## Scatter Plot: Reasoning Tokens vs. Problem Size for qwen/qwq-32b-preview ### Overview The image is a scatter plot showing the relationship between "Reasoning Tokens" and "Problem Size" for a model named "qwen/qwq-32b-preview". The plot distinguishes between successful and failed attempts using different markers: blue circles for successful attempts and orange squares for failed attempts. ### Components/Axes * **X-axis (Horizontal):** "Problem Size". The scale ranges from 0 to 400, with tick marks at intervals of 100. * **Y-axis (Vertical):** "Reasoning Tokens". The scale ranges from 0 to 20000, with tick marks at intervals of 5000. * **Legend (Top-Right):** * Blue Circle: "qwen/qwq-32b-preview (Successful)" * Orange Square: "qwen/qwq-32b-preview (Failed)" ### Detailed Analysis * **Successful Attempts (Blue Circles):** * All successful attempts occur at small problem sizes, specifically below 50. * Reasoning tokens for successful attempts range approximately from 3000 to 7000. * The trend for successful attempts is that as problem size increases (from approximately 10 to 50), the reasoning tokens appear to increase slightly. * Specific data points: * Problem Size ~10, Reasoning Tokens ~3500 * Problem Size ~15, Reasoning Tokens ~5500 * Problem Size ~20, Reasoning Tokens ~5000 * Problem Size ~25, Reasoning Tokens ~7000 * Problem Size ~30, Reasoning Tokens ~6000 * **Failed Attempts (Orange Squares):** * Failed attempts are scattered across the entire range of problem sizes (approximately 10 to 400). * Reasoning tokens for failed attempts range approximately from 5000 to 20000. * There is no clear trend between problem size and reasoning tokens for failed attempts. The data points appear randomly distributed. * Specific data points: * Problem Size ~10, Reasoning Tokens ~7000 to 16000 * Problem Size ~50, Reasoning Tokens ~8000 to 15000 * Problem Size ~100, Reasoning Tokens ~6000 to 18000 * Problem Size ~200, Reasoning Tokens ~6000 to 13000 * Problem Size ~300, Reasoning Tokens ~7000 to 13000 * Problem Size ~400, Reasoning Tokens ~12000 to 16000 ### Key Observations * The model "qwen/qwq-32b-preview" only succeeds on problems with small problem sizes (less than 50). * The number of reasoning tokens required for successful attempts is significantly lower and more consistent than for failed attempts. * Failed attempts show a wide range of reasoning tokens, regardless of problem size. ### Interpretation The scatter plot suggests that the "qwen/qwq-32b-preview" model struggles with larger problem sizes. The successful attempts are clustered at low problem sizes, indicating a limitation in the model's ability to handle complex or large-scale reasoning tasks. The wide distribution of reasoning tokens for failed attempts suggests that the model's performance is inconsistent and unpredictable when it fails. The data implies that the model may require further optimization or a different approach to handle larger problem sizes effectively. The fact that successful attempts require fewer reasoning tokens could indicate that the model is more efficient when it can solve the problem, but struggles to find a solution for larger problems, leading to a higher and more variable token count.

## Scatter Plot: Reasoning Tokens vs. Problem Size ### Overview This image presents a scatter plot visualizing the relationship between "Problem Size" and "Reasoning Tokens" for a model named "qwen/qwq-32b-preview". The data points are color-coded to distinguish between successful and failed attempts. ### Components/Axes * **X-axis:** "Problem Size" - Scale ranges from approximately 0 to 400, with tick marks at intervals of 100. * **Y-axis:** "Reasoning Tokens" - Scale ranges from approximately 0 to 20000, with tick marks at intervals of 5000. * **Legend:** Located in the top-right corner. * Blue circles: "qwen/qwq-32b-preview (Successful)" * Orange squares: "qwen/qwq-32b-preview (Failed)" * **Gridlines:** Present to aid in reading values. ### Detailed Analysis The plot shows two distinct data series: one for successful attempts (blue circles) and one for failed attempts (orange squares). **Successful Attempts (Blue Circles):** The successful attempts are concentrated in the lower-left portion of the plot. The trend is relatively flat, with a slight upward slope. * At Problem Size ≈ 0, Reasoning Tokens range from approximately 2000 to 6000. * At Problem Size ≈ 50, Reasoning Tokens range from approximately 3000 to 7000. * At Problem Size ≈ 100, Reasoning Tokens range from approximately 4000 to 6000. * At Problem Size ≈ 200, Reasoning Tokens range from approximately 4000 to 7000. * At Problem Size ≈ 300, Reasoning Tokens range from approximately 5000 to 7000. * At Problem Size ≈ 400, Reasoning Tokens range from approximately 6000 to 8000. **Failed Attempts (Orange