## Scatter Chart: Average GLUE Score vs. Model Size for BERT-type Models ### Overview The image is a scatter plot comparing the size (in MB) of various BERT-type models against their average GLUE score (a measure of language understanding performance). The plot highlights the impact of quantization and layer reduction techniques on model size and performance. ### Components/Axes * **Title:** Average over 8 GLUE tasks for BERT-type models * **X-axis:** Size (MB). Scale: 8, 16, 32, 200 * **Y-axis:** Glue Score. Scale: 82.0, 82.5, 83.0, 83.5, 84.0 * **Legend:** Located in the bottom-left and bottom-right of the chart. * **XTC-BERT*:** Orange circle * **BinaryBERT(TWN):** Purple pentagon * **BinaryBERT(BWN):** Purple diamond * **TernaryBERT:** Green triangle pointing right * **TernaryTinyBERT:** Green triangle pointing left * **XTC-BERT:** Red circle * **TinyBERT:** Teal X * **MiniLMv2:** Pink square * **Annotations:** * "L=12 (1-bit)" near the orange XTC-BERT* data point at approximately (12, 83.5) * "L=6 (1-bit)" near the orange XTC-BERT* data point at approximately (8, 81.8) * "L=12 (2-bit)" near the orange XTC-BERT* data point at approximately (28, 84.1) * "L=6" near the red XTC-BERT data point at approximately (200, 83.5) * "L=5" near the red XTC-BERT data point at approximately (200, 83.3) * **Vertical Blue Bar:** Separates "Quantization" (left) from "Layer Reduction" (right). * **Dashed Orange Line:** Connects the XTC-BERT* data points. ### Detailed Analysis * **XTC-BERT* (Orange Circles):** * Trend: As size increases, Glue Score increases. * Data Points: * (8, approximately 81.8), labeled "L=6 (1-bit)" * (approximately 12, approximately 83.5), labeled "L=12 (1-bit)" * (approximately 28, approximately 84.1), labeled "L=12 (2-bit)" * **BinaryBERT(TWN) (Purple Pentagons):** * Data Point: (approximately 16, approximately 83.3) * **BinaryBERT(BWN) (Purple Diamonds):** * Data Point: (approximately 16, approximately 82.5) * **TernaryBERT (Green Triangles pointing right):** * Data Point: (approximately 32, approximately 82.7) * **TernaryTinyBERT (Green Triangles pointing left):** * Data Point: (approximately 16, approximately 82.3) * **XTC-BERT (Red Circles):** * Data Point: (approximately 200, approximately 83.5), labeled "L=6" * Data Point: (approximately 200, approximately 83.3), labeled "L=5" * **TinyBERT (Teal X):** * Data Point: (approximately 200, approximately 83.3) * **MiniLMv2 (Pink Square):** * Data Point: (approximately 200, approximately 83.1) ### Key Observations * The XTC-BERT* model shows a clear improvement in Glue Score as size increases with quantization. * Layer reduction techniques (right side of the plot) generally result in larger models (200 MB) but varying Glue Scores. * The vertical blue bar visually separates the impact of quantization (left) from layer reduction (right). ### Interpretation The chart suggests that quantization can effectively reduce model size while maintaining or even improving performance, as seen with the XTC-BERT* model. However, layer reduction, while resulting in larger models, does not guarantee a higher Glue Score, indicating a trade-off between model size and performance. The different models employing layer reduction techniques cluster around the 200 MB size, but their performance varies, suggesting that the specific layer reduction strategy significantly impacts the final Glue Score. The XTC-BERT model appears in both the quantization and layer reduction sections, suggesting it was used as a baseline for both sets of experiments.

