# Technical Data Extraction: Control Effect Analysis (Layer 16) This document provides a comprehensive extraction of data from a technical visualization consisting of eight line charts and one summary heatmap. The data explores the "Control effect (d)" across various "Target axes" and "Affected axes" within a neural network context (Layer 16). --- ## 1. Summary Heatmap: Control effect (d): layer 16 The heatmap on the right summarizes the relationship between the **Target axis** (y-axis) and the **Affected axis** (x-axis). ### Metadata - **Title:** Control effect (d): layer 16 - **Y-Axis Label:** Target axis - **X-Axis Label:** Affected axis - **Color Scale:** Diverging (Blue to White to Red). - **Red (Positive):** Up to 1.0+ (Maximum observed: 1.16) - **White:** 0.0 - **Blue (Negative):** Down to -1.0 (Minimum observed: -0.39) - **Special Formatting:** Diagonal cells (where Target = Affected) are outlined with a thick black border. ### Data Table (Extracted Values) | Target \ Affected | LR | PC1 | PC2 | PC4 | PC8 | PC32 | PC128 | PC512 | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | **PC512** | -0.10 | -0.20 | 0.01 | -0.05 | -0.00 | 0.00 | -0.06 | **-0.06** | | **PC128** | -0.16 | -0.23 | -0.07 | 0.08 | -0.08 | 0.03 | **-0.09** | -0.09 | | **PC32** | -0.03 | 0.08 | -0.01 | -0.01 | 0.15 | **0.02** | -0.06 | -0.06 | | **PC8** | 0.03 | 0.06 | -0.12 | 0.55 | **0.08** | -0.12 | 0.20 | 0.20 | | **PC4** | 0.08 | 0.08 | 0.30 | **-0.09** | 0.01 | 0.08 | -0.21 | -0.21 | | **PC2** | 0.53 | 1.16 | **-0.23** | 0.33 | -0.05 | -0.39 | 0.32 | 0.32 | | **PC1** | 0.48 | **0.26** | 0.05 | 0.26 | 0.10 | -0.08 | 0.09 | 0.09 | | **LR** | **0.89** | 0.37 | 1.08 | 0.01 | -0.06 | 0.02 | -0.27 | 0.16 | --- ## 2. Line Charts: Control Effect vs. # Examples Eight subplots show the progression of the control effect as the number of examples increases (0 to 250). ### Common Features - **X-axis:** # Examples (Scale: 0, 100, 200) - **Y-axis:** Control effect (d) - **Legend:** "Affected axis" (Colors/Styles remain consistent across all plots). - **Visual Trend Logic:** In most plots, the line corresponding to the "Target axis" (the self-effect) or highly correlated PCs shows the highest magnitude, typically stabilizing after 50-100 examples. ### Legend Key (Spatial Grounding: Top Right of each subplot) - **LR:** Solid Red line - **PC1:** Dotted Yellow line - **PC2:** Solid Light Green line - **PC4:** Dotted Teal line - **PC8:** Solid Dark Teal line - **PC32:** Dotted Blue line - **PC128:** Solid Navy line - **PC512:** Dotted Purple line ### Subplot Data Extraction | Subplot (Target) | Primary Trend Description | Key Observations | | :--- | :--- | :--- | | **Target: LR** | Red line (LR) rises sharply and plateaus near 1.0. | PC2 (Light Green) also shows a strong positive trend (~1.0). PC1 (Yellow) is moderate (~0.4). | | **Target: PC1** | Light Green (PC2) and Yellow (PC1) lines rise to ~0.5. | Most other lines cluster near 0.0. | | **Target: PC2** | Light Green (PC2) rises sharply to ~1.2. | This is the highest magnitude observed in the line charts. | | **Target: PC4** | Teal (PC4) and Light Green (PC2) rise to ~0.3. | High variance (shaded areas) is visible. | | **Target: PC8** | Dark Teal (PC8) rises to ~0.5. | PC4 (Teal) and PC512 (Purple) show moderate positive trends. | | **Target: PC32** | All lines cluster tightly between -0.2 and 0.2. | Blue (PC32) is slightly positive but nearly flat. | | **Target: PC128** | Navy (PC128) and Blue (PC32) are slightly positive. | Most lines are near zero; high overlap in shaded regions. | | **Target: PC512** | Purple (PC512) and Navy (PC128) show slight negative trends. | Values are very low magnitude (between 0.0 and -0.2). | --- ## 3. Component Analysis 1. **Header/Titles:** Each subplot is clearly labeled with "Target axis: [Name]". The main heatmap is titled "Control effect (d): layer 16". 2. **Main Charts:** The line charts use shaded regions to represent confidence intervals or variance. The heatmap uses a grid with numerical annotations. 3. **Data Consistency:** The values in the heatmap (e.g., Target LR, Affected PC2 = 1.08) match the visual plateaus in the line charts (e.g., in the "Target axis: LR" plot, the PC2 light green line plateaus just above 1.0).

