## Line Charts: Performance Metrics vs. Number of Tokens at Target ### Overview The image contains a grid of line charts comparing the performance of different models (OPT-125M-13B, OPT-125M-30B, OPT-125M-66B, OPT-350M-13B, OPT-350M-30B, OPT-350M-66B) on different tasks (WMT, XSum) using various methods (SD, SpecTr, RSD-C, RSD-S). The charts display four metrics: block efficiency, MBSU, token rate, and accuracy, each plotted against the number of tokens at the target (6, 10, 14, 21, 30). ### Components/Axes * **Rows:** Each row represents a specific model and task combination (e.g., OPT-125M-13B on WMT). * **Columns:** Each column represents a different performance metric: * Column 1: "block efficiency" * Y-axis ranges from approximately 1.2 to 2.7. * Column 2: "MBSU" * Y-axis ranges from approximately 0.7 to 2.6. * Column 3: "token rate" * Y-axis ranges from approximately 0.0 to 1.3. * Column 4: "accuracy" * Y-axis ranges from approximately 0.7 to 1.3. * **X-axis (shared):** "num. tokens at target" with values 6, 10, 14, 21, and 30. * **Legend (bottom):** * SD (Red, dash-dot line) * SpecTr (Green, dashed line, diamond markers) * RSD-C (ours) (Orange, dotted line, triangle markers) * RSD-S (ours) (Blue, solid line, circle markers) ### Detailed Analysis Each row contains four line charts, one for each metric. The following analysis breaks down the trends and approximate values for each metric and model/task combination. **Row 1: OPT-125M-13B, WMT** * **Block Efficiency:** * SD (Red, dash-dot): Starts at ~1.7, slightly decreases to ~1.6. * SpecTr (Green, dashed): Starts at ~1.9, slightly decreases to ~1.8. * RSD-C (Orange, dotted): Starts at ~1.7, slightly decreases to ~1.6. * RSD-S (Blue, solid): Starts at ~1.7, slightly increases to ~1.8. * **MBSU:** * SD (Red, dash-dot): Starts at ~1.9, slightly decreases to ~1.8. * SpecTr (Green, dashed): Starts at ~1.9, slightly decreases to ~1.8. * RSD-C (Orange, dotted): Starts at ~1.8, slightly decreases to ~1.7. * RSD-S (Blue, solid): Starts at ~1.9, remains relatively constant at ~1.9. * **Token Rate:** * SD (Red, dash-dot): Starts at ~0.8, decreases to ~0.7. * SpecTr (Green, dashed): Starts at ~0.8, decreases to ~0.7. * RSD-C (Orange, dotted): Starts at ~0.4, decreases to ~0.3. * RSD-S (Blue, solid): Starts at ~0.8, decreases to ~0.7. * **Accuracy:** * All methods (SD, SpecTr, RSD-C, RSD-S) maintain a constant accuracy of approximately 1.0. **Row 2: OPT-125M-13B, XSum** * **Block Efficiency:** * SD (Red, dash-dot): Starts at ~2.3, slightly decreases to ~2.2. * SpecTr (Green, dashed): Starts at ~2.4, slightly decreases to ~2.3. * RSD-C (Orange, dotted): Starts at ~2.3, slightly decreases to ~2.2. * RSD-S (Blue, solid): Starts at ~2.3, remains relatively constant at ~2.3. * **MBSU:** * SD (Red, dash-dot): Starts at ~1.5, slightly decreases to ~1.4. * SpecTr (Green, dashed): Starts at ~1.5, slightly decreases to ~1.4. * RSD-C (Orange, dotted): Starts at ~1.4, decreases to ~1.3. * RSD-S (Blue, solid): Starts at ~1.5, remains relatively constant at ~1.5. * **Token Rate:** * SD (Red, dash-dot): Starts