## Bar Chart: Latency Comparison of Different Decoding Methods ### Overview The image is a bar chart comparing the latency (in seconds) of different decoding methods across five datasets: GSM8K, GSMHard, Math500, SVAMP, and ARC. The chart displays the latency for Chain-of-Thought, Predictive Decoding, Phi-Decoding, and four variations of PPCV (T1, T2, T3, and T4). ### Components/Axes * **Y-axis:** Latency (s), with a scale from 0 to 40 in increments of 5. * **X-axis:** Datasets: GSM8K, GSMHard, Math500, SVAMP, ARC. * **Legend (Top-Right):** * Chain-of-Thought (Teal) * Predictive Decoding (Light Blue) * Phi-Decoding (Pale Pink) * PPCV-T1 (Ours) (Light Pink) * PPCV-T2 (Ours) (Orange) * PPCV-T3 (Ours) (Yellow-Green) * PPCV-T4 (Ours) (Salmon Pink) ### Detailed Analysis **GSM8K Dataset:** * Chain-of-Thought: ~2.2 s * Predictive Decoding: ~15.5 s * Phi-Decoding: ~13 s * PPCV-T1: ~2.5 s * PPCV-T2: ~4 s * PPCV-T3: ~5 s * PPCV-T4: ~18 s **GSMHard Dataset:** * Chain-of-Thought: ~3 s * Predictive Decoding: ~26.5 s * Phi-Decoding: ~23 s * PPCV-T1: ~3 s * PPCV-T2: ~6.5 s * PPCV-T3: ~7 s * PPCV-T4: ~23 s **Math500 Dataset:** * Chain-of-Thought: ~6.5 s * Predictive Decoding: ~42 s * Phi-Decoding: ~37.5 s * PPCV-T1: ~2.5 s * PPCV-T2: ~28 s * PPCV-T3: ~10 s * PPCV-T4: ~38 s **SVAMP Dataset:** * Chain-of-Thought: ~2 s * Predictive Decoding: ~14 s * Phi-Decoding: ~11 s * PPCV-T1: ~2 s * PPCV-T2: ~2 s * PPCV-T3: ~3 s * PPCV-T4: ~17 s **ARC Dataset:** * Chain-of-Thought: ~2.2 s * Predictive Decoding: ~15.5 s * Phi-Decoding: ~15 s * PPCV-T1: ~2 s * PPCV-T2: ~3 s * PPCV-T3: ~3.5 s * PPCV-T4: ~12.5 s ### Key Observations * Predictive Decoding consistently exhibits the highest latency across all datasets. * Chain-of-Thought generally has the lowest latency. * PPCV-T1, T2, and T3 show relatively low latency compared to other methods. * PPCV-T4 latency varies across datasets, sometimes being comparable to Phi-Decoding. * Math500 shows the largest latency differences between Predictive Decoding and Chain-of-Thought. ### Interpretation The bar chart illustrates the performance of different decoding methods in terms of latency across various datasets. Predictive Decoding and Phi-Decoding generally have higher latencies, suggesting they are more computationally intensive. Chain-of-Thought demonstrates the lowest latency, indicating it is the most efficient in terms of processing time. The PPCV variations show varying performance, with T1, T2, and T3 consistently exhibiting low latency, while T4's performance is more dataset-dependent. The Math500 dataset appears to be the most challenging, as it shows the largest latency values for Predictive Decoding and Phi-Decoding. The data suggests that the choice of decoding method significantly impacts latency, and the optimal method may vary depending on the specific dataset.

