## Bar Charts: Normalized Decoding Speed vs. Verification Width Across Four Benchmarks ### Overview The image displays a set of four grouped bar charts arranged horizontally. Each chart compares the "Normalized Decoding Speed" of four different methods across five distinct "Verification Width" settings. The charts are labeled (a) through (d), corresponding to four different evaluation benchmarks: MT-bench, GSM8K, MBPP, and Human-Eval. The overall purpose is to demonstrate the relative performance (speed) of the methods as the verification width parameter changes. ### Components/Axes * **Legend:** Positioned at the top center of the entire figure. It defines four data series: * **Sequential:** Solid brown bar. * **Medusa:** Blue bar with horizontal hatching. * **EM+Medusa:** Orange bar with diagonal hatching (top-left to bottom-right). * **Ghidorah:** Green bar with cross-hatch (X) pattern. * **Y-Axis (All Charts):** Labeled "Normalized Decoding Speed". The scale runs from 0 to 6, with major tick marks at 0, 2, 4, and 6. * **X-Axis (All Charts):** Labeled "Verification Width". The categorical tick marks are at values: 4, 8, 16, 32, and 64. * **Subplot Titles:** Located below each chart: * (a) MT-bench * (b) GSM8K * (c) MBPP * (d) Human-Eval ### Detailed Analysis The following analysis describes the approximate height of each bar, interpreted as normalized decoding speed. Values are estimated from the y-axis scale. **Chart (a) MT-bench:** * **Trend:** All methods except Sequential show an increase in speed from width 4 to 16 or 32, followed by a slight decrease or plateau at width 64. Ghidorah is consistently the fastest. * **Data Points (Approx. Speed):** * **Width 4:** Sequential ~1.0, Medusa ~2.2, EM+Medusa ~4.1, Ghidorah ~5.3. * **Width 8:** Sequential ~1.0, Medusa ~2.6, EM+Medusa ~4.7, Ghidorah ~5.9. * **Width 16:** Sequential ~1.0, Medusa ~2.9, EM+Medusa ~5.3, Ghidorah ~6.8 (peak). * **Width 32:** Sequential ~1.0, Medusa ~3.2, EM+Medusa ~5.5, Ghidorah ~5.7. * **Width 64:** Sequential ~1.0, Medusa ~3.3, EM+Medusa ~4.4, Ghidorah ~5.2. **Chart (b) GSM8K:** * **Trend:** Similar pattern to MT-bench. Ghidorah peaks at width 16. EM+Medusa shows a steady increase up to width 32. * **Data Points (Approx. Speed):** * **Width 4:** Sequential ~1.0, Medusa ~2.4, EM+Medusa ~4.4, Ghidorah ~5.6. * **Width 8:** Sequential ~1.0, Medusa ~2.7, EM+Medusa ~4.8, Ghidorah ~6.1. * **Width 16:** Sequential ~1.0, Medusa ~3.0, EM+Medusa ~5.5, Ghidorah ~6.8 (peak). * **Width 32:** Sequential ~1.0, Medusa ~3.3, EM+Medusa ~5.7, Ghidorah ~5.9. * **Width 64:** Sequential ~1.0, Medusa ~3.5, EM+Medusa ~4.7, Ghidorah ~5.6. **Chart (c) MBPP:** * **Trend:** Ghidorah peaks at width 16. EM+Medusa peaks at width 32. The performance drop for Ghidorah at width 64 is less pronounced here. * **Data Points (Approx. Speed):** * **Width 4:** Sequential ~1.0, Medusa ~2.5, EM+Medusa ~4.6, Ghidorah ~5.9. * **Width 8:** Sequential ~1.0, Medusa ~2.9, EM+Medusa ~5.2, Ghidorah ~6.5. * **Width 16:** Sequential ~1.0, Medusa ~3.2, EM+Medusa ~5.8, Ghidorah ~7.2 (peak). * **Width 32:** Sequential ~1.0, Medusa ~3.5, EM+Medusa ~6.0, Ghidorah ~6.2. * **Width 64:** Sequential ~1.0, Medusa ~3.6, EM+Medusa ~4.9, Ghidorah ~5.7. **Chart (d) Human-Eval:** * **Trend:** Ghidorah peaks at width 16. EM+Medusa peaks at width 32. The relative performance hierarchy is very consistent. * **Data Points (Approx. Speed):** * **Width 4:** Sequential ~1.0, Medusa ~2.5, EM+Medusa ~4.5, Ghidorah ~5.8. * **Width 8:** Sequential ~1.0, Medusa ~2.9, EM+Medusa ~5.1, Ghidorah ~6.4. * **Width 16:** Sequential ~1.0, Medusa ~3.2, EM+Medusa ~5.8, Ghidorah ~7.1 (peak). * **Width 32:** Sequential ~1.0, Medusa ~3.5, EM+Medusa ~6.0, Ghidorah ~6.2. * **Width 64:** Sequential ~1.0, Medusa ~3.6, EM+Medusa ~4.9, Ghidorah ~5.8. ### Key Observations 1. **Consistent Hierarchy:** Across all benchmarks and verification widths, the performance order is almost always: **Ghidorah > EM+Medusa > Medusa > Sequential**. The only exception is at width 64 in some charts where EM+Medusa and Ghidorah converge or swap slightly. 2. **Optimal Verification Width:** For the top-performing method (Ghidorah), the optimal verification width appears to be **16**, where it achieves its peak normalized speed (~6.8-7.2) in all charts. Performance declines at widths 32 and 64. 3. **Sequential Baseline:** The "Sequential" method serves as a baseline, showing a constant normalized speed of approximately 1.0 across all conditions, indicating it is unaffected by the verification width parameter. 4. **Diminishing Returns:** For Medusa and EM+Medusa, speed generally increases with verification width up to 32, but the gains diminish, and performance often drops at width 64. 5. **Benchmark Similarity:** The relative trends and magnitudes are remarkably consistent across the four diverse benchmarks (MT-bench, GSM8K, MBPP, Human-Eval), suggesting the observed method behaviors are robust. ### Interpretation This data demonstrates a clear technical advantage for the "Ghidorah" method in terms of decoding speed under a verification-based evaluation framework. The "verification width" parameter likely controls a trade-off between computational effort per step and the number of steps or candidates verified. * **Ghidorah's Superiority:** Ghidorah's consistently higher bars indicate it achieves the fastest normalized decoding speed. Its peak at width 16 suggests an optimal balance point for this method—wider verification (32, 64) may introduce overhead that outweighs its benefits, while narrower verification (4, 8) doesn't leverage its full potential. * **Method Synergy:** The "EM+Medusa" method, which presumably combines techniques, consistently outperforms "Medusa" alone, showing the value of the added component(s). However, it does not surpass the integrated "Ghidorah" system. * **Practical Implication:** For practitioners using these decoding acceleration techniques, the charts provide a tuning guide. To maximize speed, one should use Ghidorah with a verification width around 16. If Ghidorah is unavailable, EM+Medusa with a width of 32 is the next best choice. The Sequential method is the slowest but most stable, unaffected by the width parameter. * **Underlying Mechanism:** The rise and subsequent fall of speed with increasing width for the advanced methods suggests a classic optimization curve. Initially, wider verification improves efficiency (perhaps by accepting more correct tokens per step), but beyond a point, the cost of verifying more candidates (computational or memory overhead) degrades overall throughput. Ghidorah appears to have the most efficient implementation of this trade-off.