## Line Graphs: Lichess Puzzle Accuracy vs. Training Step for Qwen2.5-7B and Llama3.1-8B ### Overview The image contains two line graphs comparing the Lichess Puzzle Accuracy of two language models, Qwen2.5-7B and Llama3.1-8B, over training steps. Each graph plots the accuracy of two methods, SAN and UCI, against the training step. ### Components/Axes **Left Graph (Qwen2.5-7B):** * **Title:** Qwen2.5-7B * **Y-axis:** Lichess Puzzle Acc, ranging from 0.00 to 0.30 in increments of 0.05. * **X-axis:** Training Step, ranging from 0 to 150 in increments of 30. * **Legend:** Located in the center-right of the left graph. * SAN: Blue line * UCI: Gray line **Right Graph (Llama3.1-8B):** * **Title:** Llama3.1-8B * **Y-axis:** Lichess Puzzle Acc, ranging from 0.00 to 0.30 in increments of 0.05. * **X-axis:** Training Step, ranging from 0 to 150 in increments of 30. * **Legend:** (Same as left graph) * SAN: Blue line * UCI: Gray line ### Detailed Analysis **Left Graph (Qwen2.5-7B):** * **SAN (Blue):** The line starts at approximately 0.00 at training step 0, increases rapidly to approximately 0.18 at step 30, continues to increase to approximately 0.24 at step 60, reaches approximately 0.27 at step 90, and plateaus around 0.29 from step 120 to 150. * **UCI (Gray):** The line starts at approximately 0.00 at training step 0, increases slightly to approximately 0.02 at step 30, and then remains relatively flat around 0.02-0.03 from step 60 to 150. **Right Graph (Llama3.1-8B):** * **SAN (Blue):** The line starts at approximately 0.00 at training step 0, increases rapidly to approximately 0.30 at step 30, dips slightly to approximately 0.28 at step 60, increases to approximately 0.32 at step 90, dips to approximately 0.31 at step 120, and plateaus around 0.29 from step 150. * **UCI (Gray):** The line starts at approximately 0.00 at training step 0, increases slightly to approximately 0.03 at step 30, and then remains relatively flat around 0.02 from step 60 to 150. ### Key Observations * In both graphs, the SAN method (blue line) shows a significantly higher Lichess Puzzle Accuracy compared to the UCI method (gray line). * For Qwen2.5-7B, the SAN accuracy increases steadily and plateaus, while for Llama3.1-8B, the SAN accuracy increases rapidly and then fluctuates slightly around a high value. * The UCI accuracy remains consistently low for both models. ### Interpretation The data suggests that the SAN method is significantly more effective than the UCI method for improving Lichess Puzzle Accuracy in both Qwen2.5-7B and Llama3.1-8B language models. The Llama3.1-8B model reaches a higher accuracy faster than the Qwen2.5-7B model, but its accuracy fluctuates more. The UCI method appears to have minimal impact on the Lichess Puzzle Accuracy for both models. The rapid increase in accuracy for the SAN method in both models indicates a strong learning curve in the initial training steps.

