# Technical Document Extraction: Control Effect Analysis (Layer 32) This document provides a comprehensive extraction of data and trends from the provided image, which consists of eight line charts and one summary heatmap. The data explores the "Control effect (d)" across various "Target axes" relative to "Affected axes" over a number of examples. --- ## 1. Component Isolation The image is segmented into two primary regions: * **Region A (Left/Center):** A grid of 8 line charts showing the progression of control effects as the number of examples increases (0 to 250). * **Region B (Right):** A summary heatmap titled "Control effect (d): layer 32" showing the final or peak relationship between Target and Affected axes. --- ## 2. Region A: Line Chart Grid Analysis Each chart represents a specific **Target axis**. The x-axis is **# Examples** (0, 100, 200) and the y-axis is **Control effect (d)**. ### Common Legend (Affected axis) The following categories are used across the line charts: * **LR:** Solid Red line. * **PC1:** Dotted Yellow line. * **PC2:** Solid Light Green line. * **PC4:** Solid Teal line. * **PC8:** Solid Dark Teal line. * **PC32:** Solid Blue-Grey line. * **PC128:** Solid Purple line. * **PC512:** Dotted Dark Purple line. ### Individual Chart Trends | Target Axis | Primary Trend (Self-Influence) | Secondary Trends (Cross-Influence) | | :--- | :--- | :--- | | **LR** | **LR (Red)**: Sharp upward slope, stabilizing at ~4.5. | Most other PCs cluster near 0.0 to 1.0. | | **PC1** | **PC1 (Yellow)**: Slopes upward to ~0.5, then declines toward 0.0. | High variance; PC512 (Dotted Purple) shows a slight upward trend. | | **PC2** | **PC2 (Light Green)**: Sharp upward slope, stabilizing at ~3.0. | PC4 (Teal) shows a slight downward trend to ~ -1.5. | | **PC4** | **PC4 (Teal)**: Sharp upward slope, stabilizing at ~2.5. | PC128 and PC32 show slight positive trends (~0.5). | | **PC8** | **PC8 (Dark Teal)**: Sharp upward slope, stabilizing at ~1.8. | PC2 (Light Green) shows a slight positive trend; others are near 0. | | **PC32** | **PC32 (Blue-Grey)**: Moderate upward slope, stabilizing at ~0.4. | PC128 and PC512 track closely with PC32. | | **PC128** | **PC128 (Purple)**: Moderate upward slope, stabilizing at ~0.3. | PC32 and PC512 show similar moderate positive trends. | | **PC512** | **PC512 (Dotted Purple)**: Initial spike, then stabilizes near 0.0. | High noise/variance across all series in this target. | --- ## 3. Region B: Heatmap Data Extraction **Title:** Control effect (d): layer 32 **X-Axis (Affected axis):** LR, PC1, PC2, PC4, PC8, PC32, PC128, PC512 **Y-Axis (Target axis):** LR, PC1, PC2, PC4, PC8, PC32, PC128, PC512 **Color Scale:** Blue (-2) to White (0) to Red (2+). ### Data Table (Reconstructed) The diagonal (Target = Affected) is highlighted with bold black borders, representing the self-control effect. | Target \ Affected | LR | PC1 | PC2 | PC4 | PC8 | PC32 | PC128 | PC512 | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | **PC512** | -0.25 | -0.23 | -0.15 | 0.19 | -0.17 | -0.19 | -0.06 | **-0.06** | | **PC128** | -0.10 | 0.27 | 0.05 | -0.21 | 0.03 | 0.17 | **0.19** | 0.19 | | **PC32** | -0.14 | 0.87 | 0.06 | -0.23 | 0.32 | **0.06** | 0.16 | 0.16 | | **PC8** | -0.09 | -0.66 | -0.18 | 1.78 | **-0.08** | -0.53 | -0.31 | -0.31 | | **PC4** | -0.29 | 0.24 | 2.55 | **-0.29** | 0.44 | 0.88 | 0.49 | 0.49 | | **PC2** | -0.02 | 2.91 | **1.27** | -0.93 | 0.49 | 0.13 | -0.36 | -0.36 | | **PC1** | 0.03 | **0.09** | -0.40 | 0.49 | 0.31 | 0.21 | 0.41 | 0.41 | | **LR** | **4.47** | -0.45 | -0.19 | 1.03 | -0.01 | 1.05 | 1.34 | 0.60 | --- ## 4. Key Observations and Trends 1. **Diagonal Dominance (Self-Effect):** The strongest control effects are generally found on the diagonal or immediately adjacent to it. The highest single value is **4.47** (Target: LR, Affected: LR). 2. **Off-Diagonal Interactions:** * There is a strong interaction between **Target PC2** and **Affected PC1** (2.91). * There is a strong interaction between **Target PC4** and **Affected PC2** (2.55). * There is a strong interaction between **Target PC8** and **Affected PC4** (1.78). 3. **Negative Effects:** Several blue cells indicate negative control effects, notably **Target PC2 / Affected PC4** (-0.93) and **Target PC8 / Affected PC1** (-0.66). 4. **Convergence:** The line charts indicate that for most axes, the control effect stabilizes after approximately 100-150 examples. 5. **Symmetry:** The matrix is not symmetric, indicating that the control effect of Axis A on Axis B is not the same as Axis B on Axis A. For example, LR on PC1 is 0.03, but PC1 on LR is -0.45.

