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## Bar Chart: Ablation study of problem-distiller
### Overview
This bar chart presents a comparative analysis of model performance (Accuracy in percentage) across four different tasks: Game of 24, Word list sorting, Checkmate-in-One, and MGSM. The chart compares the performance of models with and without the "problem-distiller" component. The models tested are BoT+Llama-3-70B and BoT+GPT-4.
### Components/Axes
* **Title:** "Ablation study of problem-distiller" (positioned at the top-center)
* **X-axis:** Task names: "Game of 24", "Word list sorting", "Checkmate-in-One", "MGSM" (placed at the bottom)
* **Y-axis:** Accuracy (%) - Scale ranges from 0 to 100 (placed on the left)
* **Legend:** Located at the top of the chart, indicating the data series:
* Blue: BoT+Llama-3-70B (w/o problem-distiller)
* Orange: BoT+Llama-3-70B (w/ problem-distiller)
* Red: BoT+GPT-4 (w/o problem-distiller)
* Yellow: BoT+GPT-4 (w/ problem-distiller)
### Detailed Analysis
The chart consists of four groups of bars, one for each task. Each group contains four bars representing the accuracy of each model configuration.
**Game of 24:**
* BoT+Llama-3-70B (w/o problem-distiller): Approximately 71.2% accuracy.
* BoT+Llama-3-70B (w/ problem-distiller): Approximately 78.4% accuracy.
* BoT+GPT-4 (w/o problem-distiller): Approximately 76.5% accuracy.
* BoT+GPT-4 (w/ problem-distiller): Approximately 82.4% accuracy.
**Word list sorting:**
* BoT+Llama-3-70B (w/o problem-distiller): Approximately 89.5% accuracy.
* BoT+Llama-3-70B (w/ problem-distiller): Approximately 92.3% accuracy.
* BoT+GPT-4 (w/o problem-distiller): Approximately 97.3% accuracy.
* BoT+GPT-4 (w/ problem-distiller): Approximately 99.6% accuracy.
**Checkmate-in-One:**
* BoT+Llama-3-70B (w/o problem-distiller): Approximately 64.3% accuracy.
* BoT+Llama-3-70B (w/ problem-distiller): Approximately 75.6% accuracy.
* BoT+GPT-4 (w/o problem-distiller): Approximately 78.9% accuracy.
* BoT+GPT-4 (w/ problem-distiller): Approximately 86.4% accuracy.
**MGSM:**
* BoT+Llama-3-70B (w/o problem-distiller): Approximately 85.6% accuracy.
* BoT+Llama-3-70B (w/ problem-distiller): Approximately 86.8% accuracy.
* BoT+GPT-4 (w/o problem-distiller): Approximately 87.4% accuracy.
* BoT+GPT-4 (w/ problem-distiller): Approximately 89.2% accuracy.
### Key Observations
* The "problem-distiller" consistently improves the accuracy of both BoT+Llama-3-70B and BoT+GPT-4 across all tasks.
* BoT+GPT-4 generally outperforms BoT+Llama-3-70B, both with and without the problem-distiller.
* The largest performance gains from the problem-distiller are observed in the "Checkmate-in-One" task for BoT+Llama-3-70B (an increase of approximately 11.3 percentage points).
* The smallest performance gains from the problem-distiller are observed in the "MGSM" task for BoT+Llama-3-70B (an increase of approximately 1.2 percentage points).
### Interpretation
The data strongly suggests that the "problem-distiller" is an effective component for improving the performance of both model architectures (Llama-3-70B and GPT-4) across a variety of reasoning tasks. The consistent improvement across all tasks indicates that the problem-distiller is not task-specific but rather provides a general benefit to the models' reasoning capabilities. The larger gains observed in "Checkmate-in-One" might indicate that this task benefits more from the problem-distiller's ability to refine or structure the problem representation. The fact that GPT-4 consistently achieves higher accuracy, even without the problem-distiller, highlights its superior inherent reasoning abilities. The ablation study demonstrates the value added by the problem-distiller, quantifying its impact on model performance. The chart provides empirical evidence supporting the integration of the problem-distiller into these models to enhance their problem-solving skills.
