Graph Of Thoughts

Problem → Step 1 → Step 2 → Step 3 → Solution
(Single linear path, fast but limited)

            Problem
           /   |   \
          A    B    C    (independent branches)
         / \   |   / \
        A1 A2 B1 C1 C2  (no cross-branch combination)
         |
      Best A1

            Problem
           /   |   \
          A ─── B ─── C    (branches can connect)
         / \   │   / \
        A1─┴──B1──┴─C1     (thoughts combine)
          \   │   /
           └──↓──┘
            Final       (aggregation/synthesis)

class GraphOfThoughts:
    """Graph-based reasoning with thought combination."""
    
    def __init__(self, num_paths=5, max_iterations=3, quality_threshold=0.85):
        self.num_paths = num_paths
        self.max_iterations = max_iterations
        self.quality_threshold = quality_threshold
        self.thought_graph = ThoughtGraph()
        self.evaluator = PathEvaluator()
    
    def reason(self, problem):
        """Main reasoning entry point."""
        
        # Phase 1: Generate multiple thought paths
        paths = self.generate_thought_paths(problem, num_paths=self.num_paths)
        
        # Phase 2: Evaluate each path independently
        evaluations = [self.evaluate_path(path) for path in paths]
        
        # Phase 3: Identify synergies between paths
        synergies = self.identify_synergies(paths, evaluations)
        
        # Phase 4: Combine promising thoughts
        combined = self.combine_thoughts(paths, synergies)
        
        # Phase 5: Evaluate combinations
        combined_evals = [self.evaluate_path(c) for c in combined]
        
        # Phase 6: Iterate with feedback loops
        refined = self.iterate_with_feedback(combined, combined_evals)
        
        # Phase 7: Aggregate final solution
        result = self.aggregate_solution(refined)
        
        # Phase 8: Execute and verify
        verified_result = self.execute_and_verify(result)
        
        return verified_result
    
    def generate_thought_paths(self, problem, num_paths):
        """Generate N diverse solution paths."""
        paths = []
        for i in range(num_paths):
            path = self.generate_diverse_path(problem, paths)
            paths.append(path)
        return paths
    
    def evaluate_path(self, path):
        """Score a thought path on multiple dimensions."""
        return {
            'feasibility': self.score_feasibility(path),
            'quality': self.score_quality(path),
            'novelty': self.score_novelty(path),
            'coverage': self.score_coverage(path),
            'confidence': self.calculate_confidence(path)
        }
    
    def identify_synergies(self, paths, evaluations):
        """Find complementary insights across paths."""
        synergies = []
        for i, path_a in enumerate(paths):
            for j, path_b in enumerate(paths):
                if i < j:
                    synergy = self.check_synergy(path_a, path_b)
                    if synergy['score'] > 0.6:
                        synergies.append(synergy)
        return synergies
    
    def combine_thoughts(self, paths, synergies):
        """Create hybrid thoughts from synergistic pairs."""
        combined = []
        for synergy in sorted(synergies, key=lambda s: s['score'], reverse=True):
            hybrid = self.create_hybrid(
                paths[synergy['path_a']], 
                paths[synergy['path_b']],
                synergy['combination_strategy']
            )
            combined.append(hybrid)
        return combined
    
    def iterate_with_feedback(self, thoughts, evaluations):
        """Refine through feedback loops."""
        refined = thoughts.copy()
        for iteration in range(self.max_iterations):
            # Identify weaknesses
            critiques = [self.critique(t, e) for t, e in zip(thoughts, evaluations)]
            
            # Generate improvements
            improvements = [self.improve(t, c) for t, c in zip(thoughts, critiques)]
            
            # Re-evaluate
            new_evals = [self.evaluate_path(imp) for imp in improvements]
            
            # Keep improvements that increased quality
            for imp, old_eval, new_eval in zip(improvements, evaluations, new_evals):
                if new_eval['quality'] > old_eval['quality']:
                    refined.append(imp)
            
            # Check if threshold met
            if max(new_evals, key=lambda e: e['quality'])['quality'] >= self.quality_threshold:
                break
                
        return refined
    
    def aggregate_solution(self, thoughts):
        """Synthesize final solution from best thoughts."""
        # Extract key insights from each thought
        insights = [self.extract_insights(t) for t in thoughts]
        
