## Line Chart: Accuracy vs. Sampled Reasoning Paths ### Overview The image is a line chart comparing the accuracy (%) of different decoding strategies against the number of sampled reasoning paths. The chart includes seven different decoding strategies, each represented by a distinct colored line. The x-axis represents the number of sampled reasoning paths, and the y-axis represents the accuracy percentage. ### Components/Axes * **X-axis:** "#Sampled Reasoning Paths" with tick marks at 0, 5, 10, 15, 20, 25, 30, 35, and 40. * **Y-axis:** "Accuracy (%)" with tick marks at 44, 48, 52, 56, 60, 64, 68, 72, and 76. * **Legend:** Located at the top-right of the chart, it identifies each line by color and decoding strategy: * Blue: T=0.7, k=40 * Orange: T=0.5, k=40 * Green: T=0.3, k=40 * Red: T=0.7, k=20 * Purple: T=0.7, no top k * Brown: p=0.95 * Pink: p=0.9 * Gray: Greedy Decode ### Detailed Analysis * **T=0.7, k=40 (Blue):** Starts at approximately 49% accuracy at 0 sampled paths, rises sharply to about 62% at 5 paths, reaches approximately 71% at 10 paths, and plateaus around 74% at 40 paths. * **T=0.5, k=40 (Orange):** Starts at approximately 44% accuracy at 0 sampled paths, rises sharply to about 65% at 5 paths, reaches approximately 70% at 10 paths, and plateaus around 72% at 40 paths. * **T=0.3, k=40 (Green):** Starts at approximately 56% accuracy at 0 sampled paths, rises sharply to about 64% at 5 paths, reaches approximately 66% at 10 paths, and plateaus around 68% at 40 paths. * **T=0.7, k=20 (Red):** Starts at approximately 56% accuracy at 0 sampled paths, rises sharply to about 64% at 5 paths, reaches approximately 70% at 10 paths, and plateaus around 72% at 40 paths. * **T=0.7, no top k (Purple):** Starts at approximately 50% accuracy at 0 sampled paths, rises sharply to about 60% at 5 paths, reaches approximately 70% at 10 paths, and plateaus around 75% at 40 paths. * **p=0.95 (Brown):** Starts at approximately 56% accuracy at 0 sampled paths, rises sharply to about 65% at 5 paths, reaches approximately 70% at 10 paths, and plateaus around 72% at 40 paths. * **p=0.9 (Pink):** Starts at approximately 48% accuracy at 0 sampled paths, rises sharply to about 65% at 5 paths, reaches approximately 71% at 10 paths, and plateaus around 74% at 40 paths. * **Greedy Decode (Gray):** Remains constant at approximately 57% accuracy regardless of the number of sampled reasoning paths. ### Key Observations * All decoding strategies, except for "Greedy Decode," show a significant increase in accuracy as the number of sampled reasoning paths increases from 0 to 10. * After 10 sampled paths, the accuracy for most strategies plateaus, with only marginal improvements beyond that point. * The "Greedy Decode" strategy has a constant accuracy, indicating that it does not benefit from increased sampling. * The "T=0.7, no top k" strategy (Purple) appears to achieve the highest accuracy at 40 sampled paths. ### Interpretation The chart suggests that sampling multiple reasoning paths can significantly improve the accuracy of decoding strategies, but the benefits diminish after a certain number of samples (around 10). The "Greedy Decode" strategy is not effective in this context, as it does not leverage multiple reasoning paths. The "T=0.7, no top k" strategy seems to be the most effective among those tested, achieving the highest accuracy with a larger number of sampled paths. The parameters T and k likely represent temperature and the number of top candidates, respectively, in a decoding algorithm. The 'p' parameter likely represents a probability threshold. The chart highlights the trade-off between computational cost (number of sampled paths) and accuracy, suggesting that an optimal balance can be achieved with around 10 sampled paths for most strategies.

