2024
* **rStar-Math (Qwen7B):**
* rStar Policy model: 26.7%
* rStar 7B PPM improvement: 50%
* **rStar-Math (Qwen1.5B):**
* rStar Policy model: 13.3%
* rStar 7B PPM improvement: 46.7%
* **rStar-Math (Phi3.8B):**
* rStar Policy model: 10%
* rStar 7B PPM improvement: 40%
* **Qwen2.5-Math-72B:**
* Qwen 72B Policy model: 30%
* Qwen 72B ORM improvement: 36.7%
#### AMC 2023
* **rStar-Math (Qwen7B):**
* rStar Policy model: 47.5%
* rStar 7B PPM improvement: 87.5%
* **rStar-Math (Qwen1.5B):**
* rStar Policy model: 47.5%
* rStar 7B PPM improvement: 80%
* **rStar-Math (Phi3.8B):**
* rStar Policy model: 37.5%
* rStar 7B PPM improvement: 77.5%
* **Qwen2.5-Math-72B:**
* Qwen 72B Policy model: 70%
* Qwen 72B ORM improvement: 72.5%
#### Olympiad Bench
* **rStar-Math (Qwen7B):**
* rStar Policy model: 47.1%
* rStar 7B PPM improvement: 65.3%
* **rStar-Math (Qwen1.5B):**
* rStar Policy model: 42.5%
* rStar 7B PPM improvement: 63.5%
* **rStar-Math (Phi3.8B):**
* rStar Policy model: 36.6%
* rStar 7B PPM improvement: 59.3%
* **Qwen2.5-Math-72B:**
* Qwen 72B Policy model: 49%
* Qwen 72B ORM improvement: 54.5%
#### College Math
* **rStar-Math (Qwen7B):**
* rStar Policy model: 52.5%
* rStar 7B PPM improvement: 59%
* **rStar-Math (Qwen1.5B):**
* rStar Policy model: 50.1%
* rStar 7B PPM improvement: 59%
* **rStar-Math (Phi3.8B):**
* rStar Policy model: N/A (value not visible, but bar is present)
* rStar 7B PPM improvement: N/A (value not visible, but bar is present)
* **Qwen2.5-Math-72B:**
* Qwen 72B Policy model: 49.5%
* Qwen 72B ORM improvement: 50.6%
### Key Observations
* For rStar models, the "PPM improvement" consistently increases the "Pass@1 accuracy" compared to the "Policy model" across all datasets.
* The AIME 2024 dataset shows the lowest accuracy scores for all models compared to the other datasets.
* Qwen2.5-Math-72B generally performs competitively with the rStar models, sometimes exceeding their "Policy model" performance.
* The performance improvement from ORM on the Qwen model is less significant than the PPM improvement on the rStar models.
### Interpretation
The data suggests that the "PPM improvement" significantly enhances the performance of rStar models on math problem-solving tasks. The AIME 2024 dataset appears to be particularly challenging for all models. The Qwen2.5-Math-72B model demonstrates a reasonable baseline performance, but the ORM improvement does not provide as substantial a boost as the PPM improvement seen in the rStar models. The relative performance of the models varies across different problem sets, indicating that certain models may be better suited for specific types of math problems.
