## Scatter Plot: Avg. test-time compute vs. Game Config ### Overview The image is a scatter plot comparing the average test-time compute for two models, o3-mini and Phi-4, across different game configurations. The x-axis represents the game configuration, denoted as (c=x, n=y), and the y-axis represents the average test-time compute. ### Components/Axes * **Title:** None * **X-axis:** * **Label:** Game Config * **Markers:** (c=2, n=4), (c=3, n=5), (c=4, n=6), (c=5, n=7), (c=6, n=8) * **Y-axis:** * **Label:** Avg. test-time compute * **Markers:** 100, 200, 300, 400, 500, 600, 700, 800 * **Legend:** Located in the top-left corner. * **Title:** Model * **Entries:** * o3-mini (blue) * Phi-4 (orange) ### Detailed Analysis * **o3-mini (blue):** * **(c=2, n=4):** Approximately 80 * **(c=3, n=5):** Approximately 220 * **(c=4, n=6):** Approximately 430 * **(c=5, n=7):** Approximately 810 * **(c=6, n=8):** Approximately 700 * **Trend:** The average test-time compute increases significantly from (c=2, n=4) to (c=5, n=7), then decreases slightly at (c=6, n=8). * **Phi-4 (orange):** * **(c=2, n=4):** Approximately 110 * **(c=3, n=5):** Approximately 200 * **(c=4, n=6):** Approximately 220 * **(c=5, n=7):** Approximately 260 * **(c=6, n=8):** Approximately 300 * **Trend:** The average test-time compute increases gradually from (c=2, n=4) to (c=6, n=8). ### Key Observations * The o3-mini model has a much higher average test-time compute for game configurations (c=5, n=7) and (c=6, n=8) compared to Phi-4. * For lower game configurations (c=2, n=4) and (c=3, n=5), the average test-time compute is relatively similar for both models. * The o3-mini model exhibits a non-linear trend, with a sharp increase in compute time at higher game configurations. * The Phi-4 model shows a more linear and gradual increase in compute time as the game configuration increases. ### Interpretation The scatter plot illustrates the performance of two models, o3-mini and Phi-4, in terms of average test-time compute across different game configurations. The data suggests that the o3-mini model becomes significantly more computationally expensive as the game configuration increases, particularly at (c=5, n=7), while Phi-4 maintains a more stable and gradual increase in compute time. This could indicate that Phi-4 is more scalable or efficient for larger or more complex game configurations. The similar performance at lower configurations suggests that o3-mini might be suitable for simpler games, but Phi-4 is preferable for more complex scenarios due to its better scalability.

## Scatter Plot: Avg. test-time compute vs. Game Config ### Overview This scatter plot visualizes the relationship between "Game Config" and "Avg. test-time compute" for two different models: "o3-mini" and "Phi-4". The x-axis represents different game configurations, and the y-axis represents the average test-time compute. Each point on the plot represents a specific game configuration and model combination. ### Components/Axes * **X-axis:** "Game Config" with markers (c=2, n=4), (c=3, n=5), (c=4, n=6), (c=5, n=7), (c=6, n=8). * **Y-axis:** "Avg. test-time compute" ranging from 0 to 800, with increments of 100. * **Legend:** Located in the top-left corner, identifying the models: * "o3-mini" (represented by blue circles) * "Phi-4" (represented by orange circles) ### Detailed Analysis The plot contains data points for both models across the five game configurations. **o3-mini (Blue Circles):** * **(c=2, n=4):** Approximately 100. * **(c=3, n=5):** Approximately 230. * **(c=4, n=6):** Approximately 440. * **(c=5, n=7):** Approximately 800. * **(c=6, n=8):** Approximately 700. The trend for o3-mini is initially upward, increasing rapidly from (c=2, n=4) to (c=5, n=7), then decreasing slightly at (c=6, n=8). **Phi-4 (Orange Circles):** * **(c=2, n=4):** Approximately 180. * **(c=3, n=5):** Approximately 210. * **(c=4, n=6):** Approximately 270. * **(c=5, n=7):** Approximately 280. * **(c=6, n=8):** Approximately 310. The trend for Phi-4 is consistently upward, but with a decreasing rate of increase as the game configuration increases. ### Key Observations * The "o3-mini" model generally requires significantly more compute time than "Phi-4" for the lower game configurations (c=2, n=4 and c=3, n=5). * At the highest game configuration (c=6, n=8), the compute time for "o3-mini" decreases, while "Phi-4" continues to increase, narrowing the gap. * The rate of increase in compute time for "Phi-4" is relatively consistent across all game configurations. * The compute time for "o3-mini" shows a peak at (c=5, n=7). ### Interpretation The data suggests that the computational cost of running the "o3-mini" model is highly sensitive to the game configuration, exhibiting a non-linear relationship. The initial rapid increase in compute time for "o3-mini" could be due to the model reaching a complexity limit or encountering performance bottlenecks as the game configuration increases. The subsequent decrease at (c=6, n=8) is unexpected and might indicate optimization or a change in the model's behavior at higher configurations. "Phi-4", on the other hand, demonstrates a more stable and predictable increase in compute time with increasing game configuration. This suggests that "Phi-4" is less susceptible to the specific characteristics of the game configurations tested. The difference in compute time between the two models highlights a trade-off between model complexity and computational efficiency. "o3-mini" might offer higher performance in certain scenarios, but at the cost of increased compute requirements, especially for more complex game configurations. "Phi-4" provides a more consistent and potentially more scalable solution, albeit with potentially lower peak performance. The peak at (c=5, n=7) for o3-mini is an anomaly that warrants further investigation. It could be a result of a specific interaction between the model and that particular game configuration.

