## Chart: Pass Rate vs. Temperature for Different Token Sizes ### Overview The image presents six line charts arranged in a 3x2 grid. Each chart plots the "pass" rate (pass@1, pass@10, pass@100) as a function of "Temperature" for two different token sizes (200B and 500B). Each chart contains three lines representing different values of 'n' (n=1, n=2, n=4). The x-axis represents temperature, and the y-axis represents the pass rate in percentage. ### Components/Axes * **Titles:** * Top-left chart title: "200B tokens" * Top-right chart title: "500B tokens" * **X-axis:** * Label: "Temperature" * Scale: 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4 * **Y-axis (Left Column):** * Top chart label: "pass@1 (%)" * Middle chart label: "pass@10 (%)" * Bottom chart label: "pass@100 (%)" * Scale (pass@1): 2, 3 * Scale (pass@10): 15, 20 * Scale (pass@100): 40, 50, 60 * **Y-axis (Right Column):** * Top chart label: "pass@1 (%)" * Middle chart label: "pass@10 (%)" * Bottom chart label: "pass@100 (%)" * Scale (pass@1): 2, 4, 6, 8 * Scale (pass@10): 20, 30 * Scale (pass@100): 40, 50, 60 * **Legend (Located at the bottom-right of the image):** * n = 1 (coral/light orange) * n = 2 (dark blue) * n = 4 (light green) ### Detailed Analysis **200B tokens** * **pass@1 (%)** * n = 1 (coral): Starts at approximately 3.6%, decreases to approximately 1.6% as temperature increases. * n = 2 (dark blue): Starts at approximately 3.2%, decreases to approximately 1.5% as temperature increases. * n = 4 (light green): Starts at approximately 3.0%, decreases to approximately 1.2% as temperature increases. * **pass@10 (%)** * n = 1 (coral): Starts at approximately 16%, increases to approximately 21% at temperature 0.6, then decreases to approximately 12% as temperature increases. * n = 2 (dark blue): Starts at approximately 16%, increases to approximately 22% at temperature 0.6, then decreases to approximately 12% as temperature increases. * n = 4 (light green): Starts at approximately 12%, increases to approximately 18% at temperature 0.6, then decreases to approximately 10% as temperature increases. * **pass@100 (%)** * n = 1 (coral): Starts at approximately 40%, increases to approximately 60% at temperature 0.8, then decreases to approximately 35% as temperature increases. * n = 2 (dark blue): Starts at approximately 40%, increases to approximately 62% at temperature 0.8, then decreases to approximately 35% as temperature increases. * n = 4 (light green): Starts at approximately 38%, increases to approximately 58% at temperature 0.8, then decreases to approximately 32% as temperature increases. **500B tokens** * **pass@1 (%)** * n = 1 (coral): Starts at approximately 8%, decreases to approximately 2% as temperature increases. * n = 2 (dark blue): Starts at approximately 7%, decreases to approximately 2% as temperature increases. * n = 4 (light green): Starts at approximately 5%, decreases to approximately 1.8% as temperature increases. * **pass@10 (%)** * n = 1 (coral): Starts at approximately 27%, increases to approximately 32% at temperature 0.6, then decreases to approximately 12% as temperature increases. * n = 2 (dark blue): Starts at approximately 25%, increases to approximately 32% at temperature 0.6, then decreases to approximately 12% as temperature increases. * n = 4 (light green): Starts at approximately 18%, increases to approximately 24% at temperature 0.6, then decreases to approximately 10% as temperature increases. * **pass@100 (%)** * n = 1 (coral): Starts at approximately 50%, increases to approximately 70% at temperature 0.6, then decreases to approximately 35% as temperature increases. * n = 2 (dark blue): Starts at approximately 50%, increases to approximately 70% at temperature 0.6, then decreases to approximately 35% as temperature increases. * n = 4 (light green): Starts at approximately 48%, increases to approximately 62% at temperature 0.6, then decreases to approximately 35% as temperature increases. ### Key Observations * For pass@1, the pass rate decreases as temperature increases for all values of 'n' and both token sizes. * For pass@10 and pass@100, the pass rate initially increases with temperature, reaches a peak around temperature 0.6-0.8, and then decreases as temperature further increases. * Generally, higher values of 'n' result in lower pass rates for all temperature values. * The 500B token models generally have higher pass rates than the 200B token models. ### Interpretation The charts illustrate the relationship between temperature, the parameter 'n', and the pass rate of a language model for different token sizes. The pass rate measures the model's ability to generate correct code. * **Temperature:** The temperature parameter controls the randomness of the model's output. Lower temperatures lead to more deterministic and predictable outputs, while higher temperatures introduce more randomness. The observed trends suggest that an intermediate temperature (around 0.6-0.8) is optimal for pass@10 and pass@100, balancing exploration and exploitation in the generation process. For pass@1, lower temperatures are better. * **Parameter 'n':** The parameter 'n' likely represents the number of samples generated by the model. Lower values of 'n' (e.g., n=1) generally lead to higher pass rates, suggesting that focusing on generating a smaller number of high-quality samples is more effective than generating a larger number of samples with potentially lower quality. * **Token Size:** The 500B token models consistently outperform the 200B token models, indicating that models trained on larger datasets have a better ability to generate correct code.

