## Line Chart: Test Time Search Performance on AMC ### Overview The image is a line chart comparing the accuracy of four different search algorithms (Self-Consistency, Best-of-N, Beam Search, and MCTS) as a function of generation rollouts. The x-axis represents generation rollouts on a logarithmic scale (base 2), and the y-axis represents accuracy in percentage. ### Components/Axes * **Title:** Test Time Search Performance on AMC * **X-axis:** * Label: Generation Rollouts * Scale: Logarithmic (base 2) * Markers: 2⁰, 2¹, 2², 2³, 2⁴, 2⁵, 2⁶ * **Y-axis:** * Label: Accuracy (%) * Scale: Linear * Markers: 58, 60, 62, 64, 66, 68 * **Legend:** Located in the bottom-right corner. * Self-Consistency (Blue) * Best-of-N (Orange) * Beam Search (Green) * MCTS (Red) ### Detailed Analysis * **Self-Consistency (Blue):** * Trend: Generally increasing with generation rollouts. * Data Points: * 2⁰: ~59% * 2¹: ~59% * 2²: ~60% * 2³: ~61.5% * 2⁴: ~62.7% * 2⁵: ~64% * 2⁶: ~64% * **Best-of-N (Orange):** * Trend: Increases initially, then decreases slightly, and increases again. * Data Points: * 2⁰: ~59% * 2¹: ~59% * 2²: ~63% * 2³: ~65% * 2⁴: ~64% * 2⁵: ~65% * 2⁶: ~67% * **Beam Search (Green):** * Trend: Increases, plateaus, then increases again. * Data Points: * 2⁰: ~59% * 2¹: ~59% * 2²: ~64% * 2³: ~65% * 2⁴: ~65% * 2⁵: ~66% * 2⁶: ~66% * **MCTS (Red):** * Trend: Consistently increasing with generation rollouts. * Data Points: * 2⁰: ~59% * 2¹: ~60% * 2²: ~64% * 2³: ~65.2% * 2⁴: ~66.3% * 2⁵: ~66.3% * 2⁶: ~67.5% ### Key Observations * MCTS (Red) generally performs the best, achieving the highest accuracy at the end. * Self-Consistency (Blue) has the lowest initial accuracy and increases steadily, but plateaus at 2⁵. * Best-of-N (Orange) and Beam Search (Green) show similar performance, with Best-of-N eventually surpassing Beam Search. * All algorithms show improvement in accuracy as the number of generation rollouts increases, but the rate of improvement varies. ### Interpretation The chart illustrates the performance of different search algorithms in terms of accuracy as the number of generation rollouts increases. MCTS appears to be the most effective algorithm for this task, consistently achieving higher accuracy compared to the others. Self-Consistency, while showing steady improvement, plateaus at higher generation rollouts. Best-of-N and Beam Search offer comparable performance, with Best-of-N eventually outperforming Beam Search. The data suggests that increasing generation rollouts generally improves accuracy, but the extent of improvement depends on the specific algorithm used. The choice of algorithm and the number of generation rollouts should be carefully considered to optimize performance for the given task.

## Line Chart: Test Time Search Performance on AMC ### Overview The image presents a line chart illustrating the performance of four different search algorithms (Self-Consistency, Best-of-N, Beam Search, and MCTS) on the AMC task, measured by accuracy as a function of generation rollouts. The chart displays how accuracy changes as the number of generation rollouts increases from 2⁰ to 2⁶. ### Components/Axes * **Title:** "Test Time Search Performance on AMC" (centered at the top) * **X-axis:** "Generation Rollouts" (bottom-horizontal). Markers are at 2⁰, 2¹, 2², 2³, 2⁴, 2⁵, and 2⁶. * **Y-axis:** "Accuracy (%)" (left-vertical). Scale ranges from 58% to 68%. * **Legend:** Located in the top-right corner. Contains the following entries with corresponding colors: * Self-Consistency (Blue) * Best-of-N (Orange) * Beam Search (Green) * MCTS (Red) ### Detailed Analysis The chart displays four distinct lines, each representing a search algorithm's accuracy as generation rollouts increase. * **Self-Consistency (Blue):** The line starts at approximately 58% accuracy at 2⁰ rollouts. It increases slowly to around 61% at 2¹, then rises more steeply to approximately 63% at 2². It plateaus around 63-64% for the remaining rollouts (2³ through 2⁶). * **Best-of-N (Orange):** The line begins at approximately 58% accuracy at 2⁰ rollouts. It dips to around 59% at 2¹, then increases rapidly to approximately 64% at 2². It continues to increase, reaching around 66% at 2⁴ and finally approximately 67% at 2⁶. * **Beam Search (Green):** The line starts at