        # Find common patterns
        patterns = self.find_patterns(insights)
        
        # Synthesize unified solution
        solution = self.synthesize(patterns, insights)
        
        return solution
    
    def execute_and_verify(self, solution):
        """Execute solution and verify results."""
        result = self.execute(solution)
        verification = self.verify(result)
        
        if not verification['passed']:
            # Backtrack and try alternative
            return self.backtrack(solution, verification['issues'])
        
        return {
            'solution': solution,
            'result': result,
            'confidence': verification['confidence'],
            'verification': verification
        }

Problem: [Complex problem]

Path A: [Conservative approach]
  - Uses proven methods
  - Lower risk, moderate reward
  
Path B: [Innovative approach]
  - Novel technique
  - Higher risk, potentially higher reward
  
Path C: [Hybrid approach]
  - Combines elements from multiple domains
  - Balanced risk/reward
  
Path D: [Minimal approach]
  - Simplest possible solution
  - Low cost, may miss edge cases
  
Path E: [Comprehensive approach]
  - Addresses all aspects
  - Higher cost, thorough coverage

synergy_analysis:
  - pair: [A, B]
    synergy_type: complementary
    score: 0.85
    reasoning: "A addresses speed, B addresses accuracy"
    combination_potential: high
    
  - pair: [A, C]
    synergy_type: redundant
    score: 0.30
    reasoning: "Both focus on same dimension"
    combination_potential: low
    
  - pair: [B, D]
    synergy_type: enhancing
    score: 0.72
    reasoning: "B's innovation + D's simplicity"
    combination_potential: medium

Combination Strategy 1: Best-of-Both
├── From Path A: Performance optimization
├── From Path B: Error handling approach
└── Result: Fast + Robust solution

Combination Strategy 2: Layered
├── Base Layer: Path D (minimal viable)
├── Enhancement Layer: Path B (innovation)
└── Result: Solid foundation + innovation

Combination Strategy 3: Parallel
├── Track 1: Path A for common cases
├── Track 2: Path B for edge cases
└── Result: Comprehensive coverage

Iteration 1:
  Input: Initial combined thought
  Critique: "Missing edge case X"
  Improvement: Add edge case handling
  Score Delta: +0.15

Iteration 2:
  Input: Improved thought
  Critique: "Performance could be better"
  Improvement: Add caching layer
  Score Delta: +0.10

Iteration 3:
  Input: Further improved
  Critique: None significant
  Improvement: Minor polish
  Score Delta: +0.02

Converged at iteration 3 (diminishing returns)

Insights Extracted:
├── From A: "Caching reduces load by 60%"
├── From B: "Async processing improves UX"
├── From C: "Rate limiting prevents overload"
└── From D: "Simple API is more usable"

Patterns Found:
├── Performance + UX focus
├── Prevention over cure
└── Simplicity as principle

Synthesized Solution:
"Implement async API with intelligent caching,
 rate limiting for protection, and minimal
 endpoint design for simplicity."

Confidence: 87%

thought_graph:
  nodes:
    - id: T0
      type: problem
      content: "How to optimize system performance?"
      
    - id: T1
      type: thought
      content: "Add caching layer"
      parent: T0
      evaluation:
        feasibility: 9
        quality: 7
        score: 8.0
        
    - id: T2
      type: thought
      content: "Optimize database queries"
      parent: T0
      evaluation:
        feasibility: 8
        quality: 8
        score: 8.0
        
    - id: T3
      type: combined
      content: "Caching + Query optimization"
      combines: [T1, T2]
      synergy_score: 0.85
      evaluation:
        feasibility: 8
        quality: 9
        score: 8.5
        
    - id: T4
      type: critique
      content: "T3 doesn't handle cache invalidation"
      critiques: T3
      
    - id: T5
      type: refined
      content: "T3 + Smart cache invalidation"
      refines: T3
      incorporates: T4
      evaluation:
        feasibility: 8
        quality: 9.5
        score: 8.8
        
    - id: T6
      type: solution
      content: "Final architecture with caching, query optimization, and smart invalidation"
      aggregates: [T5]
      confidence: 87%

  edges:
    - from: T0
      to: [T1, T2]
      type: generates
      
    - from: T1
      to: T3
      type: combines
      
    - from: T2
      to: T3
      type: combines
      
    - from: T3
      to: T4
      type: critiques
      
    - from: T3
      to: T5
      type: refines
      
    - from: T4
      to: T5
      type: incorporates
      
    - from: T5
      to: T6
      type: aggregates

## GoT Session: [Problem Name]

**Problem**: [Clear problem statement]
**Context**: [Background information]
**Constraints**: [Any limitations]
**Success Criteria**: [What defines success]