## Line Chart: Accuracy vs. Sampled Reasoning Paths ### Overview This image presents a line chart illustrating the relationship between the number of sampled reasoning paths and the resulting accuracy, for various decoding strategies. The chart compares several configurations of temperature (T) and top-k sampling (k), along with probability (p) values, against a "Greedy Decode" baseline. ### Components/Axes * **X-axis:** "#Sampled Reasoning Paths" - Ranging from 0 to 40, with markers at 0, 5, 10, 15, 20, 25, 30, 35, and 40. * **Y-axis:** "Accuracy (%)" - Ranging from 44% to 76%, with markers at 44, 48, 52, 56, 60, 64, 68, 72, and 76. * **Legend:** Located in the top-right corner, containing the following lines and their corresponding colors: * T=0.7, k=40 (Blue) * T=0.5, k=40 (Orange) * T=0.3, k=40 (Green) * T=0.7, k=20 (Red) * T=0.7, no top k (Dark Blue) * p=0.95 (Brown) * p=0.9 (Magenta) * Greedy Decode (Gray) ### Detailed Analysis Here's a breakdown of each line's trend and approximate data points: * **T=0.7, k=40 (Blue):** The line slopes upward, showing increasing accuracy with more sampled reasoning paths. * 0 Paths: ~54% * 5 Paths: ~60% * 10 Paths: ~67% * 15 Paths: ~70% * 20 Paths: ~72% * 25 Paths: ~73% * 30 Paths: ~73.5% * 35 Paths: ~74% * 40 Paths: ~75% * **T=0.5, k=40 (Orange):** The line also slopes upward, but starts lower and plateaus earlier than the blue line. * 0 Paths: ~44% * 5 Paths: ~54% * 10 Paths: ~65% * 15 Paths: ~69% * 20 Paths: ~71% * 25 Paths: ~72% * 30 Paths: ~72% * 35 Paths: ~72% * 40 Paths: ~72% * **T=0.3, k=40 (Green):** This line shows a moderate upward slope, but remains lower than the blue and orange lines. * 0 Paths: ~50% * 5 Paths: ~58% * 10 Paths: ~64% * 15 Paths: ~66% * 20 Paths: ~68% * 25 Paths: ~68% * 30 Paths: ~68% * 35 Paths: ~68% * 40 Paths: ~68% * **T=0.7, k=20 (Red):** This line exhibits a similar upward trend to the blue line, but with slightly lower accuracy values. * 0 Paths: ~54% * 5 Paths: ~62% * 10 Paths: ~68% * 15 Paths: ~70% * 20 Paths: ~71% * 25 Paths: ~72% * 30 Paths: ~72% * 35 Paths: ~73% * 40 Paths: ~73% * **T=0.7, no top k (Dark Blue):** This line shows a strong upward trend, reaching the highest accuracy values. * 0 Paths: ~56% * 5 Paths: ~64% * 10 Paths: ~71% * 15 Paths: ~73% * 20 Paths: ~74% * 25 Paths: ~75% * 30 Paths: ~75% * 35 Paths: ~75% * 40 Paths: ~76% * **p=0.95 (Brown):** This line shows a moderate upward trend, similar to the green line. * 0 Paths: ~54% * 5 Paths: ~60% * 10 Paths: ~66% * 15 Paths: ~69% * 20 Paths: ~70% * 25 Paths: ~71% * 30 Paths: ~71% * 35 Paths: ~71% * 40 Paths: ~72% * **p=0.9 (Magenta):** This line exhibits the strongest upward trend and achieves the highest accuracy values, closely following the "T=0.7, no top k" line. * 0 Paths: ~54% * 5 Paths: ~62% * 10 Paths: ~70% * 15 Paths: ~72% * 20 Paths: ~73% * 25 Paths: ~74% * 30 Paths: ~74% * 35 Paths: ~75% * 40 Paths: ~75% * **Greedy Decode (Gray):** This line remains flat at approximately 56% accuracy, regardless of the number of sampled reasoning paths. * All Paths: ~56% ### Key Observations * Increasing the number of sampled reasoning paths generally improves accuracy for most decoding strategies. * The "Greedy Decode" strategy consistently performs the worst and does not benefit from increased sampling. * The "T=0.7, no top k" and "p=0.9" strategies achieve the highest accuracy, particularly with a larger number of sampled reasoning paths. * Lower temperature values (T=0.3) result in lower accuracy compared to higher temperature values (T=0.5, T=0.7). * Reducing the top-k value (k=20 vs k=40) appears to slightly decrease accuracy. ### Interpretation The data suggests that employing sampling techniques during decoding significantly enhances the accuracy of the model, especially when combined with appropriate temperature and probability settings. The "Greedy Decode" approach, which lacks sampling, demonstrates a clear performance limitation. The superior performance of the "T=0.7, no top k" and "p=0.9" strategies indicates that removing constraints on the sampling process (no top k) or using a higher probability threshold (p=0.9) allows the model to explore a wider range of reasoning paths, leading to more accurate results. The plateauing of some lines (e.g., T=0.5, k=40) suggests diminishing returns from increasing the number of sampled paths beyond a certain point. This implies an optimal balance between sampling effort and accuracy gain. The differences in performance between the various temperature settings suggest that temperature plays a crucial role in controlling the exploration-exploitation trade-off during decoding.

