## Chart: Accuracy vs. Model Size ### Overview The image is a line chart comparing the accuracy of "Self Consistency" and "Greedy Decode" methods across different model sizes. The x-axis represents model size in billions of parameters, and the y-axis represents accuracy in percentage. ### Components/Axes * **X-axis:** Model size (#param in billions). Values: 1, 2, 5, 10, 20, 50, 100, 200. * **Y-axis:** Accuracy (%). Values range from 0 to 25, with increments of 5. * **Legend:** Located at the top-right of the chart. * Blue line with square marker: "Self Consistency" * Orange line with square marker: "Greedy Decode" ### Detailed Analysis * **Self Consistency (Blue Line):** * Trend: Generally slopes upward, indicating increasing accuracy with larger model sizes. * Data Points: * Model size 2: Accuracy ~3% * Model size 10: Accuracy ~3% * Model size 50: Accuracy ~15% * Model size 100: Accuracy ~20% * Model size 200: Accuracy ~27% * **Greedy Decode (Orange Line):** * Trend: Generally slopes upward, indicating increasing accuracy with larger model sizes. * Data Points: * Model size 2: Accuracy ~3.5% * Model size 10: Accuracy ~2% * Model size 50: Accuracy ~10% * Model size 100: Accuracy ~17% ### Key Observations * Both methods show an increase in accuracy as the model size increases. * "Self Consistency" consistently outperforms "Greedy Decode" across all model sizes. * The accuracy of "Self Consistency" increases more rapidly than "Greedy Decode" as the model size grows beyond 50 billion parameters. ### Interpretation The chart demonstrates that increasing model size generally improves the accuracy of both "Self Consistency" and "Greedy Decode" methods. However, "Self Consistency" appears to be more effective at leveraging larger models, resulting in higher accuracy gains compared to "Greedy Decode." This suggests that "Self Consistency" may be a more scalable approach for improving model performance as computational resources allow for larger models. The flattening of the "Greedy Decode" line at larger model sizes could indicate a diminishing return for this method, or that it requires further optimization to fully utilize the increased model capacity.

\n ## Line Chart: Accuracy vs. Model Size ### Overview This line chart compares the accuracy of two decoding methods, "Self Consistency" and "Greedy Decode", across varying model sizes. Accuracy is measured in percentage (%) and model size is measured in billions of parameters. The chart demonstrates how accuracy scales with model size for each method. ### Components/Axes * **X-axis:** "Model size (#param in billions)". Markers are present at 1, 2, 5, 10, 20, 50, 100, and 200. * **Y-axis:** "Accuracy (%)". Scale ranges from 0 to 25, with increments of 5. * **Legend:** Located in the top-right corner. * "Self Consistency" - Represented by a blue line with triangle markers. * "Greedy Decode" - Represented by an orange line with square markers. * **Gridlines:** Horizontal and vertical gridlines are present to aid in reading values. ### Detailed Analysis **Self Consistency (Blue Line):** The blue line representing "Self Consistency" shows a generally upward trend. * At Model Size = 1 billion parameters, Accuracy ≈ 2%. * At Model Size = 2 billion parameters, Accuracy ≈ 3%. * At Model Size = 5 billion parameters, Accuracy ≈ 3%. * At Model Size = 10 billion parameters, Accuracy ≈ 4%. * At Model Size = 20 billion parameters, Accuracy ≈ 8%. * At Model Size = 50 billion parameters, Accuracy ≈ 12%. * At Model Size = 100 billion parameters, Accuracy ≈ 16%. * At Model Size = 200 billion parameters, Accuracy ≈ 25%. **Greedy Decode (Orange Line):** The orange line representing "Greedy Decode" also shows an upward trend, but is generally lower than "Self Consistency". * At Model Size = 1 billion parameters, Accuracy ≈ 2%. * At Model Size = 2 billion parameters, Accuracy ≈ 3%. * At Model Size = 5 billion parameters, Accuracy ≈ 3%. * At Model Size = 10 billion parameters, Accuracy ≈ 3%. * At Model Size = 20 billion parameters, Accuracy ≈ 5%. * At Model Size = 50 billion parameters, Accuracy ≈ 8%. * At Model Size = 100 billion parameters, Accuracy ≈ 10%. * At Model Size = 200 billion parameters, Accuracy ≈ 18%. ### Key Observations * "Self Consistency" consistently outperforms "Greedy Decode" across all model sizes. * The accuracy gap between the two methods widens as the model size increases. * Both methods show relatively little improvement in accuracy between 1 and 10 billion parameters. * The most significant gains in accuracy for both methods occur when the model size exceeds 20 billion parameters. * The "Self Consistency" method shows a particularly steep increase in accuracy between 50 and 200 billion parameters. ### Interpretation The data suggests that increasing model size generally improves accuracy for both decoding methods. However, "Self Consistency" is a more effective decoding strategy, especially as model size grows. This could be because "Self Consistency" leverages multiple generated outputs to arrive at a more robust and accurate answer, which becomes more beneficial with larger, more complex models. The relatively flat performance curve for both methods at smaller model sizes (1-10 billion parameters) indicates that the benefits of increased model capacity are limited until a certain threshold is reached. The substantial gains observed at larger model sizes (50-200 billion parameters) suggest that these models have the capacity to learn more complex patterns and relationships, but require a more sophisticated decoding strategy like "Self Consistency" to fully realize their potential. The difference in performance between the two methods is likely due to the inherent limitations of "Greedy Decode", which selects the most probable token at each step without considering alternative possibilities. This can lead to suboptimal results, especially in complex tasks where multiple valid solutions exist.

## Line Chart: Accuracy vs. Model Size for Two Decoding Methods ### Overview The image is a line chart comparing the performance (accuracy) of two decoding methods—"Self Consistency" and "Greedy Decode"—across a range of model sizes. The chart demonstrates how accuracy scales with the number of parameters in the model. ### Components/Axes * **Chart Type:** Line chart with markers. * **X-Axis (Horizontal):** * **Title:** `Model size (#param in billions)` * **Scale:** Logarithmic (base 10). * **Tick Labels/Markers:** 1, 2, 5, 10, 20, 50, 100, 200. * **Y-Axis (Vertical):** * **Title:** `Accuracy (%)` * **Scale:** Linear. * **Range:** 0 to 30. * **Tick Labels:** 0, 5, 10, 15, 20, 25, 30. * **Legend:** * **Position:** Top-left corner of the plot area. * **Entry 1:** `Self Consistency` - Represented by a blue line with square markers. * **Entry 2:** `Greedy Decode` - Represented by an orange line with triangle markers. * **Background:** Light gray grid lines are present. ### Detailed Analysis **Data Series 1: Self Consistency (Blue line, square markers)** * **Visual Trend:** The line shows a gradual, shallow increase from 1B to 10B parameters, followed by a steep, accelerating upward slope from 20B to 100B parameters. * **Approximate Data Points:** * At 1B params: ~3% accuracy * At 2B params: ~3% accuracy * At 5B params: ~4% accuracy * At 10B params: ~5% accuracy * At 20B params: ~8% accuracy * At 50B params: ~15% accuracy * At 100B params: ~27% accuracy **Data Series 2: Greedy Decode (Orange line, triangle markers)** * **Visual Trend:** The line shows a steady, moderate upward slope across the entire range of model sizes. The rate of increase is more consistent and less dramatic than the Self Consistency line. * **Approximate Data Points:** * At 1B params: ~2% accuracy * At 2B params: ~2% accuracy * At 5B params: ~3% accuracy * At 10B params: ~4% accuracy * At 20B params: ~6% accuracy * At 50B params: ~10% accuracy * At 100B params: ~17% accuracy ### Key Observations 1. **Performance Gap:** The "Self Consistency" method consistently achieves higher accuracy than "Greedy Decode" at every model size shown. 