## Scatter Plot: Average Test-Time Compute by Game Configuration for Two Models ### Overview The image is a scatter plot comparing the average test-time compute (y-axis) of two AI models, "o3-mini" and "Phi-4", across five different game configurations (x-axis). The plot uses colored circles to represent data points for each model at each configuration. ### Components/Axes * **Chart Type:** Scatter Plot * **X-Axis:** * **Title:** "Game Config" * **Categories/Labels (from left to right):** 1. `(c=2, n=4)` 2. `(c=3, n=5)` 3. `(c=4, n=6)` 4. `(c=5, n=7)` 5. `(c=6, n=8)` * **Y-Axis:** * **Title:** "Avg. test-time compute" * **Scale:** Linear, ranging from approximately 50 to 850. * **Major Tick Marks:** 100, 200, 300, 400, 500, 600, 700, 800. * **Legend:** * **Position:** Top-left corner of the plot area. * **Title:** "Model" * **Series:** * Blue circle: `o3-mini` * Orange circle: `Phi-4` ### Detailed Analysis Data points are extracted by matching the color of the circle to the legend and reading its approximate position against the y-axis grid. **1. Game Config: (c=2, n=4)** * **o3-mini (Blue):** Positioned just below the 100 line. Approximate value: **~80**. * **Phi-4 (Orange):** Positioned just above the 100 line. Approximate value: **~110**. **2. Game Config: (c=3, n=5)** * **o3-mini (Blue):** Positioned slightly above the 200 line. Approximate value: **~220**. * **Phi-4 (Orange):** Positioned just below the 200 line. Approximate value: **~195**. **3. Game Config: (c=4, n=6)** * **o3-mini (Blue):** Positioned between the 400 and 500 lines, closer to 400. Approximate value: **~430**. * **Phi-4 (Orange):** Positioned just above the 200 line. Approximate value: **~220**. **4. Game Config: (c=5, n=7)** * **o3-mini (Blue):** Positioned just above the 800 line. Approximate value: **~820**. * **Phi-4 (Orange):** Positioned between the 200 and 300 lines, closer to 300. Approximate value: **~260**. **5. Game Config: (c=6, n=8)** * **o3-mini (Blue):** Positioned on the 700 line. Approximate value: **~700**. * **Phi-4 (Orange):** Positioned on the 300 line. Approximate value: **~300**. ### Key Observations * **Diverging Trends:** The two models exhibit fundamentally different scaling behaviors. * **o3-mini (Blue):** Shows a steep, non-linear increase in compute from config 1 to 4, peaking at config 4 (`c=5, n=7`), followed by a significant drop at config 5 (`c=6, n=8`). The trend is sharply upward then downward. * **Phi-4 (Orange):** Shows a steady, near-linear increase in compute across all five configurations. The trend is consistently upward. * **Crossover Point:** At the simplest configuration (`c=2, n=4`), Phi-4 uses slightly more compute than o3-mini. By the second configuration (`c=3, n=5`), o3-mini's compute surpasses Phi-4's, and the gap widens dramatically thereafter. * **Peak Compute:** The highest compute value on the chart is for o3-mini at configuration `(c=5, n=7)` (~820). The lowest is for o3-mini at `(c=2, n=4)` (~80). * **Anomaly:** The data point for o3-mini at `(c=6, n=8)` (~700) is a notable drop from its peak at the previous configuration, breaking its prior steep upward trend. ### Interpretation This chart visualizes the computational cost (test-time compute) of running two different AI models on tasks of increasing complexity, parameterized by `c` and `n` (likely representing game or problem dimensions). The data suggests a critical trade-off in model architecture or strategy: * **Phi-4** demonstrates **predictable, scalable efficiency**. Its compute requirements grow proportionally and manageably with problem size, making it potentially more suitable for scaling to very complex tasks where resource predictability is key. * **o3-mini** exhibits **highly variable, non-linear