## Line Chart: Accuracy vs. Number of Sampled Reasoning Paths for Various Decoding Strategies ### Overview The image is a line chart comparing the performance (accuracy) of different text generation decoding strategies as the number of sampled reasoning paths increases. The chart demonstrates how accuracy generally improves with more sampling paths for most methods, with notable differences in performance ceilings and rates of improvement. ### Components/Axes * **Chart Type:** Multi-line chart with markers. * **X-Axis:** * **Label:** `#Sampled Reasoning Paths` * **Scale:** Linear, from 0 to 40. * **Major Ticks/Markers:** 0, 5, 10, 20, 30, 40. * **Y-Axis:** * **Label:** `Accuracy (%)` * **Scale:** Linear, from 44 to 76. * **Major Ticks:** 44, 48, 52, 56, 60, 64, 68, 72, 76. * **Legend:** Positioned on the right side, outside the main plot area. It lists 8 distinct data series with corresponding colors and marker styles. 1. `T=0.7, k=40` (Blue line, square marker) 2. `T=0.5, k=40` (Orange line, square marker) 3. `T=0.3, k=40` (Green line, square marker) 4. `T=0.7, k=20` (Red line, square marker) 5. `T=0.7, no top k` (Purple line, square marker) 6. `p=0.95` (Brown line, square marker) 7. `p=0.9` (Pink line, square marker) 8. `Greedy Decode` (Gray line, circle marker) ### Detailed Analysis The chart plots accuracy (%) against the number of sampled reasoning paths (0, 5, 10, 20, 30, 40) for each decoding strategy. Below is an analysis of each series, including its visual trend and approximate data points. **Trend Verification & Data Points (Approximate):** 1. **`T=0.7, k=40` (Blue, Square):** * **Trend:** Steep initial rise, then plateaus at a high level. * **Points:** (0, ~56%), (5, ~68%), (10, ~70%), (20, ~72%), (30, ~73%), (40, ~74%). 2. **`T=0.5, k=40` (Orange, Square):** * **Trend:** Very similar to the blue line, slightly lower final accuracy. * **Points:** (0, ~56%), (5, ~67%), (10, ~69%), (20, ~71%), (30, ~72%), (40, ~73%). 3. **`T=0.3, k=40` (Green, Square):** * **Trend:** Rises more slowly and plateaus at a significantly lower accuracy than the T=0.5/0.7 lines. * **Points:** (0, ~56%), (5, ~62%), (10, ~64%), (20, ~65%), (30, ~66%), (40, ~66%). 4. **`T=0.7, k=20` (Red, Square):** * **Trend:** Follows a path very close to the `T=0.7, k=40` line, nearly indistinguishable at many points. * **Points:** (0, ~56%), (5, ~68%), (10, ~70%), (20, ~72%), (30, ~73%), (40, ~74%). 5. **`T=0.7, no top k` (Purple, Square):** * **Trend:** Starts lower than the top-k variants but rises to meet them at higher path counts. * **Points:** (0, ~48%), (5, ~64%), (10, ~68%), (20, ~71%), (30, ~72%), (40, ~73%). 6. **`p=0.95` (Brown, Square):** * **Trend:** Starts very low, rises sharply, and converges with the top-performing group. * **Points:** (0, ~44%), (5, ~64%), (10, ~69%), (20, ~72%), (30, ~73%), (40, ~74%). 7. **`p=0.9` (Pink, Square):** * **Trend:** Nearly identical to the `p=0.95` line. * **Points:** (0, ~46%), (5, ~64%), (10, ~69%), (20, ~72%), (30, ~73%), (40, ~74%). 8. **`Greedy Decode` (Gray, Circle):** * **Trend:** **Flat line.** Accuracy does not change with the number of sampled reasoning paths. * **Points:** Constant at approximately 56% across all x-values (0, 5, 10, 20, 30, 40). ### Key Observations 1. **Performance Ceiling:** Most sampling-based methods (all except Greedy Decode) converge to a similar high accuracy range of approximately 72-74% when 20 or more reasoning paths are sampled. 2. **Greedy Decode Baseline:** Greedy Decode serves as a flat baseline at ~56% accuracy, indicating that simply taking the most likely token at each step does not benefit from increased computational effort (more paths). 3. **Temperature (T) Impact:** Lower temperature (T=0.3) results in a lower performance ceiling compared to higher temperatures (T=0.5, T=0.7) when using top-k sampling (k=40). 4. **Top-k (k) Impact:** For T=0.7, reducing k from 40 to 20 (`T=0.7, k=20`) has a negligible effect on the final accuracy trend. Removing top-k entirely (`T=0.7, no top k`) hurts initial performance at low path counts but catches up. 5. **Nucleus Sampling (p):** Both p=0.9 and p=0.95 perform nearly identically, starting from a low point but rapidly achieving top-tier accuracy. 