## Scatter Plot: BERT-type Model Performance vs. Size ### Overview This scatter plot visualizes the performance (Glue Score) of various BERT-type models against their size (in MB). The plot shows the trade-off between model size and performance, with different models employing techniques like quantization and layer reduction. The data is averaged over 8 GLUE tasks. ### Components/Axes * **X-axis:** Size (MB), ranging from approximately 8 MB to 200 MB. * **Y-axis:** Glue Score, ranging from approximately 82.0 to 84.0. * **Title:** "Average over 8 GLUE tasks for BERT-type models" * **Annotations:** Two horizontal arrows labeled "Quantization" (pointing left) and "Layer Reduction" (pointing right). * **Legend:** Located in the bottom-center of the plot, with the following entries: * XTC-BERT* (Orange) * BinaryBERT(TWN) (Purple) * BinaryBERT(BWN) (Dark Purple) * TernaryBERT (Green) * TernaryTinyBERT (Light Green) * XTC-BERT (Red) * TinyBERT (Teal) * MiniLMv2 (Pink) ### Detailed Analysis The plot contains several data series represented by different colored markers. * **XTC-BERT* (Orange):** This series shows a strong upward trend. * At approximately 8 MB, the Glue Score is around 82.2 (labeled "L=6 (1-bit)"). * At approximately 16 MB, the Glue Score is around 83.6 (labeled "L=12 (1-bit)"). * At approximately 32 MB, the Glue Score is around 84.0 (labeled "L=12 (2-bit)"). * **BinaryBERT(TWN) (Purple):** This series shows a decreasing trend. * At approximately 8 MB, the Glue Score is around 83.2. * At approximately 16 MB, the Glue Score is around 83.1. * **BinaryBERT(BWN) (Dark Purple):** This series shows a decreasing trend. * At approximately 8 MB, the Glue Score is around 82.7. * At approximately 16 MB, the Glue Score is around 82.4. * **TernaryBERT (Green):** This series shows a relatively flat trend. * At approximately 32 MB, the Glue Score is around 82.7. * **TernaryTinyBERT (Light Green):** This series shows a relatively flat trend. * At approximately 32 MB, the Glue Score is around 82.5. * **XTC-BERT (Red):** This series shows a relatively flat trend. * At approximately 200 MB, the Glue Score is around 83.7 (labeled "L=6"). * **TinyBERT (Teal):** This series shows a relatively flat trend. * At approximately 200 MB, the Glue Score is around 83.5 (labeled "L=5"). * **MiniLMv2 (Pink):** This series shows a relatively flat trend. * At approximately 200 MB, the Glue Score is around 83.4. ### Key Observations * The XTC-BERT* model demonstrates the most significant improvement in Glue Score with increasing size, particularly when moving from 8 MB to 32 MB. * Models employing quantization (indicated by the "Quantization" arrow) generally have smaller sizes but potentially lower Glue Scores compared to models with layer reduction. * Models with layer reduction (indicated by the "Layer Reduction" arrow) tend to have larger sizes but potentially higher Glue Scores. * BinaryBERT(TWN) and BinaryBERT(BWN) show a slight decrease in performance as size increases. * The models on the right side of the plot (XTC-BERT, TinyBERT, MiniLMv2) are significantly larger in size (around 200 MB) compared to the models on the left (8-32 MB). ### Interpretation The data suggests a trade-off between model size and performance for BERT-type models. Increasing model size generally leads to improved performance, as demonstrated by the XTC-BERT* series. However, techniques like quantization and layer reduction can be used to optimize model size while maintaining acceptable performance levels. The horizontal arrows indicate the direction of these optimization strategies. The plot highlights that different models achieve different balances between size and performance, and the optimal choice depends on the specific application and resource constraints. The slight decrease in performance for BinaryBERT(TWN) and BinaryBERT(BWN) as size increases could indicate diminishing returns or potential overfitting. The clustering of models around 83-84 Glue Score at 200MB suggests a performance ceiling for these architectures.