at ~0.6, decreases to ~0.5. * SpecTr (Green, dashed): Starts at ~0.6, decreases to ~0.5. * RSD-C (Orange, dotted): Starts at ~0.1, remains relatively constant at ~0.1. * RSD-S (Blue, solid): Starts at ~0.6, decreases to ~0.5. * **Accuracy:** * All methods (SD, SpecTr, RSD-C, RSD-S) maintain a constant accuracy of approximately 1.0. **Row 3: OPT-125M-30B, WMT** * **Block Efficiency:** * SD (Red, dash-dot): Starts at ~1.7, slightly decreases to ~1.6. * SpecTr (Green, dashed): Starts at ~1.9, slightly decreases to ~1.8. * RSD-C (Orange, dotted): Starts at ~1.7, slightly decreases to ~1.6. * RSD-S (Blue, solid): Starts at ~1.7, slightly increases to ~1.8. * **MBSU:** * SD (Red, dash-dot): Starts at ~1.6, slightly decreases to ~1.5. * SpecTr (Green, dashed): Starts at ~1.6, slightly decreases to ~1.5. * RSD-C (Orange, dotted): Starts at ~1.5, slightly decreases to ~1.4. * RSD-S (Blue, solid): Starts at ~1.6, remains relatively constant at ~1.6. * **Token Rate:** * SD (Red, dash-dot): Starts at ~0.7, decreases to ~0.6. * SpecTr (Green, dashed): Starts at ~0.7, decreases to ~0.6. * RSD-C (Orange, dotted): Starts at ~0.1, remains relatively constant at ~0.1. * RSD-S (Blue, solid): Starts at ~0.7, decreases to ~0.6. * **Accuracy:** * All methods (SD, SpecTr, RSD-C, RSD-S) maintain a constant accuracy of approximately 1.0. **Row 4: OPT-125M-30B, XSum** * **Block Efficiency:** * SD (Red, dash-dot): Starts at ~2.5, slightly decreases to ~2.4. * SpecTr (Green, dashed): Starts at ~2.6, slightly decreases to ~2.5. * RSD-C (Orange, dotted): Starts at ~2.4, slightly decreases to ~2.3. * RSD-S (Blue, solid): Starts at ~2.4, remains relatively constant at ~2.4. * **MBSU:** * SD (Red, dash-dot): Starts at ~1.3, slightly decreases to ~1.2. * SpecTr (Green, dashed): Starts at ~1.3, slightly decreases to ~1.2. * RSD-C (Orange, dotted): Starts at ~1.2, decreases to ~1.1. * RSD-S (Blue, solid): Starts at ~1.3, remains relatively constant at ~1.3. * **Token Rate:** * SD (Red, dash-dot): Starts at ~0.3, decreases to ~0.2. * SpecTr (Green, dashed): Starts at ~0.3, decreases to ~0.2. * RSD-C (Orange, dotted): Starts at ~0.1, remains relatively constant at ~0.1. * RSD-S (Blue, solid): Starts at ~0.3, decreases to ~0.2. * **Accuracy:** * All methods (SD, SpecTr, RSD-C, RSD-S) maintain a constant accuracy of approximately 1.0. **Row 5: OPT-125M-66B, WMT** * **Block Efficiency:** * SD (Red, dash-dot): Starts at ~1.7, slightly decreases to ~1.6. * SpecTr (Green, dashed): Starts at ~1.9, slightly decreases to ~1.8. * RSD-C (Orange, dotted): Starts at ~1.7, slightly decreases to ~1.6. * RSD-S (Blue, solid): Starts at ~1.7, slightly increases to ~1.8. * **MBSU:** * SD (Red, dash-dot): Starts at ~1.6, slightly decreases to ~1.5. * SpecTr (Green, dashed): Starts at ~1.6, slightly decreases to ~1.5. * RSD-C (Orange, dotted): Starts at ~1.5, slightly decreases to ~1.4. * RSD-S (Blue, solid): Starts at ~1.6, remains relatively constant at ~1.6. * **Token Rate:** * SD (Red, dash-dot): Starts at ~0.7, decreases to ~0.6. * SpecTr (Green, dashed): Starts at ~0.7, decreases to ~0.6. * RSD-C (Orange, dotted): Starts at ~0.1, remains relatively constant at ~0.1. * RSD-S (Blue, solid): Starts at ~0.7, decreases to ~0.6. * **Accuracy:** * All methods (SD, SpecTr, RSD-C, RSD-S) maintain a constant accuracy of approximately 1.0. **Row 6: OPT-125M-66B, XSum** * **Block Efficiency:** * SD (Red, dash-dot): Starts at ~2.5, slightly decreases to ~2.4. * SpecTr (Green, dashed): Starts at ~2.6, slightly decreases to ~2.5. * RSD-C (Orange, dotted): Starts at ~2.4, slightly decreases to ~2.3. * RSD-S (Blue, solid): Starts at ~2.4, remains relatively constant at ~2.4. * **MBSU:** * SD (Red, dash-dot): Starts at ~1.3, slightly decreases to ~1.2. * SpecTr (Green, dashed): Starts at ~1.3, slightly decreases to ~1.2. * RSD-C (Orange, dotted): Starts at ~1.2, decreases to ~1.1. * RSD-S (Blue, solid): Starts at ~1.3, remains relatively constant at ~1.3. * **Token Rate:** * SD (Red, dash-dot): Starts at ~0.3, decreases to ~0.2. * SpecTr (Green, dashed): Starts at ~0.3, decreases to ~0.2. * RSD-C (Orange, dotted): Starts at ~0.1, remains relatively constant at ~0.1. * RSD-S (Blue, solid): Starts at ~0.3, decreases to ~0.2. * **Accuracy:** * All methods (SD, SpecTr, RSD-C, RSD-S) maintain a constant accuracy of approximately 1.0. **Row 7: OPT-350M-13B, WMT** * **Block Efficiency:** * SD (Red, dash-dot): Starts at ~1.4, slightly decreases to ~1.3. * SpecTr (Green, dashed): Starts at ~1.6, slightly decreases to ~1.5. * RSD-C (Orange, dotted): Starts at ~1.4, slightly decreases to ~1.3. * RSD-S (Blue, solid): Starts at ~1.4, slightly increases to ~1.5. * **MBSU:** * SD (Red, dash-dot): Starts at ~1.1, slightly decreases to ~1.0. * SpecTr (Green, dashed): Starts at ~1.1, slightly decreases to ~1.0. * RSD-C (Orange, dotted): Starts at ~0.7, remains relatively constant at ~0.7. * RSD-S (Blue, solid): Starts at ~1.1, remains relatively constant at ~1.1. * **Token Rate:** * SD (Red, dash-dot): Starts at ~0.6, decreases to ~0.5. * SpecTr (Green, dashed): Starts at ~0.6, decreases to ~0.5. * RSD-C (Orange, dotted): Starts at ~0.0, remains relatively constant at ~0.0. * RSD-S (Blue, solid): Starts at ~0.6, decreases to ~0.5. * **Accuracy:** * All methods (SD, SpecTr, RSD-C, RSD-S) maintain a constant accuracy of approximately 1.0. **Row 8: OPT-350M-13B, XSum** * **Block Efficiency:** * SD (Red, dash-dot): Starts at ~2.2, slightly decreases to ~2.1. * SpecTr (Green, dashed): Starts at ~2.4, slightly decreases to ~2.3. * RSD-C (Orange, dotted): Starts at ~2.2, slightly decreases to ~2.1. * RSD-S (Blue, solid): Starts at ~2.2, remains relatively constant at ~2.2. * **MBSU:** * SD (Red, dash-dot): Starts at ~0.8, slightly decreases to ~0.7. * SpecTr (Green, dashed): Starts at ~0.8, slightly decreases to ~0.7. * RSD-C (Orange, dotted): Starts at ~0.7, remains relatively constant at ~0.7. * RSD-S (Blue, solid): Starts at ~0.8, remains relatively constant at ~0.8. * **Token Rate:** * SD (Red, dash-dot): Starts at ~0.4, decreases to ~0.3. * SpecTr (Green, dashed): Starts at ~0.4, decreases to ~0.3. * RSD-C (Orange, dotted): Starts at ~0.0, remains relatively constant