Squares):** The failed attempts are more dispersed throughout the plot, with a higher concentration in the upper-left and center regions. The trend is more variable. * At Problem Size ≈ 0, Reasoning Tokens range from approximately 2000 to 12000. * At Problem Size ≈ 50, Reasoning Tokens range from approximately 5000 to 16000. * At Problem Size ≈ 100, Reasoning Tokens range from approximately 6000 to 20000. * At Problem Size ≈ 150, Reasoning Tokens range from approximately 5000 to 13000. * At Problem Size ≈ 200, Reasoning Tokens range from approximately 5000 to 11000. * At Problem Size ≈ 300, Reasoning Tokens range from approximately 6000 to 12000. * At Problem Size ≈ 400, Reasoning Tokens range from approximately 8000 to 15000. ### Key Observations * Successful attempts generally require fewer reasoning tokens than failed attempts. * The number of reasoning tokens required for successful attempts appears to increase slightly with problem size, but the increase is relatively small. * Failed attempts exhibit a wider range of reasoning token usage, suggesting more variability in the model's performance on challenging problems. * There is a cluster of failed attempts with very high reasoning token counts (above 15000) even for relatively small problem sizes. ### Interpretation The data suggests that the "qwen/qwq-32b-preview" model is more likely to succeed when the problem size is smaller and the number of reasoning tokens required is lower. The wide range of reasoning token usage for failed attempts indicates that the model sometimes struggles with problems that require more extensive reasoning, even if the problem size is not particularly large. The presence of failed attempts with high reasoning token counts suggests that the model can get "stuck" in a reasoning loop without reaching a solution. This could be due to issues with the model's architecture, training data, or decoding strategy. The relatively flat trend for successful attempts suggests that the model's reasoning efficiency does not significantly degrade as the problem size increases, at least within the observed range. Further investigation could explore the characteristics of the problems that lead to high reasoning token counts and failures, and identify potential strategies for improving the model's performance on these challenging cases.

## Scatter Plot: Model Performance by Problem Size and Reasoning Tokens ### Overview This image is a scatter plot comparing the performance outcomes (Successful vs. Failed) of a specific AI model, `qwen/qwq-32b-preview`, across two metrics: "Problem Size" and "Reasoning Tokens". The plot visualizes the relationship between the complexity of a task (problem size) and the computational effort expended (reasoning tokens), categorized by the final success or failure of the model's attempt. ### Components/Axes * **X-Axis (Horizontal):** Labeled "Problem Size". The scale runs from 0 to 400, with major tick marks at 0, 100, 200, 300, and 400. * **Y-Axis (Vertical):** Labeled "Reasoning Tokens". The scale runs from 0 to 20,000, with major tick marks at 0, 5000, 10000, 15000, and 20000. * **Legend:** Located in the top-right corner of the plot area. * **Blue Circle (●):** `qwen/qwq-32b-preview (Successful)` * **Orange Square (■):** `qwen/qwq-32b-preview (Failed)` * **Grid:** A light gray grid is present, aiding in the estimation of data point coordinates. ### Detailed Analysis The data is segmented into two distinct series based on the legend. **1. Successful Attempts (Blue Circles):** * **Trend & Placement:** These points form a tight cluster exclusively in the lower-left quadrant of the chart. * **Data Points:** All successful attempts are confined to a narrow range. * **Problem Size:** Approximately between 10 and 30. * **Reasoning Tokens:** Approximately between 3,500 and 7,500. * **Observation:** There is a positive correlation within this small cluster; as problem size increases slightly, the reasoning tokens used also increase. No successful attempts are recorded for problem sizes greater than ~30. **2. Failed Attempts (Orange Squares):** * **Trend & Placement:** These points are widely dispersed across the entire chart area, showing no single tight cluster. * **Data Points:** They span the full ranges of both axes. * **Problem Size:** From as low as ~15 to the maximum shown, 400. * **Reasoning Tokens:** From as low as ~2,500 to the maximum shown, ~20,000. * **Distribution:** * A dense concentration exists for lower problem sizes (0-100), where token counts vary dramatically from ~2,500 to ~18,000. * For larger problem sizes (100-400), the points are more sparse but still show high variability in token usage, ranging from ~5,000 to ~15,000+. * The highest token count (≈20,000) is associated with a failed attempt at a problem size of approximately 120. ### Key Observations 1. **Clear Performance Boundary:** There is a stark, almost binary separation. Successful outcomes are strictly limited to very small problem sizes (< ~30) and moderate token usage (< ~7,500). 