6. **Diminishing Returns:** For all improving methods, the most significant gains occur between 0 and 10 sampled paths. The improvement from 20 to 40 paths is marginal. ### Interpretation This chart provides a technical comparison of decoding strategies for tasks requiring reasoning (e.g., chain-of-thought or self-consistency prompting). The data suggests: * **Sampling is Crucial:** Methods that sample multiple reasoning paths and aggregate results (likely via majority vote) significantly outperform the deterministic Greedy Decode baseline. This validates the "self-consistency" paradigm. * **Robustness of High Temperature:** Higher temperatures (0.5, 0.7) combined with top-k or nucleus sampling appear more effective for this task than a low temperature (0.3), likely because they encourage more diverse, exploratory reasoning paths that can correct early errors. * **Efficiency vs. Performance:** There is a clear trade-off. Using 10-20 sampled paths captures most of the potential accuracy gain. Going to 40 paths yields only slight improvements at the cost of linearly increased computation. * **Method Equivalence at Scale:** With sufficient sampling (≥20 paths), the specific choice between top-k (with k=20 or 40) and nucleus sampling (p=0.9/0.95) at T=0.7 becomes less critical, as they all converge to a similar high-performance plateau. The initial starting point (accuracy at 0 paths) varies greatly, but the system "recovers" with more samples. **In essence, the chart demonstrates that for complex reasoning tasks, investing computational resources into sampling and aggregating multiple diverse reasoning paths is a highly effective strategy, with diminishing returns beyond a certain point (≈20 paths).**

## Line Graph: Accuracy vs. #Sampled Reasoning Paths ### Overview The graph compares the accuracy of different sampling strategies for a reasoning task, plotting accuracy (%) against the number of sampled reasoning paths (0–40). Multiple lines represent variations in temperature (T), top-k sampling (k), probability thresholds (p), and greedy decoding. All lines show upward trends, with accuracy increasing as more paths are sampled. ### Components/Axes - **Y-axis**: Accuracy (%) ranging from 44% to 76%. - **X-axis**: #Sampled Reasoning Paths (0–40). - **Legend**: Located on the right, with 8 entries: - Blue: T=0.7, k=40 - Orange: T=0.5, k=40 - Green: T=0.3, k=40 - Red: T=0.7, k=20 - Purple: T=0.7, no top k - Brown: p=0.95 - Pink: p=0.9 - Gray: Greedy Decode ### Detailed Analysis 1. **Blue Line (T=0.7, k=40)**: Starts at ~52% (0 paths) and rises to ~72% (40 paths). Steepest slope. 2. **Orange Line (T=0.5, k=40)**: Begins at ~54%, reaches ~70% at 40 paths. Slightly less steep than blue. 3. **Green Line (T=0.3, k=40)**: Flattest curve, starting at ~56% and plateauing at ~66%. 4. **Red Line (T=0.7, k=20)**: Starts at ~54%, ends at ~68%. Less effective than k=40. 5. **Purple Line (T=0.7, no top k)**: Begins at ~50%, reaches ~66%. Similar to red line but lower initial accuracy. 6. **Brown Line (p=0.95)**: Starts at ~48%, ends at ~64%. Lower than all T-based strategies. 7. **Pink Line (p=0.9)**: Starts at ~46%, ends at ~62%. Worst-performing strategy. 8. **Gray Line (Greedy Decode)**: Flat line at ~56%, indicating no improvement with sampling. ### Key Observations - **Temperature and Top-k Impact**: Higher T (0.7) and larger k (40) yield the highest accuracy. Reducing T to 0.3 or k to 20 significantly lowers performance. - **Probability Thresholds**: Lower p (0.9) results in the poorest accuracy, suggesting stricter thresholds degrade performance. - **Greedy Decoding**: Performs consistently worse than all sampling methods, highlighting the value of sampling. ### Interpretation The data demonstrates that **sampling strategies with higher temperature (T) and larger top-k values** (e.g., T=0.7, k=40) maximize accuracy, likely by exploring more diverse reasoning paths. Conversely, **probability-based methods** (p=0.9, 0.95) underperform, possibly due to overly restrictive sampling. **Greedy decoding** (no sampling) is the least effective, underscoring the importance of stochastic exploration. The trade-off between computational cost (more paths) and accuracy is evident, with diminishing returns observed as paths increase beyond ~20–25. This suggests optimizing sampling parameters for balance between efficiency and performance.