\n ## Bar Chart: Latency Comparison of Decoding Methods ### Overview This bar chart compares the latency (in seconds) of several decoding methods – Chain-of-Thought, Predictive Decoding, Phi-Decoding, and four variations of PPCV (PPCV-T1 to PPCV-T4) – across five different datasets: GSM8K, GSMHard, Math500, SVAMP, and ARC. The chart uses stacked bars to represent the contribution of each decoding method to the total latency for each dataset. ### Components/Axes * **X-axis:** Datasets - GSM8K, GSMHard, Math500, SVAMP, ARC. * **Y-axis:** Latency (s) - Scale ranges from 0 to 40 seconds, with increments of 5 seconds. * **Legend (Top-Right):** * Chain-of-Thought (Light Teal) * Predictive Decoding (Medium Teal) * Phi-Decoding (Light Orange) * PPCV-T1 (Ours) (Medium Orange) * PPCV-T2 (Ours) (Dark Orange) * PPCV-T3 (Ours) (Yellow) * PPCV-T4 (Ours) (Pink) ### Detailed Analysis Here's a breakdown of the latency values for each dataset and decoding method, based on the bar heights. Note that these are approximate values read from the chart. * **GSM8K:** * Chain-of-Thought: ~15s * Predictive Decoding: ~2s * Phi-Decoding: ~0.5s * PPCV-T1: ~1s * PPCV-T2: ~0.5s * PPCV-T3: ~0.2s * PPCV-T4: ~0.2s * Total: ~19.4s * **GSMHard:** * Chain-of-Thought: ~24s * Predictive Decoding: ~3s * Phi-Decoding: ~1s * PPCV-T1: ~1.5s * PPCV-T2: ~0.5s * PPCV-T3: ~0.3s * PPCV-T4: ~0.3s * Total: ~30.6s * **Math500:** * Chain-of-Thought: ~42s * Predictive Decoding: ~2s * Phi-Decoding: ~0.5s * PPCV-T1: ~1.5s * PPCV-T2: ~0.5s * PPCV-T3: ~0.2s * PPCV-T4: ~0.2s * Total: ~46.9s * **SVAMP:** * Chain-of-Thought: ~13s * Predictive Decoding: ~2s * Phi-Decoding: ~0.5s * PPCV-T1: ~1.5s * PPCV-T2: ~0.5s * PPCV-T3: ~0.2s * PPCV-T4: ~0.2s * Total: ~17.9s * **ARC:** * Chain-of-Thought: ~15s * Predictive Decoding: ~2s * Phi-Decoding: ~0.5s * PPCV-T1: ~1.5s * PPCV-T2: ~0.5s * PPCV-T3: ~0.2s * PPCV-T4: ~0.2s * Total: ~19.9s **Trends:** * Chain-of-Thought consistently contributes the largest portion of latency across all datasets. * PPCV-T3 and PPCV-T4 have very similar, minimal contributions to latency. * Predictive Decoding and Phi-Decoding contribute relatively small amounts of latency compared to Chain-of-Thought. * PPCV-T1 and PPCV-T2 contribute slightly more latency than PPCV-T3 and PPCV-T4. ### Key Observations * The Math500 dataset exhibits the highest overall latency, primarily driven by the Chain-of-Thought method. * The latency for Chain-of-Thought is significantly higher than all other methods across all datasets. * The PPCV methods (T1-T4) consistently show low latency contributions. * The differences in latency between the PPCV methods are relatively small. ### Interpretation The chart demonstrates a clear trade-off between decoding method and latency. Chain-of-Thought, while potentially offering higher accuracy or quality of results (not shown in this chart), incurs a substantial latency cost. The PPCV methods, particularly T3 and T4, appear to offer a significant reduction in latency, albeit potentially at the expense of performance on the tasks. The consistent pattern across datasets suggests that this latency difference is inherent to the decoding methods themselves and not specific to the characteristics of the datasets. The "Ours" label on PPCV-T1 through PPCV-T4 indicates these methods were developed by the authors of the study, and the chart serves to highlight their efficiency gains compared to established methods like Chain-of-Thought, Predictive Decoding, and Phi-Decoding. The stacked bar format effectively visualizes the composition of total latency, allowing for a clear comparison of the contribution of each method.

## Grouped Bar Chart: Latency Comparison of Decoding Methods Across Datasets ### Overview The image is a grouped bar chart comparing the latency (in seconds) of seven different decoding methods across five distinct datasets. The chart visually demonstrates the performance trade-offs between a baseline method (Chain-of-Thought), two existing methods (Predictive Decoding, Phi-Decoding), and four variants of a proposed method labeled "PPCV" (Ours). ### Components/Axes * **Chart Type:** Grouped Bar Chart. * **X-Axis (Categorical):** Represents five different evaluation datasets. From left to right: `GSM8K`, `GSMHard`, `Math500`, `SVAMP`, `ARC`. * **Y-Axis (Numerical):** Labeled `Latency (s)`. The scale runs from 0 to approximately 43 seconds, with major