approximately 58% accuracy at 2⁰ rollouts. It increases steadily to around 62% at 2¹, then rises more sharply to approximately 65% at 2². It continues to increase, reaching approximately 66% at 2³ and 67% at 2⁶. * **MCTS (Red):** The line begins at approximately 58% accuracy at 2⁰ rollouts. It increases rapidly to approximately 63% at 2¹, then continues to increase sharply to approximately 65% at 2². It continues to increase, reaching approximately 67% at 2⁴ and approximately 68% at 2⁶. ### Key Observations * MCTS consistently demonstrates the highest accuracy across all generation rollout values. * Self-Consistency shows the slowest improvement in accuracy and plateaus at a lower level compared to the other algorithms. * Best-of-N and Beam Search exhibit similar trends, with Beam Search slightly outperforming Best-of-N at higher rollout values. * All algorithms show a significant performance boost between 2⁰ and 2² rollouts. * The performance gains diminish as the number of rollouts increases beyond 2³. ### Interpretation The data suggests that increasing the number of generation rollouts generally improves the accuracy of all four search algorithms on the AMC task. However, the extent of improvement varies significantly between algorithms. MCTS appears to be the most effective algorithm, consistently achieving the highest accuracy. Self-Consistency, while improving with rollouts, reaches a performance ceiling relatively quickly. The diminishing returns observed at higher rollout values suggest that there is a point of diminishing returns where further increasing rollouts does not yield substantial accuracy gains. This could be due to factors such as computational cost or the inherent limitations of the algorithms themselves. The initial rapid improvement likely reflects the algorithms' ability to explore the search space more effectively with increased computational effort. The differences in performance between the algorithms highlight the importance of algorithm selection for optimal performance on this task.

\n ## Line Chart: Test Time Search Performance on AMC ### Overview The image displays a line chart comparing the performance of four different search algorithms or strategies on the AMC (likely a benchmark dataset or task) as a function of computational budget, measured in "Generation Rollouts." The chart plots Accuracy (%) against the number of rollouts on a logarithmic scale (base 2). ### Components/Axes * **Chart Title:** "Test Time Search Performance on AMC" (centered at the top). * **Y-Axis:** Labeled "Accuracy (%)". The scale runs from 58 to 68, with major tick marks every 2 units (58, 60, 62, 64, 66, 68). * **X-Axis:** Labeled "Generation Rollouts". The scale is logarithmic, with tick marks at powers of two: 2⁰, 2¹, 2², 2³, 2⁴, 2⁵, 2⁶. * **Legend:** Positioned in the bottom-right quadrant of the chart area. It contains four entries, each with a colored line segment and a marker: * **Blue line with circle markers:** "Self-Consistency" * **Orange line with circle markers:** "Best-of-N" * **Green line with circle markers:** "Beam Search" * **Red line with circle markers:** "MCTS" ### Detailed Analysis The chart tracks four data series. All series begin at the same point (59% accuracy at 2⁰ rollouts). Below is the extracted data and trend for each series. **1. Self-Consistency (Blue Line)** * **Trend:** Shows a steady, near-linear increase in accuracy as rollouts increase, but plateaus at the highest rollout counts. * **Data Points (Approximate):** * 2⁰: 59.0% * 2¹: 59.0% * 2²: 60.2% * 2³: 61.4% * 2⁴: 62.7% * 2⁵: 63.9% * 2⁶: 63.9% **2. Best-of-N (Orange Line)** * **Trend:** Exhibits a volatile but overall strong upward trend. It shows a significant jump between 2¹ and 2², a peak at 2³, a dip at 2⁴, and then a strong recovery to reach the highest final accuracy. * **Data Points (Approximate):** * 2⁰: 59.0% * 2¹: 59.0% * 2²: 62.7% * 2³: 65.1% * 2⁴: 63.9% * 2⁵: 65.1% * 2⁶: 67.5% **3. Beam Search (Green Line)** * **Trend:** Demonstrates a consistent upward trend that plateaus in the middle range (2³ to 2⁴) before a final increase. * **Data Points (Approximate):** * 2⁰: 59.0% * 2¹: 59.0% * 2²: 63.9% * 2³: 65.1% * 2⁴: 65.1% * 2⁵: 66.3% * 2⁶: 66.3% **4. MCTS (Red Line)** * **Trend:** Shows the most consistent and steepest upward trajectory, with no dips. It matches the highest accuracy at the final data point. * **Data Points (Approximate):** * 2⁰: 59.0% * 2¹: 60.2% * 2²: 63.9% * 2³: 65.1% * 2⁴: 66.3% * 2⁵: 66.3% * 2⁶: 67.5% ### Key Observations 1. **Common Starting Point:** All four methods begin at an identical accuracy of 59% with a single rollout (2⁰). 