# Technical Document Extraction: Control Effect Analysis ## Image Description The image contains **eight line graphs** and a **heatmap**, organized in a 2x4 grid of line graphs (top and bottom rows) with a heatmap on the right. Each line graph visualizes the **control effect (d)** across different principal components (PCs) as a function of the number of training examples. The heatmap summarizes pairwise control effects between target and affected axes in layer 32. --- ## Line Graphs Analysis ### General Structure - **X-axis**: Number of examples (# Examples), ranging from 0 to 200. - **Y-axis**: Control effect (d), with values varying between -2 and +2. - **Lines**: Represent individual PCs (PC1–PC512), with shaded regions indicating confidence intervals. - **Legends**: Located on the right side of each graph, mapping colors to PCs. ### Key Trends and Data Points #### Target Axis: LR - **PC1**: Sharp upward trend (d ≈ 0 → 4.47) by ~50 examples, then plateaus. Shaded region widens initially, then stabilizes. - **PC2–PC512**: Gradual upward trends (d ≈ 0 → 2), with minimal variation between PCs. Confidence intervals remain narrow. #### Target Axis: PC1 - **PC1**: Steep decline (d ≈ 1 → -0.5) by ~100 examples, then stabilizes. Shaded region narrows post-decline. - **PC2–PC512**: Slight upward trends (d ≈ 0 → 0.5), with overlapping confidence intervals. #### Target Axis: PC2 - **PC2**: Rapid increase (d ≈ 0 → 2) by ~50 examples, then plateaus. Shaded region widens initially. - **PC1, PC4–PC512**: Stable trends (d ≈ 0 → 0.5), with PC4 showing the steepest rise. #### Target Axis: PC4 - **PC4**: Moderate increase (d ≈ 0 → 2) by ~150 examples. Shaded region remains narrow. - **PC1–PC3, PC8–PC512**: Stable or slightly declining trends (d ≈ 0 → -0.5). #### Target Axis: PC8 - **PC8**: Sharp decline (d ≈ 2 → -1) by ~50 examples, then stabilizes. Shaded region widens initially. - **PC1–PC4, PC32–PC512**: Gradual upward trends (d ≈ 0 → 1), with PC32 showing the steepest rise. #### Target Axis: PC32 - **PC32**: Steady increase (d ≈ 0 → 1) by ~200 examples. Shaded region narrows slightly. - **PC1–PC8, PC128–PC512**: Stable trends (d ≈ 0 → 0.5), with PC128 showing minor fluctuations. #### Target Axis: PC128 - **PC128**: Slight decline (d ≈ 0 → -0.5) by ~100 examples, then stabilizes. Shaded region remains narrow. - **PC1–PC4, PC8–PC32, PC512**: Gradual upward trends (d ≈ 0 → 0.5), with PC4 showing the steepest rise. #### Target Axis: PC512 - **PC512**: Minimal change (d ≈ 0 → 0.5) by ~200 examples. Shaded region remains narrow. - **PC1–PC4, PC8–PC128**: Stable trends (d ≈ 0 → 0.5), with PC1 showing the steepest rise. --- ## Heatmap Analysis ### Structure - **Rows**: Target axes (LR, PC1, PC2, PC4, PC8, PC32, PC128, PC512). - **Columns**: Affected axes (PC1, PC2, PC4, PC8, PC32, PC128, PC512, LR). - **Color Scale**: Red (positive control effect) to blue (negative control effect), with values ranging from -2.91 to 2.55. ### Key Values | Target Axis | PC1 | PC2 | PC4 | PC8 | PC32 | PC128 | PC512 | LR | |-------------|-------|-------|-------|-------|-------|-------|-------|-------| | **LR** | -0.25 | -0.23 | -0.15 | 0.19 | -0.17 | -0.19 | -0.06 | **4.47** | | **PC1** | -0.10 | 0.27 | 0.05 | -0.21 | 0.03 | 0.17 | 0.19 | -0.45 | | **PC2** | -0.14 | 0.87 | 0.06 | -0.23 | 0.32 | 0.06 | 0.16 | 0.03 | | **PC4** | -0.09 | -0.66 | 1.78 | -0.08 | -0.53 | -0.31 | -0.29 | -0.19 | | **PC8** | -0.29 | 0.24 | -0.29 | 0.44 | 0.88 | 0.49 | 0.24 | 1.27 | | **PC32** | -0.02 | 2.91 | 1.27 | -0.93 | 0.49 | 0.13 | 0.41 | 0.09 | | **PC128** | 0.03 | 0.09 | -0.40 | 0.49 | 1.03 | 1.34 | 0.60 | -0.19 | | **PC512** | -0.45 | -0.19 | 1.03 | -0.08 | 1.05 | 1.34 | 0.60 | 0.41 | ### Observations - **Strongest Positive Effects**: - PC32 → PC2 (2.91) - PC32 → PC4 (1.27) - PC512 → PC2 (1.03) - **Strongest Negative Effects**: - PC4 → PC2 (-0.66) - PC8 → PC32 (-0.93) - PC128 → PC4 (-0.40) --- ## Legend Cross-Reference - **Color Consistency**: All line graphs and heatmap cells align with the legend (e.g., PC1 = red, PC2 = green, etc.). - **Confidence Intervals**: Shaded regions in line graphs match the legend's color coding for each PC. --- ## Spatial Grounding - **Legend Position**: Right-aligned for all line graphs. - **Heatmap Position**: Rightmost column, spanning all rows. --- ## Conclusion The line graphs reveal dynamic control effects across PCs, with PC1 and PC8 showing the most pronounced trends. The heatmap highlights strong pairwise interactions, particularly involving PC32 and PC2. All data points and trends are consistent with the legend and color coding.