tick marks at intervals of 5 seconds (0, 5, 10, 15, 20, 25, 30, 35, 40). * **Legend:** Located in the top-right corner of the plot area. It defines seven data series by color: 1. `Chain-of-Thought` (Teal) 2. `Predictive Decoding` (Light Seafoam Green) 3. `Phi-Decoding` (Light Beige) 4. `PPCV-T₁ (Ours)` (Light Pink) 5. `PPCV-T₂ (Ours)` (Orange) 6. `PPCV-T₃ (Ours)` (Yellow-Green) 7. `PPCV-T₄ (Ours)` (Salmon Pink) ### Detailed Analysis The latency values for each method across the datasets are approximate, derived from visual inspection of the bar heights against the y-axis. **1. GSM8K Dataset:** * Chain-of-Thought: ~2.0 s * Predictive Decoding: ~15.5 s * Phi-Decoding: ~13.0 s * PPCV-T₁ (Ours): ~2.5 s * PPCV-T₂ (Ours): ~4.8 s (stacked on T₁) * PPCV-T₃ (Ours): ~5.0 s (stacked on T₂) * PPCV-T₄ (Ours): ~17.8 s (stacked on T₃) **2. GSMHard Dataset:** * Chain-of-Thought: ~3.0 s * Predictive Decoding: ~26.2 s * Phi-Decoding: ~23.2 s * PPCV-T₁ (Ours): ~3.0 s * PPCV-T₂ (Ours): ~6.0 s (stacked on T₁) * PPCV-T₃ (Ours): ~6.2 s (stacked on T₂) * PPCV-T₄ (Ours): ~23.0 s (stacked on T₃) **3. Math500 Dataset:** * Chain-of-Thought: ~6.2 s * Predictive Decoding: ~42.5 s (highest bar in the chart) * Phi-Decoding: ~38.0 s * PPCV-T₁ (Ours): ~2.5 s * PPCV-T₂ (Ours): ~10.0 s (stacked on T₁) * PPCV-T₃ (Ours): ~10.5 s (stacked on T₂) * PPCV-T₄ (Ours): ~37.5 s (stacked on T₃) **4. SVAMP Dataset:** * Chain-of-Thought: ~1.8 s * Predictive Decoding: ~14.2 s * Phi-Decoding: ~11.2 s * PPCV-T₁ (Ours): ~2.0 s * PPCV-T₂ (Ours): ~4.0 s (stacked on T₁) * PPCV-T₃ (Ours): ~4.2 s (stacked on T₂) * PPCV-T₄ (Ours): ~16.8 s (stacked on T₃) **5. ARC Dataset:** * Chain-of-Thought: ~2.2 s * Predictive Decoding: ~15.6 s * Phi-Decoding: ~15.4 s * PPCV-T₁ (Ours): ~1.2 s * PPCV-T₂ (Ours): ~3.8 s (stacked on T₁) * PPCV-T₃ (Ours): ~3.9 s (stacked on T₂) * PPCV-T₄ (Ours): ~12.5 s (stacked on T₃) **Note on PPCV Bars:** The bars for the four PPCV variants are **stacked** on top of each other for each dataset, forming a single composite bar. The total height of this composite bar represents the cumulative latency of the T₁ through T₄ components. The individual segment heights are listed above. ### Key Observations 1. **Consistent Baseline:** `Chain-of-Thought` consistently exhibits the lowest latency across all five datasets, ranging from ~1.8s to ~6.2s. 2. **High-Latency Methods:** `Predictive Decoding` and `Phi-Decoding` show significantly higher latency than Chain-of-Thought, with Predictive Decoding often being the slowest method (peaking at ~42.5s on Math500). 3. **PPCV Variant Performance:** The latency of the proposed `PPCV` method varies dramatically by its configuration (T₁ to T₄). * `PPCV-T₁` is very fast, comparable to Chain-of-Thought. * `PPCV-T₂` and `PPCV-T₃` add moderate latency. * `PPCV-T₄` contributes the vast majority of the latency in the composite PPCV bar, making the total latency for the full PPCV stack often comparable to or exceeding Phi-Decoding and Predictive Decoding (e.g., on GSM8K, GSMHard, SVAMP). 4. **Dataset Difficulty:** The `Math500` dataset elicits the highest latency from all methods except Chain-of-Thought, suggesting it is the most computationally demanding task among those tested. ### Interpretation This chart is a performance analysis from a research paper, likely evaluating a new decoding method called **PPCV**. The key takeaway is a **latency-accuracy trade-off**. The authors are demonstrating that their method can be configured for different operating points: * **Low-Latency Mode (`PPCV-T₁`):** Achieves speed comparable to the simple Chain-of-Thought baseline. * **High-Latency/High-Accuracy Mode (Full `PPCV-T₄` stack):** Incurs latency similar to or greater than existing complex methods like Predictive Decoding and Phi-Decoding. The implication is that this higher latency configuration likely yields better accuracy or reasoning quality, which would be shown in a separate accuracy chart. The stacking of the PPCV bars visually emphasizes that the latency cost is additive across its components (T₁ through T₄). The chart effectively argues that the PPCV framework is flexible, allowing users to choose a configuration that balances speed against the desired level of performance (presumably accuracy). The outlier performance on `Math500` highlights that the computational cost of advanced decoding is highly dependent on the complexity of the problem domain.

