# 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 heatmap. The data explores the "Control effect (d)" across various "Target axes" and "Affected axes" within a neural network context (Layer 16). --- ## 1. Component Isolation The image is divided into two primary sections: - **Left Section (Grid of 8 Line Charts):** Shows the progression of the control effect as the number of examples increases (0 to 250). - **Right Section (Heatmap):** Summarizes the final control effect values in a matrix format. --- ## 2. Line Chart Series Analysis (Left Section) Each chart represents a specific **Target axis**. The x-axis is labeled **"# Examples"** (ranging 0–250) and the y-axis is **"Control effect (d)"**. Each line represents an **"Affected axis"**. ### Common Legend (Affected axis) The following categories are used across all line charts: - **LR:** Solid Red line - **PC1:** Yellow (Solid or Dotted) - **PC2:** Light Green (Solid or Dotted) - **PC4:** Medium Green (Solid or Dotted) - **PC8:** Teal (Solid or Dotted) - **PC32:** Blue (Solid or Dotted) - **PC128:** Dark Purple (Solid or Dotted) - **PC512:** Deep Indigo (Solid or Dotted) *Note: In each chart, the line corresponding to the Target axis is typically solid and thicker, while others are dotted.* ### Individual Chart Trends 1. **Target axis: LR** * **Trend:** The LR line (Red) shows a sharp logarithmic increase, plateauing around $d \approx 5.5$. * **Secondary Effects:** PC2 (Light Green dotted) shows a slight positive trend ($d \approx 3.0$). Other axes remain near zero. 2. **Target axis: PC1** * **Trend:** PC1 (Yellow) increases steadily, peaking near $d \approx 2.0$ before a slight decline. * **Secondary Effects:** PC2 and PC4 show minor positive correlations. 3. **Target axis: PC2** * **Trend:** PC2 (Light Green) rises sharply and plateaus at $d \approx 4.5$. * **Secondary Effects:** LR (Red dotted) shows a significant secondary effect ($d \approx 3.0$). 4. **Target axis: PC4** * **Trend:** PC4 (Medium Green) rises and plateaus at $d \approx 1.5$. 5. **Target axis: PC8** * **Trend:** PC8 (Teal) rises and plateaus at $d \approx 2.0$. 6. **Target axis: PC32** * **Trend:** PC32 (Blue) shows a low-magnitude peak ($d < 0.5$) and remains relatively flat. 7. **Target axis: PC128** * **Trend:** PC128 (Dark Purple) shows high variance with a slight upward trend toward $d \approx 0.3$. 8. **Target axis: PC512** * **Trend:** PC512 (Deep Indigo) shows a small initial spike followed by a decline toward zero. --- ## 3. Heatmap Data Extraction (Right Section) **Title:** Control effect (d): layer 16 **Spatial Grounding:** The legend indicates a color scale from -4 (Blue) to 0 (White) to +4 (Red). **Structure:** A matrix where rows are **Target axis** and columns are **Affected axis**. Values in the diagonal (top-left to bottom-right orientation in this specific plot) are highlighted with thick black borders. ### Data Table (Reconstructed) | Target \ Affected | LR | PC1 | PC2 | PC4 | PC8 | PC32 | PC128 | PC512 | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | **PC512** | -0.38 | -0.56 | -0.23 | -0.24 | -0.11 | 0.10 | -0.04 | **N/A** | | **PC128** | 0.38 | 0.34 | -0.28 | -0.18 | -0.23 | -0.08 | 0.33 | | | **PC32** | -0.36 | 0.53 | 0.11 | 0.14 | 0.23 | -0.06 | -0.08 | | | **PC8** | -0.07 | 0.24 | -0.22 | **1.90** | 0.17 | 0.00 | 0.12 | | | **PC4** | 0.12 | 0.14 | **1.36** | -0.00 | -0.46 | -0.23 | -0.52 | | | **PC2** | 1.22 | **4.27** | -0.61 | 1.24 | 0.08 | -0.33 | 0.32 | | | **PC1** | 1.23 | 0.98 | -0.05 | 0.38 | 0.04 | -0.40 | 0.38 | | | **LR** | **5.30** | 0.45 | 3.04 | 0.40 | 0.03 | -0.16 | -0.14 | -0.18 | *Note: The heatmap values are transcribed directly from the cells. The bolded values represent the highest positive control effects (Red cells).* --- ## 4. Key Findings and Trends 1. **Self-Control Dominance:** The highest values are generally found on the diagonal (e.g., LR on LR = 5.30, PC2 on PC1 = 4.27). 2. **Cross-Axis Interference:** There is a strong cross-effect between **LR** and **PC2** (3.04) and **PC2** and **PC1** (4.27). 3. **Diminishing Effect:** As the PC index increases (PC32, PC128, PC512), the control effect (d) significantly decreases, with values approaching zero or becoming slightly negative (blue-tinted cells). 4. **Consistency:** The line charts and the heatmap are consistent; for example, the "Target axis: LR" line chart shows a plateau at ~5.5, which matches the heatmap value of 5.30.