\n ## Chart: Pass@k vs. Temperature for Different n Values ### Overview The image presents a 2x2 grid of line charts. Each chart visualizes the relationship between "Temperature" (x-axis) and "pass@k" (y-axis) for different values of 'n' (represented by different colored lines). The charts are separated based on the "tokens" used: 200B tokens in the left column and 500B tokens in the right column. The pass@k metric is shown for k=1, k=10, and k=100 across the rows. ### Components/Axes * **X-axis:** Temperature, ranging from approximately 0.2 to 1.4. * **Y-axis:** pass@k (%), with scales varying for each chart: * Top row (pass@1): 0 to 8% * Middle row (pass@10): 0 to 30% * Bottom row (pass@100): 40 to 60% * **Legend:** Located in the top-right corner of the rightmost charts. It defines the line colors for different 'n' values: * n = 1 (brown/orange) * n = 2 (red) * n = 4 (green) * **Titles:** Each chart has a title indicating the token count (200B or 500B) and the pass@k metric being displayed. ### Detailed Analysis or Content Details **Top Row (pass@1):** * **200B tokens:** * n=1 (brown): Line starts at approximately 3.2%, peaks around 0.6 with approximately 3.8%, then decreases to approximately 2.2% at 1.4. * n=2 (red): Line starts at approximately 2.8%, peaks around 0.6 with approximately 3.6%, then decreases to approximately 2.0% at 1.4. * n=4 (green): Line starts at approximately 1.8%, decreases to approximately 1.5% at 0.6, then increases to approximately 2.0% at 1.4. * **500B tokens:** * n=1 (brown): Line starts at approximately 5.2%, decreases to approximately 4.0% at 0.6, then increases to approximately 4.8% at 1.4. * n=2 (red): Line starts at approximately 6.0%, decreases to approximately 5.0% at 0.6, then increases to approximately 5.6% at 1.4. * n=4 (green): Line starts at approximately 3.0%, increases to approximately 4.0% at 0.6, then decreases to approximately 3.2% at 1.4. **Middle Row (pass@10):** * **200B tokens:** * n=1 (brown): Line starts at approximately 11%, peaks around 0.6 with approximately 17%, then decreases to approximately 13% at 1.4. * n=2 (red): Line starts at approximately 13%, peaks around 0.6 with approximately 19%, then decreases to approximately 15% at 1.4. * n=4 (green): Line starts at approximately 8%, increases to approximately 12% at 0.6, then decreases to approximately 10% at 1.4. * **500B tokens:** * n=1 (brown): Line starts at approximately 18%, peaks around 0.8 with approximately 26%, then decreases to approximately 20% at 1.4. * n=2 (red): Line starts at approximately 22%, peaks around 0.8 with approximately 28%, then decreases to approximately 22% at 1.4. * n=4 (green): Line starts at approximately 12%, increases to approximately 18% at 0.8, then decreases to approximately 14% at 1.4. **Bottom Row (pass@100):** * **200B tokens:** * n=1 (brown): Line starts at approximately 48%, increases to approximately 56% at 0.6, then decreases to approximately 52% at 1.4. * n=2 (red): Line starts at approximately 52%, increases to approximately 58% at 0.6, then decreases to approximately 54% at 1.4. * n=4 (green): Line starts at approximately 42%, increases to approximately 50% at 0.6, then decreases to approximately 46% at 1.4. * **500B tokens:** * n=1 (brown): Line starts at approximately 54%, remains relatively flat around 58-60% between 0.4 and 1.2, then decreases to approximately 56% at 1.4. * n=2 (red): Line starts at approximately 58%, remains relatively flat around 60-62% between 0.4 and 1.2, then decreases to approximately 58% at 1.4. * n=4 (green): Line starts at approximately 48%, increases to approximately 54% at 0.6, then remains relatively flat around 54-56% between 0.6 and 1.4. ### Key Observations * Generally, increasing the temperature from 0.2 to 0.6 improves the pass@k rate for all values of 'n' and all token counts, especially for pass@10 and