## Bar Chart: Latency Comparison Across Datasets and Methods ### Overview The chart compares latency (in seconds) across five datasets (GSM8K, GSMHard, Math500, SVAMP, ARC) for six different methods: Chain-of-Thought, Predictive Decoding, Phi-Decoding, and four variants of PPCV (PPCV-T1 to T4). Latency values are represented as stacked bar segments, with each method assigned a distinct color. ### Components/Axes - **X-axis (Datasets)**: GSM8K, GSMHard, Math500, SVAMP, ARC (categorical, left to right). - **Y-axis (Latency)**: 0–40 seconds (linear scale, increments of 5). - **Legend**: Located in the top-right corner, mapping colors to methods: - **Chain-of-Thought**: Teal (#008080) - **Predictive Decoding**: Light blue (#ADD8E6) - **Phi-Decoding**: Light pink (#FFD1DC) - **PPCV-T1 (Ours)**: Dark pink (#FF69B4) - **PPCV-T2 (Ours)**: Orange (#FFA500) - **PPCV-T3 (Ours)**: Yellow (#FFFF00) - **PPCV-T4 (Ours)**: Red (#FF0000) ### Detailed Analysis 1. **GSM8K**: - **Chain-of-Thought**: ~2s (teal, shortest segment). - **Predictive Decoding**: ~15s (light blue, second tallest). - **Phi-Decoding**: ~13s (light pink, third tallest). - **PPCV-T1**: ~18s (dark pink, tallest). - **PPCV-T2**: ~5s (orange, second shortest). - **PPCV-T3**: ~1s (yellow, shortest). - **PPCV-T4**: ~3s (red, second shortest). 2. **GSMHard**: - **Chain-of-Thought**: ~3s (teal). - **Predictive Decoding**: ~26s (light blue, tallest). - **Phi-Decoding**: ~23s (light pink, second tallest). - **PPCV-T1**: ~24s (dark pink, third tallest). - **PPCV-T2**: ~6s (orange, fourth tallest). - **PPCV-T3**: ~1s (yellow, shortest). - **PPCV-T4**: ~4s (red, second shortest). 3. **Math500**: - **Chain-of-Thought**: ~6s (teal). - **Predictive Decoding**: ~42s (light blue, tallest). - **Phi-Decoding**: ~38s (light pink, second tallest). - **PPCV-T1**: ~37s (dark pink, third tallest). - **PPCV-T2**: ~10s (orange, fourth tallest). - **PPCV-T3**: ~1s (yellow, shortest). - **PPCV-T4**: ~12s (red, fifth tallest). 4. **SVAMP**: - **Chain-of-Thought**: ~2s (teal). - **Predictive Decoding**: ~14s (light blue, tallest). - **Phi-Decoding**: ~11s (light pink, second tallest). - **PPCV-T1**: ~17s (dark pink, third tallest). - **PPCV-T2**: ~4s (orange, fourth tallest). - **PPCV-T3**: ~1s (yellow, shortest). - **PPCV-T4**: ~6s (red, fifth tallest). 5. **ARC**: - **Chain-of-Thought**: ~2.5s (teal). - **Predictive Decoding**: ~15.5s (light blue, tallest). - **Phi-Decoding**: ~15s (light pink, second tallest). - **PPCV-T1**: ~12.5s (dark pink, third tallest). - **PPCV-T2**: ~3.5s (orange, fourth tallest). - **PPCV-T3**: ~1.5s (yellow, shortest). - **PPCV-T4**: ~4.5s (red, fifth tallest). ### Key Observations - **Predictive Decoding** consistently shows the highest latency across all datasets, peaking at ~42s for Math500. - **Chain-of-Thought** has the lowest latency (~1.5–6s) but is often the shortest segment. - **Phi-Decoding** and **PPCV-T1** exhibit moderate-to-high latency, with PPCV-T1 being the tallest in GSM8K and SVAMP. - **PPCV-T3** (yellow) is the shortest segment in all datasets, indicating the fastest performance. - **Math500** has the highest overall latency values, while **GSM8K** and **ARC** show the lowest. ### Interpretation The data suggests that **PPCV-T3** (yellow) is the most efficient method across all datasets, with latencies consistently below 2s. **Predictive Decoding** (light blue) performs poorly in terms of latency, particularly on Math500, which may reflect the dataset's complexity. **Phi-Decoding** and **PPCV-T1** show intermediate performance, with PPCV-T1 being the most variable. The **Chain-of-Thought** method, while fast, may lack accuracy or robustness compared to other methods. The segmentation of bars highlights trade-offs between speed and performance, with no single method dominating all datasets.