2. **Failure Across All Scales:** Failures occur across the entire spectrum of problem sizes, from small to large. 3. **Inefficiency in Failure:** Many failed attempts, especially at lower problem sizes, consume significantly more reasoning tokens (e.g., 10,000-18,000) than any successful attempt. This suggests a pattern of "spinning wheels" or inefficient reasoning on tasks that are ultimately not solved. 4. **No Success at Scale:** The complete absence of blue circles beyond a problem size of ~30 indicates a potential hard limit or severe degradation in the model's capability to successfully solve larger problems within this evaluation. ### Interpretation This chart suggests a critical performance limitation for the `qwen/qwq-32b-preview` model on the evaluated task suite. * **Capability Ceiling:** The model appears capable of solving only the simplest problems (small "Problem Size"). Its success is not just less likely but *non-existent* for more complex tasks in this dataset. * **Resource Misallocation:** The high token counts for many failures indicate that the model often engages in extensive, yet unproductive, reasoning when it is destined to fail. This is particularly notable for small problems where it fails, using 2-3 times the tokens of a successful run. * **Diagnostic Value:** The plot is a powerful diagnostic tool. It doesn't just show *that* the model fails on hard problems, but *how* it fails—often after expending considerable computational effort. This points to potential issues in the model's reasoning strategy, its ability to recognize dead ends, or a fundamental mismatch between its training and the nature of larger problems in this domain. * **Actionable Insight:** To improve performance, focus should be on either: 1) Enhancing the model's core reasoning capability to handle larger problem sizes, or 2) Implementing better early-stopping or confidence-calibration mechanisms to prevent the wasteful expenditure of tokens on attempts that are unlikely to succeed.

## Scatter Plot: Reasoning Tokens vs Problem Size for qwen/qwq-32b-preview ### Overview The image shows a scatter plot comparing reasoning token usage against problem size for two categories of outcomes: successful and failed runs of the qwen/qwq-32b-preview model. The plot uses distinct markers (blue circles for successful, orange squares for failed) to differentiate outcomes across problem sizes from 0 to 400. ### Components/Axes - **X-axis (Problem Size)**: - Range: 0 to 400 - Increment: 100 - Label: "Problem Size" - **Y-axis (Reasoning Tokens)**: - Range: 0 to 20,000 - Increment: 5,000 - Label: "Reasoning Tokens" - **Legend**: - Position: Top-right corner - Entries: - Blue circles: "qwen/qwq-32b-preview (Successful)" - Orange squares: "qwen/qwq-32b-preview (Failed)" ### Detailed Analysis - **Successful Runs (Blue Circles)**: - Concentrated in the lower-left quadrant (Problem Size: 0–100, Reasoning Tokens: 3,000–7,000). - No data points observed beyond Problem Size 100. - Clustered tightly, suggesting consistent token usage for smaller problems. - **Failed Runs (Orange Squares)**: - Distributed across the entire Problem Size range (0–400). - Token usage spans 3,000–20,000, with a notable outlier at (400, 20,000). - Higher density of points in the 100–300 Problem Size range (Tokens: 8,000–15,000). ### Key Observations 1. **Problem Size Correlation**: - Successful runs cluster at smaller problem sizes (≤100), while failed runs span all sizes. - Token usage increases with problem size for failed cases, peaking at 20,000 tokens for Problem Size 400. 2. **Outlier**: - A single failed run at (400, 20,000) represents the maximum token usage observed. 3. **Efficiency Gap**: - Successful runs use ≤7,000 tokens, while failed runs often exceed this threshold, especially at larger problem sizes. ### Interpretation The data suggests that problem size significantly impacts both success rates and token efficiency. Successful runs are confined to smaller problem sizes and exhibit lower token consumption, indicating the model's capacity limits. Failed runs show a clear trend of increasing token usage with problem size, culminating in the outlier at Problem Size 400. This outlier may represent an edge case where the model expended maximum resources but still failed, highlighting potential scalability challenges. The stark contrast between successful and failed runs implies that token efficiency is a critical factor in determining task success, with larger problem sizes correlating with higher computational demands and lower success rates.