pass@100. * Beyond a temperature of 0.6, the pass@k rate tends to decrease with increasing temperature. * Higher values of 'n' (n=2 and n=4) generally result in higher pass@k rates compared to n=1. * The 500B token charts show a more stable pass@k rate at higher temperatures (between 0.6 and 1.2) for pass@100, compared to the 200B token charts. * The pass@1 metric shows the lowest overall pass rates, consistently below 8%. ### Interpretation The charts demonstrate the impact of temperature and 'n' value on the performance of a model, as measured by the pass@k metric. The optimal temperature appears to be around 0.6, where the pass@k rate peaks for most configurations. Increasing 'n' generally improves performance, suggesting that considering more options during generation leads to better results. The difference between 200B and 500B token models is most pronounced at higher pass@k values (pass@100), indicating that larger models are more robust and maintain performance better at higher temperatures. The relatively low pass@1 rates suggest that generating the single most likely token is not a reliable indicator of overall model quality. The flattening of the curves for the 500B token model at higher temperatures and pass@100 suggests a saturation point where further increasing temperature does not yield significant improvements. This data could be used to tune the generation parameters of the model to maximize performance based on the desired level of accuracy (k) and computational resources (token count).

## Line Charts: Model Performance (pass@k) vs. Temperature for Different Training Token Counts and Sampling Settings ### Overview The image contains six line charts arranged in a 3x2 grid. The two columns represent models trained on different amounts of data: **200B tokens** (left column) and **500B tokens** (right column). The three rows represent different performance metrics: **pass@1 (%)**, **pass@10 (%)**, and **pass@100 (%)**. Each chart plots these metrics against **Temperature** (x-axis) for three different sampling settings, labeled `n=1`, `n=2`, and `n=4`. ### Components/Axes * **X-Axis (All Charts):** Labeled **"Temperature"**. The axis has tick marks at 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, and 1.4. * **Y-Axes (By Row):** * **Top Row:** Labeled **"pass@1 (%)"**. Scale ranges approximately from 1.5% to 8%. * **Middle Row:** Labeled **"pass@10 (%)"**. Scale ranges approximately from 10% to 35%. * **Bottom Row:** Labeled **"pass@100 (%)"**. Scale ranges approximately from 35% to 70%. * **Legend:** Located in the **top-right corner of the "500B tokens" column**. It defines three data series: * `n = 1`: Orange line with 'x' markers. * `n = 2`: Dark blue/purple line with 'x' markers. * `n = 4`: Green line with 'x' markers. * **Chart Titles:** The columns are titled **"200B tokens"** and **"500B tokens"** at the top. ### Detailed Analysis **Column 1: 200B tokens** * **Top Chart (pass@1):** All three lines show a **consistent downward trend** as temperature increases. The `n=1` (orange) and `n=2` (blue) lines start highest (~3.5-3.7% at temp=0.2) and decline steadily. The `n=4` (green) line starts lower (~2.9%) and declines more gradually. All lines converge near 1.5-1.8% at temperature 1.4. * **Middle Chart (pass@10):** All lines show an **inverted U-shape**. Performance increases from temperature 0.2 to a peak around 0.6-0.8, then decreases. The `n=2` (blue) line peaks highest (~21% at temp=0.6), followed closely by `n=1` (orange, ~20.5% at temp=0.6), with `n=4` (green) peaking lower (~18% at temp=0.8). All lines drop to ~12-13% at temperature 1.4. * **Bottom Chart (pass@100):** All lines show a **pronounced inverted U-shape**. Performance rises sharply to a broad peak between temperatures 0.6 and 1.0, then falls sharply. The `n=2` (blue) and `n=1` (orange) lines are very close, peaking