## Line Chart: Lichess Puzzle Accuracy vs. Training Step for Two Models ### Overview The image presents two line charts side-by-side, comparing the performance of two language models – Qwen2.5-7B and Llama3.1-8B – on Lichess puzzles during training. The y-axis represents the puzzle accuracy (Lichess Puzzle Acc), and the x-axis represents the training step. Each chart displays two lines representing different evaluation methods: SAN and UCI. ### Components/Axes * **X-axis:** Training Step (ranging from 0 to 150, with markers at 0, 30, 60, 90, 120, and 150). * **Y-axis:** Lichess Puzzle Acc (ranging from 0.00 to 0.30, with markers at 0.05 intervals). * **Left Chart Title:** Qwen2.5-7B * **Right Chart Title:** Llama3.1-8B * **Legend (Left Chart):** * SAN (Blue Line) * UCI (Gray Line) * **Legend (Right Chart):** * SAN (Blue Line) * UCI (Gray Line) ### Detailed Analysis or Content Details **Qwen2.5-7B Chart:** * **SAN Line (Blue):** The SAN line starts at approximately 0.02 at Training Step 0. It exhibits a steep upward trend until around Training Step 60, reaching approximately 0.26. It plateaus between Training Steps 60 and 120, hovering around 0.28. Finally, it slightly decreases to approximately 0.27 at Training Step 150. * **UCI Line (Gray):** The UCI line starts at approximately 0.01 at Training Step 0. It shows a slow, gradual increase throughout the entire training process. At Training Step 150, it reaches approximately 0.04. **Llama3.1-8B Chart:** * **SAN Line (Blue):** The SAN line begins at approximately 0.03 at Training Step 0. It rapidly increases to approximately 0.28 by Training Step 30. It then fluctuates between approximately 0.28 and 0.31, peaking at around 0.31 at Training Step 90. It decreases slightly to approximately 0.30 at Training Step 150. * **UCI Line (Gray):** The UCI line starts at approximately 0.01 at Training Step 0. It shows a slow, gradual increase throughout the training process, similar to the Qwen2.5-7B model. At Training Step 150, it reaches approximately 0.04. ### Key Observations * Both models show significantly higher accuracy when evaluated using the SAN method compared to the UCI method. * Qwen2.5-7B reaches a plateau in SAN accuracy relatively early in training (around step 60), while Llama3.1-8B continues to fluctuate and maintain a higher accuracy for a longer period. * The UCI accuracy for both models remains consistently low throughout the training process. * Llama3.1-8B demonstrates a faster initial learning rate (SAN line) compared to Qwen2.5-7B. ### Interpretation The data suggests that both Qwen2.5-7B and Llama3.1-8B models improve their ability to solve Lichess puzzles as they are trained. The substantial difference in accuracy between the SAN and UCI evaluation methods indicates that the UCI method may be less sensitive to the models' performance or may be evaluating different aspects of the problem-solving process. The plateau observed in Qwen2.5-7B's SAN accuracy could indicate that the model has reached its maximum performance level with the given training data and parameters. The continued fluctuation in Llama3.1-8B's SAN accuracy suggests that it may still be learning and adapting, potentially benefiting from further training. The consistently low UCI accuracy for both models raises questions about the effectiveness of the UCI method for evaluating these models on Lichess puzzles. It's possible that the UCI method is more susceptible to noise or that it requires a different training approach to yield meaningful results. The faster initial learning rate of Llama3.1-8B suggests it may be more efficient at learning the underlying patterns in the Lichess puzzle data.