\n ## Scatter Plot: Average over 8 GLUE tasks for BERT-type models ### Overview This is a scatter plot comparing the performance (GLUE Score) versus model size (in MB) for various compressed BERT-type models. The chart is divided into two distinct regions by a vertical blue line, illustrating two different compression strategies: "Quantization" (left side) and "Layer Reduction" (right side). Data points represent different model architectures and compression levels, with some points annotated to indicate specific layer counts (L) and bit-widths. ### Components/Axes * **Title:** "Average over 8 GLUE tasks for BERT-type models" * **Y-Axis:** Labeled "Glue Score". Scale ranges from 82.0 to 84.0, with major tick marks at 0.5 intervals (82.0, 82.5, 83.0, 83.5, 84.0). * **X-Axis:** Labeled "Size (MB)". The scale is non-linear, with labeled tick marks at 8, 16, 32, and 200 MB. The region between 32 and 200 MB is compressed. * **Legend:** Located in the bottom-right quadrant. It lists 8 model types with corresponding color and symbol markers: * Orange Circle: XTC-BERT* * Purple Pentagon: BinaryBERT(TWN) * Dark Purple Diamond: BinaryBERT(BWN) * Green Hexagon: TernaryBERT * Light Green Right-Pointing Triangle: TernaryTinyBERT * Red Circle: XTC-BERT * Teal X: TinyBERT * Pink Square: MiniLMv2 * **Annotations & Structural Elements:** * A thick vertical blue line at approximately 100 MB divides the chart. * A blue arrow pointing left from the line is labeled "Quantization". * A blue arrow pointing right from the line is labeled "Layer Reduction". * Several data points have gray text boxes with arrows pointing to them, indicating model configuration: * "L=6 (1-bit)" points to the orange circle at ~8 MB. * "L=12 (1-bit)" points to the orange circle at ~16 MB. * "L=12 (2-bit)" points to the orange circle at ~32 MB. * "L=8" points to the red circle at ~200 MB. * "L=6" points to the red circle at ~200 MB (slightly above the L=8 point). ### Detailed Analysis **Left Region (Quantization, Size < ~100 MB):** * **XTC-BERT* (Orange Circles):** Shows a strong positive trend. Performance increases sharply with model size. * Point 1: Size ≈ 8 MB, Glue Score ≈ 81.8. Annotated as "L=6 (1-bit)". * Point 2: Size ≈ 16 MB, Glue Score ≈ 83.4. Annotated as "L=12 (1-bit)". * Point 3: Size ≈ 32 MB, Glue Score ≈ 84.1. Annotated as "L=12 (2-bit)". This is the highest-performing model on the entire chart. * **BinaryBERT(TWN) (Purple Pentagon):** One point at Size ≈ 16 MB, Glue Score ≈ 82.5. * **BinaryBERT(BWN) (Dark Purple Diamond):** One point at Size ≈ 16 MB, Glue Score ≈ 83.3. * **TernaryBERT (Green Hexagon):** One point at Size ≈ 32 MB, Glue Score ≈ 82.7. * **TernaryTinyBERT (Light Green Triangle):** One point at Size ≈ 16 MB, Glue Score ≈ 82.3. **Right Region (Layer Reduction, Size ≈ 200 MB):** * Models in this region are clustered tightly around 200 MB but show a spread in performance. * **XTC-BERT (Red Circles):** Two points. * Lower point: Size ≈ 200 MB, Glue Score ≈ 83.3. Annotated as "L=8". * Higher point: Size ≈ 200 MB, Glue Score ≈ 83.5. Annotated as "L=6". * **TinyBERT (Teal X):** One point at Size ≈ 200 MB, Glue Score ≈ 83.4. * **MiniLMv2 (Pink Square):** One point at Size ≈ 200 MB, Glue Score ≈ 83.2. ### Key Observations 1. **Performance-Size Trade-off:** The most dramatic performance gains in the quantization region come from increasing bit-width (1-bit to 2-bit) and layer count (L=6 to L=12) for the XTC-BERT* model, albeit at the cost of increased size. 2. **Efficiency Frontier:** The XTC-BERT* models (orange) form a clear "Pareto frontier" on the left side, offering the best performance for their respective size classes. 3. **Clustering by Strategy:** Models are strictly separated by compression strategy (quantization vs. layer reduction) with no overlap in size. 4. **Performance Range:** The highest score (≈84.1) is achieved by a quantized model (XTC-BERT*, L=12, 2-bit) at 32 MB. The layer-reduced models at 200 MB achieve scores between ≈83.2 and ≈83.5. 5. **Anomaly/Notable Point:** The "L=6" XTC-BERT (red circle) in the layer reduction region performs slightly better than its "L=8" counterpart, which is counterintuitive as fewer layers typically mean a smaller, less capable model. This suggests other factors (like width or training) are at play. ### Interpretation This chart visually argues for the effectiveness of aggressive quantization (especially the XTC-BERT* approach) as a method for creating highly efficient models. It demonstrates that a 32 MB model using 2-bit quantization can outperform much larger 200 MB models that rely on layer reduction. The data suggests that for the GLUE benchmark, intelligently reducing numerical precision (quantization) may be a more effective compression strategy than simply removing layers, as it achieves superior performance at a fraction of the size. The clear separation of the two strategies highlights a fundamental design choice in model compression: reduce the precision of computations or reduce the number of computational steps. The chart strongly favors the former for this specific task and model family.