at ~0.0. * RSD-S (Blue, solid): Starts at ~0.4, decreases to ~0.3. * **Accuracy:** * All methods (SD, SpecTr, RSD-C, RSD-S) maintain a constant accuracy of approximately 1.0. **Row 9: OPT-350M-30B, WMT** * **Block Efficiency:** * SD (Red, dash-dot): Starts at ~1.4, slightly decreases to ~1.3. * SpecTr (Green, dashed): Starts at ~1.6, slightly decreases to ~1.5. * RSD-C (Orange, dotted): Starts at ~1.4, slightly decreases to ~1.3. * RSD-S (Blue, solid): Starts at ~1.4, slightly increases to ~1.5. * **MBSU:** * SD (Red, dash-dot): Starts at ~1.2, slightly decreases to ~1.1. * SpecTr (Green, dashed): Starts at ~1.2, slightly decreases to ~1.1. * RSD-C (Orange, dotted): Starts at ~0.9, remains relatively constant at ~0.9. * RSD-S (Blue, solid): Starts at ~1.2, remains relatively constant at ~1.2. * **Token Rate:** * SD (Red, dash-dot): Starts at ~0.8, decreases to ~0.7. * SpecTr (Green, dashed): Starts at ~0.8, decreases to ~0.7. * RSD-C (Orange, dotted): Starts at ~0.0, remains relatively constant at ~0.0. * RSD-S (Blue, solid): Starts at ~0.8, decreases to ~0.7. * **Accuracy:** * All methods (SD, SpecTr, RSD-C, RSD-S) maintain a constant accuracy of approximately 1.0. **Row 10: OPT-350M-30B, XSum** * **Block Efficiency:** * SD (Red, dash-dot): Starts at ~2.3, slightly decreases to ~2.2. * SpecTr (Green, dashed): Starts at ~2.5, slightly decreases to ~2.4. * RSD-C (Orange, dotted): Starts at ~2.3, slightly decreases to ~2.2. * RSD-S (Blue, solid): Starts at ~2.3, remains relatively constant at ~2.3. * **MBSU:** * SD (Red, dash-dot): Starts at ~1.4, slightly decreases to ~1.3. * SpecTr (Green, dashed): Starts at ~1.4, slightly decreases to ~1.3. * RSD-C (Orange, dotted): Starts at ~1.3, remains relatively constant at ~1.3. * RSD-S (Blue, solid): Starts at ~1.4, remains relatively constant at ~1.4. * **Token Rate:** * SD (Red, dash-dot): Starts at ~0.4, decreases to ~0.3. * SpecTr (Green, dashed): Starts at ~0.4, decreases to ~0.3. * RSD-C (Orange, dotted): Starts at ~0.1, remains relatively constant at ~0.1. * RSD-S (Blue, solid): Starts at ~0.4, decreases to ~0.3. * **Accuracy:** * All methods (SD, SpecTr, RSD-C, RSD-S) maintain a constant accuracy of approximately 1.0. **Row 11: OPT-350M-66B, WMT** * **Block Efficiency:** * SD (Red, dash-dot): Starts at ~1.4, slightly decreases to ~1.3. * SpecTr (Green, dashed): Starts at ~1.6, slightly decreases to ~1.5. * RSD-C (Orange, dotted): Starts at ~1.4, slightly decreases to ~1.3. * RSD-S (Blue, solid): Starts at ~1.4, slightly increases to ~1.5. * **MBSU:** * SD (Red, dash-dot): Starts at ~1.3, slightly decreases to ~1.2. * SpecTr (Green, dashed): Starts at ~1.3, slightly decreases to ~1.2. * RSD-C (Orange, dotted): Starts at ~1.1, remains relatively constant at ~1.1. * RSD-S (Blue, solid): Starts at ~1.3, remains relatively constant at ~1.3. * **Token Rate:** * SD (Red, dash-dot): Starts at ~0.6, decreases to ~0.5. * SpecTr (Green, dashed): Starts at ~0.6, decreases to ~0.5. * RSD-C (Orange, dotted): Starts at ~0.0, remains relatively constant at ~0.0. * RSD-S (Blue, solid): Starts at ~0.6, decreases