# Technical Data Extraction: Control Effect Analysis (Layer 1)
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" relative to the number of training examples.
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## 1. Component Isolation
The image is divided into two primary sections:
- **Left Section (Line Charts):** Eight individual plots showing the progression of control effects as the number of examples increases (from 0 to 250).
- **Right Section (Heatmap):** A summary matrix titled "Control effect (d): layer 1" showing the final or aggregate effect between target and affected axes.
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## 2. Line Charts Analysis (Progression Data)
Each chart represents a specific **Target axis**. The x-axis is **# Examples** (0 to 250), and the y-axis is **Control effect (d)**.
### Shared Legend (Affected axis)
The following categories are tracked in each plot, distinguished by color and line style:
- **LR:** Solid Red line
- **PC1:** Dotted Yellow line
- **PC2:** Solid Light Green line
- **PC4:** Solid Teal/Green line
- **PC8:** Solid Dark Teal line
- **PC32:** Dotted Blue-Grey line
- **PC128:** Dotted Purple line
- **PC512:** Dotted Dark Purple line
### Individual Plot Trends
| Target Axis | Primary Trend Observation | Key Data Behavior |
| :--- | :--- | :--- |
| **LR** | Strong positive divergence for LR. | The red line (LR) climbs sharply to ~1.5. Other PC axes remain below 1.0, with PC1 (yellow) trending downward toward -1.0. |
| **PC1** | High variance, PC1 dominates. | PC1 (yellow) trends upward toward ~1.5. Most other axes cluster between -0.5 and 0.5. |
| **PC2** | Moderate positive trend for PC2. | PC2 (light green) rises to ~0.7. PC4 and PC8 follow closely. PC1 (yellow) shows a slight negative trend. |
| **PC4** | PC4 shows the strongest positive effect. | PC4 (teal) rises to ~0.6. Other axes remain relatively flat or slightly positive around 0.2. |
| **PC8** | PC8 and PC1 show positive trends. | PC8 (dark teal) and PC1 (yellow) both trend upward toward 0.5. |
| **PC32** | Low magnitude, high overlap. | Most lines cluster near 0.0. PC32 (blue-grey) shows a slight peak then decline. |
| **PC128** | PC128 shows a late positive trend. | PC128 (purple) rises slightly above 0.2 after 100 examples. |
| **PC512** | PC512 shows a late positive trend. | PC512 (dark purple) rises to ~0.2. PC1 (yellow) also shows a positive trend here. |
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## 3. Heatmap Analysis (Summary Matrix)
**Title:** Control effect (d): layer 1
**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:** Red (Positive, up to >1), White (Zero), Blue (Negative, down to -1).
### Data Table Reconstruction
The diagonal (Target axis = Affected axis) is highlighted with thick black borders, representing the self-control effect.
| Target \ Affected | LR | PC1 | PC2 | PC4 | PC8 | PC32 | PC128 | PC512 |
| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| **PC512** | 0.30 | -0.03 | 0.22 | 0.03 | 0.28 | -0.29 | 0.11 | **[0.11]** |
| **PC128** | 0.42 | -0.10 | 0.06 | -0.34 | 0.12 | -0.08 | **[-0.01]** | - |
| **PC32** | -0.13 | 0.31 | 0.05 | -0.13 | -0.10 | **[-0.03]** | -0.33 | - |
| **PC8** | 0.63 | -0.19 | 0.38 | 0.34 | **[0.38]** | -0.22 | 0.18 | - |
| **PC4** | 0.65 | -0.19 | 0.55 | **[-0.19]** | 0.22 | 0.09 | 0.05 | - |
| **PC2** | 0.73 | -0.37 | **[0.17]** | -0.38 | -0.34 | -0.01 | 0.38 | - |
| **PC1** | 1.46 | **[-0.99]** | -0.07 | 0.07 | -0.50 | 0.10 | 0.53 | - |
| **LR** | **[1.58]** | -1.08 | 0.96 | -0.29 | 0.33 | 0.58 | -0.55 | -0.57 |
*(Note: Values in brackets [ ] denote the diagonal/self-influence cells.)*
### Key Observations from Heatmap:
1. **Strongest Positive Effect:** The interaction of Target: LR on Affected: LR (1.58, deep red).
2. **Strongest Negative Effect:** The interaction of Target: LR on Affected: PC1 (-1.08, deep blue).
3. **Cross-Talk:** Target PC1 has a very strong positive effect on Affected LR (1.46), suggesting a high degree of coupling between these two axes.
4. **Diminishing Effects:** As the PC index increases (moving toward PC512), the absolute values in the heatmap generally decrease, indicated by lighter colors (closer to white/zero).
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## 4. Technical Metadata
* **Language:** English
* **Metric:** Control effect (d), likely Cohen's d or a similar standardized effect size.
* **Layer:** Data specifically pertains to "layer 1" of the model/system under study.