## Scatter Plot: Average over 8 GLUE tasks for BERT-type models ### Overview The chart compares BERT-type models across two dimensions: **model size (MB)** and **GLUE task performance (Glue Score)**. It highlights trade-offs between model efficiency (size) and accuracy, with annotations for quantization and layer reduction techniques. Data points are color-coded and shaped to represent specific models, with trends visualized via lines and arrows. --- ### Components/Axes - **X-axis (Size)**: Labeled "Size (MB)" with ticks at 8, 16, 32, and 200 MB. - **Y-axis (Glue Score)**: Labeled "Glue Score" with increments of 0.5, ranging from 82.0 to 84.0. - **Legend**: Located in the bottom-right, mapping colors/shapes to models: - **Orange circle**: XTC-BERT* - **Purple pentagon**: BinaryBERT(TWN) - **Dark purple diamond**: BinaryBERT(BWN) - **Green hexagon**: TernaryBERT - **Light green triangle**: TernaryTinyBERT - **Red circle**: XTC-BERT - **Teal cross**: TinyBERT - **Pink square**: MiniLMv2 - **Arrows**: Two blue arrows labeled "Quantization" (left) and "Layer Reduction" (right), pointing toward increasing model size. --- ### Detailed Analysis 1. **XTC-BERT* (Orange Circle)**: - **Size**: 8 MB (smallest). - **Glue Score**: ~82.0 (lowest). - **Label**: "L=12 (1-bit)" (12 layers, 1-bit quantization). 2. **BinaryBERT(TWN) (Purple Pentagon)**: - **Size**: ~16 MB. - **Glue Score**: ~82.5. - **Label**: "L=12 (1-bit)" (same as XTC-BERT*). 3. **TernaryBERT (Green Hexagon)**: - **Size**: ~32 MB. - **Glue Score**: ~82.7. - **Label**: "L=12 (2-bit)" (12 layers, 2-bit quantization). 4. **TernaryTinyBERT (Light Green Triangle)**: - **Size**: ~32 MB. - **Glue Score**: ~82.3. - **Label**: "L=6 (1-bit)" (6 layers, 1-bit quantization). 5. **XTC-BERT (Red Circle)**: - **Size**: 200 MB (largest). - **Glue Score**: ~83.5. - **Label**: "L=6 (1-bit)" (6 layers, 1-bit quantization). 6. **TinyBERT (Teal Cross)**: - **Size**: 200 MB. - **Glue Score**: ~83.3. - **Label**: "L=5 (1-bit)" (5 layers, 1-bit quantization). 7. **MiniLMv2 (Pink Square)**: - **Size**: 200 MB. - **Glue Score**: ~83.2. - **Label**: Not explicitly labeled but inferred from position. --- ### Key Observations 1. **Size vs. Performance Trade-off**: - Smaller models (8–32 MB) achieve lower Glue Scores (82.0–82.7). - Larger models (200 MB) achieve higher scores (83.2–83.5), suggesting improved performance with increased size. 2. **Quantization Impact**: - The orange dashed line connects XTC-BERT* (8 MB, 82.0) to TernaryBERT (32 MB, 82.7), showing a steep upward trend. This implies quantization (1-bit to 2-bit) improves performance while increasing size. 3. **Layer Reduction**: - Models at 200 MB (XTC-BERT, TinyBERT, MiniLMv2) use fewer layers (L=5–6) but achieve higher scores than smaller models. This suggests layer reduction (e.g., L=12 → L=6) may optimize performance without sacrificing accuracy. 4. **Anomalies**: - TernaryTinyBERT (32 MB, 82.3) underperforms TernaryBERT (32 MB, 82.7) despite similar size, possibly due to differences in quantization or architecture. --- ### Interpretation The chart demonstrates that **larger models (200 MB)** with fewer layers (L=5–6) and 1-bit quantization outperform smaller models (8–32 MB) with more layers (L=12) and lower quantization (1–2-bit). This suggests: - **Quantization** (1-bit vs. 2-bit) improves performance but increases size. - **Layer reduction** (L=12 → L=6) may enhance efficiency without significant accuracy loss. - The **orange line** (XTC-BERT*) highlights a trade-off: increasing size via quantization boosts performance but requires more resources. The data underscores the balance between model complexity (size, layers) and efficiency (quantization) in achieving optimal GLUE task performance.