# Technical Document Analysis of Search Strategy Diagrams
## Key
- **Apply Verifier**: Dashed box (→)
- **Full Solution**: Orange circle (●)
- **Intermediate Solution Step**: Light orange circle (○)
- **Selected by Verifier**: Green circle (●)
- **Rejected by Verifier**: Red circle (○)
---
## Diagram 1: Best-of-N Search
### Structure
- **Question Node**: Central blue box labeled "Question"
- **Solution Nodes**: Four nodes at the bottom (left to right):
- Red ○ (Rejected)
- Green ● (Selected)
- Red ○ (Rejected)
- Red ○ (Rejected)
- **Connections**:
- Red wavy lines from Question to all solution nodes
- Green wavy line from Question to the second solution node
### Textual Elements
- **Instruction**: "Select the best final answer using the verifier"
- **Process Description**:
- "Generate N full solutions, applying the verifier to each solution with the verifier"
---
## Diagram 2: Beam Search
### Structure
- **Question Node**: Central blue box labeled "Question"
- **Solution Grid**: 3x4 grid of nodes (12 total):
- **Rows**:
- Row 1: ○ ○ ○ ○
- Row 2: ○ ● ○ ○
- Row 3: ● ○ ● ○
- **Colors**:
- Green ● (Selected)
- Red ○ (Rejected)
- Light orange ○ (Intermediate)
- **Connections**:
- Red lines from Question to all grid nodes
- Green lines between selected nodes (e.g., Row 2, Column 2 → Row 3, Column 1)
### Textual Elements
- **Instruction**: "Select the best final answer using the verifier"
- **Process Description**:
- "Select the top K samples from the previous step using the pruner"
- "Beam search, but at each step, the solution is pruned using the verifier"
---
## Diagram 3: Lookahead Search
### Structure
- **Question Node**: Central blue box labeled "Question"
- **Solution Nodes**:
- **Top Row**: Four nodes (left to right):
- Orange ○ (Intermediate)
- Orange ○ (Intermediate)
- Orange ○ (Intermediate)
- Orange ○ (Intermediate)
- **Middle Row**: Two nodes (left to right):
- Green ● (Selected)
- Green ● (Selected)
- **Bottom Row**: Four nodes (left to right):
- Orange ○ (Intermediate)
- Orange ○ (Intermediate)
- Orange ○ (Intermediate)
- Orange ○ (Intermediate)
- **Connections**:
- Red lines from Question to all top-row nodes
- Green lines from middle-row nodes to bottom-row nodes
- Dashed red lines indicating rejected paths (e.g., top-row nodes → middle-row nodes)
### Textual Elements
- **Instruction**: "Continue search from the top K options"
- **Process Description**:
- "Beam search, but at each step, the solution is pruned using the verifier"
- "Rejected by verifier" (dashed red lines)
- "Propagate back to top K options" (dashed black lines)
---
## Spatial Grounding & Color Verification
- **Legend Position**: Bottom of the image (x-axis: 0–100%, y-axis: 90–100%)
- **Color Consistency**:
- Green ● matches "Selected by Verifier"
- Red ○ matches "Rejected by Verifier"
- Orange ○ matches "Intermediate Solution Step"
---
## Trend Verification
- **Best-of-N**:
- Single green line indicates one solution selected; others rejected.
- **Beam Search**:
- Grid shows iterative pruning (green lines connect selected nodes across rows).
- **Lookahead Search**:
- Branching paths with pruning (dashed red lines) and propagation (dashed black lines).
---
## Component Isolation
1. **Header**: Question node (blue box) in all diagrams.
2. **Main Chart**:
- Best-of-N: Linear flow with verifier selection.
- Beam Search: Grid-based iterative pruning.
- Lookahead Search: Branching with backtracking.
3. **Footer**: Key and process descriptions.
---
## Conclusion
The diagrams illustrate three search strategies for question-answering systems:
1. **Best-of-N**: Parallel solution generation with final selection.
2. **Beam Search**: Iterative pruning of top candidates.
3. **Lookahead Search**: Branching with verifier-guided backtracking.
All strategies rely on the verifier to distinguish valid solutions, with varying approaches to exploration and pruning.