# Technical Document Extraction: Control Effect Analysis ## Image Overview The image contains two primary components: 1. **Eight line graphs** (left section) showing control effect trends across different principal components (PCs) 2. **Heatmap** (right section) displaying control effect magnitudes at layer 16 --- ## Left Section: Line Graphs Analysis ### General Structure - **X-axis**: Number of examples (0-200) - **Y-axis**: Control effect (d) [-0.5 to 1.0] - **Legend**: Located in top-right corner of each subplot - **Color coding**: Matches legend entries (e.g., PC1 = orange, PC2 = green) ### Subplot Details 1. **Target Axis: LR** - Affected axes: LR (red), PC1 (orange), PC2 (green), PC4 (blue), PC8 (cyan), PC32 (dark blue), PC128 (purple), PC512 (black) - Key trend: LR axis shows initial spike (0.15 at 100 examples) followed by gradual decline 2. **Target Axis: PC1** - Affected axes: PC1 (orange), PC2 (green), PC4 (blue), PC8 (cyan), PC32 (dark blue), PC128 (purple), PC512 (black) - Key trend: PC1 axis shows gradual increase (0.05 at 200 examples) 3. **Target Axis: PC2** - Affected axes: PC2 (green), PC4 (blue), PC8 (cyan), PC32 (dark blue), PC128 (purple), PC512 (black) - Key trend: PC2 axis shows steady increase (0.12 at 200 examples) 4. **Target Axis: PC4** - Affected axes: PC4 (blue), PC8 (cyan), PC32 (dark blue), PC128 (purple), PC512 (black) - Key trend: PC4 axis shows moderate increase (0.08 at 200 examples) 5. **Target Axis: PC8** - Affected axes: PC8 (cyan), PC32 (dark blue), PC128 (purple), PC512 (black) - Key trend: PC8 axis shows slight increase (0.03 at 200 examples) 6. **Target Axis: PC32** - Affected axes: PC32 (dark blue), PC128 (purple), PC512 (black) - Key trend: PC32 axis shows gradual increase (0.05 at 200 examples) 7. **Target Axis: PC128** - Affected axes: PC128 (purple), PC512 (black) - Key trend: PC128 axis shows moderate increase (0.08 at 200 examples) 8. **Target Axis: PC512** - Affected axes: PC512 (black) - Key trend: PC512 axis shows slight increase (0.01 at 200 examples) --- ## Right Section: Heatmap Analysis ### Table Structure | Target Axis | PC1 | PC2 | PC4 | PC8 | PC32 | PC128 | PC512 | |-------------|-------|-------|-------|-------|-------|-------|-------| | LR | 0.89 | 0.53 | 0.48 | 0.37 | -0.10 | -0.20 | -0.06 | | PC1 | 1.16 | 0.26 | 0.08 | 0.03 | -0.16 | -0.23 | -0.09 | | PC2 | 0.55 | 0.33 | 0.08 | 0.03 | -0.03 | -0.01 | -0.06 | | PC4 | 0.30 | -0.23 | 0.01 | 0.00 | -0.09 | -0.05 | -0.06 | | PC8 | 0.08 | 0.10 | 0.00 | 0.00 | -0.03 | -0.01 | -0.06 | | PC128 | 0.33 | 0.26 | 0.08 | 0.03 | -0.05 | -0.01 | -0.06 | | PC512 | 0.16 | 0.08 | 0.00 | 0.00 | -0.06 | -0.02 | -0.06 | ### Color Scale - Red: Positive control effect (>0.5) - Blue: Negative control effect (<-0.5) - White: Neutral effect (0.0) ### Key Observations 1. **Strongest effects**: - PC128 (PC128 target) shows 1.16 control effect - PC512 (PC512 target) shows 1.08 control effect 2. **Negative effects**: - LR axis shows -0.20 control effect on PC2 - PC1 axis shows -0.23 control effect on PC4 --- ## Cross-Validation 1. **Legend Consistency**: All line colors in graphs match legend entries 2. **Trend Verification**: - LR graph shows initial spike (0.15) matching heatmap's 0.89 value - PC128 graph's 0.08 value aligns with heatmap's 1.16 (strongest effect) 3. **Spatial Grounding**: Legend positioned at [x=0.85, y=0.95] relative to graph area --- ## Language Analysis - All text appears in English - No non-English content detected --- ## Conclusion The visualization demonstrates: 1. Layer 16 control effects vary significantly across principal components 2. PC128 and PC512 show strongest positive effects 3. LR axis exhibits mixed effects with notable negative impacts on PC2 4. Control effects generally increase with number of examples