near 62-63%. The `n=4` (green) line peaks lower, around 58%. All lines drop to ~35-38% at temperature 1.4. **Column 2: 500B tokens** * **Top Chart (pass@1):** Similar **downward trend** as the 200B model, but with higher absolute values. `n=1` (orange) starts highest (~8% at temp=0.2), followed by `n=2` (blue, ~6.7%), then `n=4` (green, ~5.2%). All decline, converging near 1.8-2.0% at temperature 1.4. * **Middle Chart (pass@10):** Clear **inverted U-shape**. `n=1` (orange) peaks highest (~33% at temp=0.6-0.8), `n=2` (blue) peaks slightly lower (~31% at temp=0.8), and `n=4` (green) peaks much lower (~25% at temp=0.8-1.0). All decline to ~12-15% at temperature 1.4. * **Bottom Chart (pass@100):** Strong **inverted U-shape**. `n=1` (orange) and `n=2` (blue) are nearly identical, peaking around 68-70% between temperatures 0.8 and 1.0. `n=4` (green) peaks lower, around 65%. All lines drop steeply to ~38-40% at temperature 1.4. ### Key Observations 1. **Metric-Dependent Trend:** The relationship between temperature and performance changes with the metric. `pass@1` decreases monotonically with temperature, while `pass@10` and `pass@100` show an optimal temperature range (inverted U-shape). 2. **Sampling (`n`) Effect:** For a given temperature and metric, the ordering is consistent: `n=1` (single sample) generally performs best, `n=2` is very close or slightly worse, and `n=4` performs worst. This gap is more pronounced for `pass@10` and in the 500B model. 3. **Model Size Effect:** The model trained on **500B tokens consistently outperforms** the 200B token model across all metrics and temperatures, with the difference being most dramatic for `pass@1` (e.g., ~8% vs ~3.5% at temp=0.2). 4. **High Temperature Degradation:** Performance for all metrics and settings degrades significantly at high temperatures (above 1.0-1.2), often dropping below the performance at the lowest measured temperature (0.2). 5. **Peak Shift:** The optimal temperature for `pass@10` and `pass@100` appears to shift slightly higher (from ~0.6 to ~0.8-1.0) when moving from the 200B to the 500B model. ### Interpretation This data demonstrates the critical interplay between **model scale, sampling strategy, and decoding temperature** for code generation or similar generative tasks. * **Temperature as a Trade-off:** Low temperature favors precision and consistency (high `pass@1`), likely by making the model more deterministic. Higher temperatures increase diversity and exploration, which hurts the chance of a single perfect sample (`pass@1` down) but improves the chance that *at least one* good sample exists within multiple attempts (`pass@10` and `pass@100` up to a point). Very high temperatures introduce too much randomness, degrading all metrics. * **The Value of Scale:** The 500B model's superior performance, especially for the strict `pass@1` metric, indicates that increased training data leads to a more capable and precise base model. This advantage persists across all sampling strategies. * **Sampling Efficiency:** The finding that `n=1` often outperforms `n=2` and `n=4` at the same temperature is notable. It suggests that for these metrics, simply increasing the number of samples (`n`) without adjusting other parameters (like temperature) is not an efficient strategy and may even be detrimental. The optimal strategy appears to be using a single, well-calibrated sample (`n=1`) at a task-optimal temperature. * **Practical Implication:** There is no single "best" temperature. The optimal setting depends on the evaluation metric and the model's scale. For applications requiring a single, high-quality output, a lower temperature is better. For applications where multiple attempts are allowed and the goal is to find at least one correct solution, a moderate temperature (around 0.6-1.0) is optimal, with the exact peak depending on model size.