# Technical Document Extraction: Control Effect Analysis ## Line Graphs (Left Section) Eight line graphs depict control effect (d) across different target and affected axes. Each graph includes: - **X-axis**: `# Examples` (0-200) - **Y-axis**: `Control effect (d)` (range varies by graph) - **Legend**: Located in top-right corner of each graph, listing affected axes with color coding ### Key Observations: 1. **Legend Color Consistency**: - Red = LR - Yellow = PC1 - Green = PC2 - Teal = PC4 - Purple = PC8 - Dark Blue = PC32 - Light Purple = PC128 - Dark Purple = PC512 2. **Graph Trends**: - **LR Target Axis**: Sharp initial decline (5.0 → 0.0) followed by plateau - **PC1 Target Axis**: Gradual decline with significant variance (2.0 → 0.0) - **PC2 Target Axis**: Steep initial rise (0.0 → 4.0) then stabilization - **PC4 Target Axis**: Moderate increase (0.0 → 1.0) with persistent variability - **PC8 Target Axis**: Sustained moderate effect (0.0 → 2.0) - **PC32 Target Axis**: Complex pattern with multiple peaks/troughs - **PC128 Target Axis**: Gradual increase with high variance - **PC512 Target Axis**: Stable baseline with minor fluctuations ## Heatmap (Right Section) Labeled "Control effect (d): layer 16", showing matrix of control effects between target and affected axes. ### Matrix Structure: - **Rows (Target Axes)**: LR, PC1, PC2, PC4, PC8, PC32, PC128, PC512 - **Columns (Affected Axes)**: PC1, PC2, PC4, PC8, PC32, PC128, PC512 - **Color Scale**: Blue (-4) to Red (+4) ### Key Values: | Target\Affected | PC1 | PC2 | PC4 | PC8 | PC32 | PC128 | PC512 | |-----------------|--------|--------|--------|--------|--------|--------|--------| | **LR** | -0.38 | -0.56 | -0.23 | -0.11 | 0.10 | -0.04 | | | **PC1** | 0.38 | 0.34 | -0.28 | -0.18 | -0.23 | -0.08 | 0.33 | | **PC2** | -0.36 | 0.53 | 0.11 | 0.14 | 0.23 | -0.06 | -0.08 | | **PC4** | -0.07 | 0.24 | -0.22 | 1.90 | 0.17 | 0.00 | 0.12 | | **PC8** | 1.22 | 4.27 | -0.61 | 1.24 | 0.08 | -0.33 | 0.32 | | **PC32** | 1.23 | 0.98 | -0.05 | 0.38 | 0.04 | -0.40 | 0.38 | | **PC128** | 5.30 | 3.04 | 0.40 | 0.03 | -0.16 | -0.14 | -0.18 | ### Notable Patterns: - **High Positive Effects**: - PC8→PC2 (4.27) - LR→PC128 (5.30) - **Strong Negative Effects**: - PC1→PC2 (-0.56) - PC2→PC4 (-0.22) - **Diagonal Dominance**: Strongest effects along main diagonal (target=affected) ## Spatial Grounding - **Legend Position**: Top-right corner of each line graph - **Heatmap Coordinates**: - Rows: Top to bottom (LR → PC512) - Columns: Left to right (PC1 → PC512) ## Language Note All text appears in English. No non-English content detected.