2. **Diverging Trends:** The performance gap between the two methods widens significantly as model size increases. At 1B parameters, the difference is ~1 percentage point. At 100B parameters, the difference is ~10 percentage points. 3. **Scaling Behavior:** The "Self Consistency" line exhibits a "hockey stick" or exponential-like growth curve, particularly after the 20B parameter mark. The "Greedy Decode" line shows more linear growth on this log-linear plot. 4. **Critical Threshold:** The most dramatic acceleration in accuracy for "Self Consistency" occurs between 20B and 100B parameters. ### Interpretation The chart provides strong evidence that the **Self Consistency decoding method scales more effectively with model size than Greedy Decode**. While both methods improve as models grow larger, the benefit of using Self Consistency becomes disproportionately greater for very large models (50B+ parameters). This suggests that the computational overhead or sampling strategy inherent to Self Consistency is particularly well-suited to leveraging the increased capacity and potential reasoning capabilities of large-scale models. The data implies that for state-of-the-art performance at the largest scales, employing a method like Self Consistency is not just beneficial but may be critical, as the performance gap becomes substantial. The chart does not show data beyond 100B parameters, leaving open the question of whether this divergent trend continues.

## Line Graph: Accuracy vs. Model Size for Self Consistency and Greedy Decode ### Overview The image is a line graph comparing the accuracy of two methods—**Self Consistency** (blue line with square markers) and **Greedy Decode** (orange line with square markers)—across varying model sizes (measured in billions of parameters). Accuracy is plotted on the y-axis (0–25%), and model size is on the x-axis (1–200 billion parameters). The graph shows distinct performance trends between the two methods as model size increases. --- ### Components/Axes - **X-axis (Model size)**: Labeled "Model size (#param in billions)" with tick marks at 1, 2, 5, 10, 20, 50, 100, and 200. - **Y-axis (Accuracy)**: Labeled "Accuracy (%)" with tick marks at 0, 5, 10, 15, 20, and 25. - **Legend**: Located in the top-right corner, with: - **Blue squares**: Self Consistency - **Orange squares**: Greedy Decode --- ### Detailed Analysis #### Self Consistency (Blue Line) - **Trend**: Starts flat (3.5% accuracy at 1–10B parameters), then rises sharply after 20B. - **Data Points**: - 1B: ~3.5% - 2B: ~3.5% - 5B: ~3.5% - 10B: ~3.5% - 20B: ~7% - 50B: ~15% - 100B: ~25% - 200B: ~28% (exceeds y-axis maximum; likely an outlier or extrapolation). #### Greedy Decode (Orange Line) - **Trend**: Gradual, linear increase across all model sizes. - **Data Points**: - 1B: ~2.5% - 2B: ~2.5% - 5B: ~2.5% - 10B: ~2.5% - 20B: ~5% - 50B: ~10% - 100B: ~17% - 200B: ~18% --- ### Key Observations 1. **Performance Gap**: Self Consistency outperforms Greedy Decode at all model sizes, with the gap widening as model size increases (e.g., 28% vs. 18% at 200B). 2. **Scalability**: Self Consistency shows exponential growth in accuracy for models >50B, while Greedy Decode’s improvement plateaus. 3. **Anomaly**: The Self Consistency line at 200B exceeds the y-axis maximum (25%), suggesting either a data error or an intentional extrapolation. --- ### Interpretation The data demonstrates that **Self Consistency** is significantly more effective for large-scale models, likely due to its ability to handle complex reasoning tasks through iterative self-verification. In contrast, **Greedy Decode** performs poorly at scale, suggesting it is better suited for smaller models or simpler tasks. The 200B Self Consistency value (28%) may require validation, as it exceeds the chart’s y-axis range. This trend underscores the importance of method selection in large language model deployment, favoring consistency-driven approaches for high-accuracy requirements.