to ~0.5. * **Accuracy:** * All methods (SD, SpecTr, RSD-C, RSD-S) maintain a constant accuracy of approximately 1.0. **Row 12: OPT-350M-66B, XSum** * **Block Efficiency:** * SD (Red, dash-dot): Starts at ~2.3, slightly decreases to ~2.2. * SpecTr (Green, dashed): Starts at ~2.5, slightly decreases to ~2.4. * RSD-C (Orange, dotted): Starts at ~2.3, slightly decreases to ~2.2. * RSD-S (Blue, solid): Starts at ~2.3, remains relatively constant at ~2.3. * **MBSU:** * SD (Red, dash-dot): Starts at ~1.5, slightly decreases to ~1.4. * SpecTr (Green, dashed): Starts at ~1.5, slightly decreases to ~1.4. * RSD-C (Orange, dotted): Starts at ~1.5, remains relatively constant at ~1.5. * RSD-S (Blue, solid): Starts at ~1.5, remains relatively constant at ~1.5. * **Token Rate:** * SD (Red, dash-dot): Starts at ~0.3, decreases to ~0.2. * SpecTr (Green, dashed): Starts at ~0.3, decreases to ~0.2. * RSD-C (Orange, dotted): Starts at ~0.1, remains relatively constant at ~0.1. * RSD-S (Blue, solid): Starts at ~0.3, decreases to ~0.2. * **Accuracy:** * All methods (SD, SpecTr, RSD-C, RSD-S) maintain a constant accuracy of approximately 1.0. ### Key Observations * **Accuracy:** The accuracy metric remains almost constant across all models, tasks, and methods, hovering around 1.0. * **Block Efficiency:** Block efficiency generally decreases slightly as the number of tokens at the target increases for SD, SpecTr, and RSD-C. RSD-S shows a slight increase or remains constant. * **MBSU:** MBSU generally decreases slightly as the number of tokens at the target increases for SD, SpecTr, and RSD-C. RSD-S remains relatively constant. * **Token Rate:** Token rate consistently decreases as the number of tokens at the target increases for SD, SpecTr, and RSD-S. RSD-C has a very low and relatively constant token rate. * **RSD-C (ours):** This method consistently exhibits the lowest token rate across all model/task combinations. * **RSD-S (ours):** This method generally shows a more stable block efficiency and MBSU compared to other methods. ### Interpretation The data suggests that increasing the number of tokens at the target has a limited impact on accuracy, which remains relatively stable. However, it generally leads to a slight decrease in block efficiency, MBSU, and token rate for most methods. RSD-C appears to prioritize a very low token rate, potentially at the expense of other metrics. RSD-S seems to offer a more stable performance in terms of block efficiency and MBSU. The choice of method (SD, SpecTr, RSD-C, RSD-S) appears to influence the trade-off between different performance metrics. The "ours" methods (RSD-C and RSD-S) likely represent modifications or improvements to the standard SD and SpecTr approaches. The consistent accuracy across all methods suggests that the core task performance is maintained, while the variations in other metrics reflect different optimization strategies. Further investigation would be needed to understand the specific design choices and trade-offs associated with each method and their implications for different applications.