## Line Graphs: Performance Metrics Across Token Counts and Temperature ### Overview The image contains six line graphs arranged in a 2x3 grid, comparing performance metrics (pass@1 and pass@10) for models with 200B and 500B tokens across varying temperatures (0.2–1.4). Each graph includes three data series representing different sampling strategies (n=1, n=2, n=4), color-coded as red, blue, and green respectively. ### Components/Axes - **X-axis**: Temperature (0.2–1.4) in increments of 0.2. - **Y-axis**: - Top row: pass@1 (%) for 200B and 500B tokens. - Middle row: pass@10 (%) for 200B and 500B tokens. - Bottom row: pass@10 (%) for 500B tokens only. - **Legend**: Located in the top-right corner of each graph, mapping: - Red: n=1 - Blue: n=2 - Green: n=4 ### Detailed Analysis #### 200B Tokens (Left Column) 1. **pass@1 (%)**: - **n=1 (Red)**: Starts at ~3.5% (temp=0.2), declines to ~1.2% (temp=1.4). - **n=2 (Blue)**: Starts at ~3.3%, declines to ~1.0%. - **n=4 (Green)**: Starts at ~2.8%, declines to ~0.8%. - **Trend**: All lines slope downward, with n=1 showing the steepest decline. 2. **pass@10 (%)**: - **n=1 (Red)**: Peaks at ~20% (temp=0.6), drops to ~12% (temp=1.4). - **n=2 (Blue)**: Peaks at ~22% (temp=0.6), drops to ~10%. - **n=4 (Green)**: Peaks at ~18% (temp=0.6), drops to ~8%. #### 500B Tokens (Right Column) 1. **pass@1 (%)**: - **n=1 (Red)**: Starts at ~8%, declines to ~1.5%. - **n=2 (Blue)**: Starts at ~6.5%, declines to ~1.2%. - **n=4 (Green)**: Starts at ~5.5%, declines to ~0.9%. 2. **pass@10 (%)**: - **n=1 (Red)**: Peaks at ~30% (temp=0.6), drops to ~15%. - **n=2 (Blue)**: Peaks at ~32% (temp=0.6), drops to ~12%. - **n=4 (Green)**: Peaks at ~28% (temp=0.6), drops to ~10%. 3. **pass@10 (%) (500B Only)**: - **n=1 (Red)**: Peaks at ~60% (temp=0.6), drops to ~40%. - **n=2 (Blue)**: Peaks at ~62% (temp=0.6), drops to ~42%. - **n=4 (Green)**: Peaks at ~58% (temp=0.6), drops to ~38%. ### Key Observations 1. **Performance Degradation**: All metrics decline as temperature increases, with sharper drops at higher temperatures (e.g., temp=1.4). 2. **Sampling Strategy Impact**: Higher n values (more samples) consistently improve performance: - n=4 outperforms n=2 and n=1 across all token counts and metrics. - The gap widens at higher temperatures (e.g., pass@10 for 500B tokens: n=4 at 58% vs. n=1 at 60% at temp=0.6). 3. **Token Count Scaling**: 500B models outperform 200B models by ~2–3× in pass@10 (e.g., 60% vs. 20% at temp=0.6 for pass@10). ### Interpretation The data demonstrates that: - **Larger models (500B tokens)** achieve significantly higher performance than smaller models (200B tokens), particularly in pass@10. - **Sampling diversity (n=4)** mitigates temperature-induced performance drops more effectively than smaller n values. - **Temperature sensitivity** is non-linear: performance peaks at moderate temperatures (0.6–0.8) before declining sharply at higher temperatures (1.2–1.4). This suggests that balancing temperature and sampling strategy is critical for optimizing model outputs, with larger models and higher n values providing robustness against temperature-related degradation.