scaling**. It is very efficient for simple tasks but its computational cost explodes for mid-range complexity before dropping for the most complex task shown. This could indicate an internal strategy shift, a different algorithmic approach that becomes inefficient at certain scales, or that the model hits a performance ceiling and changes its behavior. The drop at the final data point is particularly intriguing—it may suggest the model fails or adopts a much simpler (and cheaper) strategy for the most complex configuration. In essence, the chart doesn't just show "which model is faster," but reveals **how their underlying computational strategies respond to scaling pressure**. Phi-4 appears robust and consistent, while o3-mini's performance is highly sensitive to the specific problem parameters, with a potential breakdown or phase change at high complexity.

## Scatter Plot: Average Test-Time Compute by Game Configuration and Model ### Overview The image is a scatter plot comparing the average test-time compute (y-axis) for two models, **o3-mini** (blue) and **Phi-4** (orange), across five game configurations (x-axis). The x-axis labels represent tuples of parameters `(c, n)`, where `c` and `n` are integers. The y-axis ranges from 0 to 800, with gridlines for reference. --- ### Components/Axes - **X-axis (Game Config)**: - Labels: `(c=2, n=4)`, `(c=3, n=5)`, `(c=4, n=6)`, `(c=5, n=7)`, `(c=6, n=8)` - Position: Bottom of the plot, centered below each data point. - **Y-axis (Avg. test-time compute)**: - Range: 0 to 800, with increments of 100. - Position: Left side of the plot. - **Legend**: - Located in the top-left corner. - Labels: - **o3-mini** (blue circle) - **Phi-4** (orange circle) --- ### Detailed Analysis #### Data Points (approximate values with uncertainty): 1. **(c=2, n=4)**: - o3-mini: ~80 - Phi-4: ~120 2. **(c=3, n=5)**: - o3-mini: ~220 - Phi-4: ~200 3. **(c=4, n=6)**: - o3-mini: ~430 - Phi-4: ~220 4. **(c=5, n=7)**: - o3-mini: ~820 (outlier, significantly higher than other points) - Phi-4: ~260 5. **(c=6, n=8)**: - o3-mini: ~700 - Phi-4: ~300 #### Trends: - **o3-mini** (blue): - Shows a **non-linear increase** in test-time compute as `c` and `n` increase. - The largest jump occurs at `(c=5, n=7)`, where the value spikes to ~820, far exceeding other configurations. - At `(c=6, n=8)`, the value drops slightly to ~700, suggesting a possible anomaly or optimization. - **Phi-4** (orange): - Exhibits a **gradual, linear increase** across configurations. - Values remain consistently lower than o3-mini, with no outliers. --- ### Key Observations 1. **o3-mini** demonstrates **higher computational demands** compared to Phi-4, particularly at higher configurations. 2. The **outlier at (c=5, n=7)** for o3-mini (~820) is **~2.5x higher** than its value at `(c=6, n=8)` (~700), indicating a potential inconsistency or unique behavior in that configuration. 3. **Phi-4** maintains a **steady, predictable scaling** with increasing `c` and `n`, suggesting more efficient resource utilization. --- ### Interpretation The data suggests that **o3-mini** is more computationally intensive than Phi-4, with performance scaling disproportionately at higher configurations. The spike at `(c=5, n=7)` for o3-mini could indicate: - A **bug or inefficiency** in that specific configuration. - A **deliberate optimization** for that case, though the subsequent drop at `(c=6, n=8)` contradicts this. - **Phi-4**’s linear scaling implies better algorithmic efficiency, making it more suitable for configurations with larger `c` and `n`. The plot highlights the importance of **model-specific optimization** for game configurations, as o3-mini’s performance varies unpredictably compared to Phi-4’s consistent behavior.