2. **Performance Hierarchy at Scale:** At the maximum rollout count (2⁶ = 64), MCTS and Best-of-N are tied for the highest performance (~67.5%), followed by Beam Search (~66.3%), with Self-Consistency performing the lowest (~63.9%). 3. **Divergence Point:** The performance of the methods begins to diverge significantly after 2¹ rollouts. 4. **Plateau Behavior:** Self-Consistency plateaus after 2⁵ rollouts. Beam Search shows a plateau between 2³ and 2⁴. MCTS and Best-of-N show no sign of plateauing within the measured range. 5. **Volatility:** Best-of-N is the only method to show a decrease in accuracy (at 2⁴) before recovering. ### Interpretation This chart demonstrates the scaling behavior of different search strategies with respect to computational budget (rollouts). The key insight is that more sophisticated search methods (MCTS, Best-of-N) exhibit better scaling laws—they continue to gain significant accuracy as more computation is allocated, whereas simpler methods like Self-Consistency see diminishing returns earlier. The data suggests that for the AMC task, investing in increased rollouts is most beneficial when using MCTS or Best-of-N strategies. The dip in Best-of-N at 2⁴ could indicate sensitivity to a specific rollout count or a potential instability in the method that is overcome with even more samples. The identical starting point implies that with minimal computation, the choice of search strategy is irrelevant; their value is unlocked only when sufficient computational resources are available for exploration. The final tie between MCTS and Best-of-N at 2⁶ raises the question of whether one might eventually outperform the other with even larger budgets, or if they have converged to a similar performance ceiling for this task.

## Line Chart: Test Time Search Performance on AMC ### Overview The chart visualizes the accuracy performance of four search methods (Self-Consistency, Best-of-N, Beam Search, MCTS) across logarithmic generation rollouts (2⁰ to 2⁶). Accuracy is measured on the y-axis (58%–68%), with distinct colored lines representing each method. ### Components/Axes - **X-axis**: Generation Rollouts (logarithmic scale: 2⁰, 2¹, ..., 2⁶) - **Y-axis**: Accuracy (%) (linear scale: 58%–68%) - **Legend**: Located in the bottom-right corner, mapping colors to methods: - Blue: Self-Consistency - Orange: Best-of-N - Green: Beam Search - Red: MCTS ### Detailed Analysis 1. **Self-Consistency (Blue)**: - Starts at ~59% (2⁰), increases steadily to ~64% (2⁶), with a plateau at 2⁵–2⁶. - Values: 59% (2⁰), 59% (2¹), 60% (2²), 61% (2³), 62.5% (2⁴), 64% (2⁵–2⁶). 2. **Best-of-N (Orange)**: - Begins at ~59% (2⁰), peaks at ~65% (2³), dips to ~64% (2⁴), then rises to ~67% (2⁶). - Values: 59% (2⁰), 59% (2¹), 63% (2²), 65% (2³), 64% (2⁴), 65% (2⁵), 67% (2⁶). 3. **Beam Search (Green)**: - Starts at ~59% (2⁰), rises to ~66% (2⁵–2⁶), with a plateau at 2⁵–2⁶. - Values: 59% (2⁰), 59% (2¹), 60% (2²), 65% (2³), 65% (2⁴), 66% (2⁵–2⁶). 4. **MCTS (Red)**: - Consistently increases from ~59% (2⁰) to ~67.5% (2⁶), with no plateaus. - Values: 59% (2⁰), 60% (2¹), 64% (2²), 65% (2³), 66.5% (2⁴), 66.5% (2⁵), 67.5% (2⁶). ### Key Observations - **MCTS** demonstrates the highest and most consistent growth, outperforming all methods by 2⁶. - **Best-of-N** shows volatility, peaking at 2³ before recovering at 2⁶. - **Beam Search** lags initially but matches MCTS at 2⁵–2⁶. - **Self-Consistency** has the slowest growth, plateauing at 64% by 2⁵. ### Interpretation The data suggests **MCTS** is the most effective method for improving search accuracy over time, with a clear advantage at higher rollouts. **Best-of-N** and **Beam Search** show competitive performance but with less stability. **Self-Consistency** underperforms relative to others, indicating potential limitations in scalability. The logarithmic x-axis emphasizes performance gains at larger rollouts, highlighting MCTS's efficiency in resource-intensive scenarios.