## Line Graphs: Qwen2.5-7B and Llama3.1-8B Performance Comparison ### Overview The image contains two side-by-side line graphs comparing the performance of two AI models (Qwen2.5-7B and Llama3.1-8B) across training steps. Each graph tracks two metrics: "SAN" (blue line) and "UCI" (gray line), measured as "Lichess Puzzle Acc" (accuracy) on a scale from 0.00 to 0.30. Training steps range from 0 to 150 on the x-axis. --- ### Components/Axes - **Left Graph (Qwen2.5-7B)**: - **Title**: "Qwen2.5-7B" - **X-axis**: "Training Step" (0–150, increments of 30) - **Y-axis**: "Lichess Puzzle Acc" (0.00–0.30, increments of 0.05) - **Legend**: Located in the bottom-right corner, labeled "SAN" (blue) and "UCI" (gray). - **Lines**: - **Blue (SAN)**: Starts near 0.01, rises sharply to ~0.29 by step 150. - **Gray (UCI)**: Starts near 0.005, peaks at ~0.03 around step 40, then declines to ~0.02. - **Right Graph (Llama3.1-8B)**: - **Title**: "Llama3.1-8B" - **X-axis**: "Training Step" (0–150, increments of 30) - **Y-axis**: "Lichess Puzzle Acc" (0.00–0.30, increments of 0.05) - **Legend**: Located in the bottom-right corner, labeled "SAN" (blue) and "UCI" (gray). - **Lines**: - **Blue (SAN)**: Starts near 0.01, rises sharply to ~0.30 by step 60, fluctuates between 0.28–0.30 by step 150. - **Gray (UCI)**: Starts near 0.005, peaks at ~0.025 around step 20, then declines to ~0.015. --- ### Detailed Analysis #### Qwen2.5-7B - **SAN (Blue)**: - Initial value: ~0.01 at step 0. - Rapid increase to ~0.25 by step 60. - Gradual plateau to ~0.29 by step 150. - **UCI (Gray)**: - Initial value: ~0.005 at step 0. - Peaks at ~0.03 around step 40. - Declines to ~0.02 by step 150. #### Llama3.1-8B - **SAN (Blue)**: - Initial value: ~0.01 at step 0. - Sharp rise to ~0.25 by step 30. - Peaks at ~0.30 by step 60. - Fluctuates between 0.28–0.30 by step 150. - **UCI (Gray)**: - Initial value: ~0.005 at step 0. - Peaks at ~0.025 around step 20. - Declines to ~0.015 by step 150. --- ### Key Observations 1. **SAN Performance**: - Both models show a steep initial improvement in SAN accuracy, but Llama3.1-8B achieves a higher peak (~0.30 vs. ~0.29). - Qwen2.5-7B’s SAN plateaus earlier (~step 60), while Llama3.1-8B’s SAN remains volatile after step 60. 2. **UCI Performance**: - UCI accuracy peaks early in both models (~step 20–40) and declines sharply afterward. - Llama3.1-8B’s UCI peak is higher (~0.025 vs. ~0.03), but its decline is more pronounced. 3. **Model Comparison**: - Llama3.1-8B outperforms Qwen2.5-7B in SAN accuracy, suggesting better scalability or efficiency. - Both models’ UCI metrics indicate potential overfitting or inefficiency in later training stages. --- ### Interpretation - **SAN Trends**: The sharp rise in SAN accuracy for both models suggests effective learning in early training steps. Llama3.1-8B’s higher peak implies superior performance, possibly due to its larger parameter count (8B vs. 7B). The plateau in Qwen2.5-7B may reflect a learning limit, while Llama3.1-8B’s fluctuations could indicate instability or adaptation to complex patterns. - **UCI Trends**: The early peak and subsequent decline in UCI accuracy for both models suggest that UCI metrics may measure short-term gains or overfitting. The steeper decline in Llama3.1-8B’s UCI could indicate greater sensitivity to training noise or complexity. - **Model Differences**: Llama3.1-8B’s larger size correlates with higher SAN performance but also greater volatility, highlighting trade-offs between scale and stability. Qwen2.5-7B’s smoother plateau might indicate more robust training dynamics. --- ### Spatial Grounding - **Legends**: Both legends are positioned in the bottom-right corner of their respective graphs, ensuring clarity without obstructing data. - **Line Colors**: Blue (SAN) and gray (UCI) are consistently used across both graphs, avoiding confusion. ### Content Details - **Qwen2.5-7B SAN**: 0.01 → 0.25 (step 60) → 0.29 (step 150). - **Qwen2.5-7B UCI**: 0.005 → 0.03 (step 40) → 0.02 (step 150). - **Llama3.1-8B SAN**: 0.01 → 0.25 (step 30) → 0.30 (step 60) → 0.28–0.30 (step 150). - **Llama3.1-8B UCI**: 0.005 → 0.025 (step 20) → 0.015 (step 150). --- ### Final Notes The graphs emphasize the importance of training step efficiency and model architecture in achieving high puzzle-solving accuracy. Llama3.1-8B’s superior SAN performance suggests it may be better suited for tasks requiring rapid learning, while Qwen2.5-7B’s stability could be advantageous in scenarios prioritizing consistency.