---

### Phase 1: Generate Paths (N=5)

| Path | Approach | Key Feature | Initial Score |
|------|----------|-------------|---------------|
| A | [Conservative] | Proven method | 7.2 |
| B | [Innovative] | Novel technique | 6.8 |
| C | [Hybrid] | Cross-domain | 7.5 |
| D | [Minimal] | Simplest viable | 6.5 |
| E | [Comprehensive] | Full coverage | 7.0 |

---

### Phase 2: Evaluate Paths

#### Path A Evaluation
- Feasibility: 9/10 (High confidence - proven approach)
- Quality: 7/10 (Medium confidence - standard result)
- Novelty: 5/10 (Low - common approach)
- Coverage: 8/10 (High - addresses most cases)
- Efficiency: 8/10 (High - optimized)
- **Total Score**: 7.4/10
- **Confidence**: 82%

#### Path B Evaluation
- Feasibility: 6/10 (Medium - unproven)
- Quality: 9/10 (Medium confidence - potential high)
- Novelty: 9/10 (High - innovative)
- Coverage: 7/10 (Medium - may miss some)
- Efficiency: 6/10 (Medium - unknown)
- **Total Score**: 7.4/10
- **Confidence**: 65%

[... continue for all paths ...]

---

### Phase 3: Identify Synergies

| Pair | Synergy Type | Score | Combination Potential |
|------|--------------|-------|----------------------|
| A + B | Complementary | 0.88 | HIGH - Proven + Innovative |
| A + C | Overlapping | 0.45 | LOW - Similar approaches |
| B + D | Enhancing | 0.72 | MEDIUM - Novel + Simple |
| C + E | Complementary | 0.81 | HIGH - Hybrid + Comprehensive |

**Top Synergies to Combine**:
1. A + B: Reliability + Innovation
2. C + E: Hybrid approach + Full coverage

---

### Phase 4: Combine Thoughts

#### Combination 1: A + B

#### Combination 2: C + E

---

### Phase 5: Iterate with Feedback

#### Iteration 1
**Input**: Combination 1 (Smart caching)
**Critique**: "What about cache invalidation?"
**Improvement**: Add event-based invalidation
**New Score**: 8.8/10

#### Iteration 2
**Input**: Improved C1
**Critique**: "Memory usage could spike"
**Improvement**: Add LRU eviction policy
**New Score**: 9.0/10

#### Iteration 3
**Input**: Further improved
**Critique**: None significant
**Improvement**: Minor polish
**New Score**: 9.1/10

**Converged**: Diminishing returns after iteration 3

---

### Phase 6: Aggregate Final Solution

**Key Insights from All Paths**:
- Caching dramatically improves performance (A, C)
- Predictive loading reduces latency (B)
- Error handling prevents cascading failures (E)
- Simplicity improves maintainability (D)

**Patterns Identified**:
1. Performance through caching + prediction
2. Reliability through error handling
3. Maintainability through simplicity

**Synthesized Solution**:

**Confidence**: 87%

---

### Phase 7: Verification

**Verification Checklist**:
- [ ] Addresses original problem
- [ ] Meets success criteria
- [ ] Within constraints
- [ ] No major gaps identified
- [ ] Confidence > 80%

**Result**: ✅ PASSED

---

### Summary

| Metric | Value |
|--------|-------|
| Paths Generated | 5 |
| Combinations Created | 2 |
| Feedback Iterations | 3 |
| Final Score | 9.1/10 |
| Confidence | 87% |
| Improvement over best individual | +1.9 points |

**Selected Solution**: [Final synthesized solution]

Use ToT for initial exploration
Convert to GoT when synergies detected
Combine best of both structures

Run GoT multiple times
Vote on synthesized solutions
Higher confidence through consensus

When GoT solution fails:
1. Add failure as critique node
2. Generate recovery thoughts
3. Combine with original solution
4. Re-aggregate

Use self-criticism as feedback loop:
1. Generate GoT solution
2. Apply 7-step criticism
3. Add critiques as nodes
4. Refine and re-aggregate

Meta-reasoning decides:
- Should I use GoT or ToT?
- How many paths to generate?
- How many iterations?
- When to stop refining?

## GoT: API Architecture Design

**Problem**: Design API architecture for high-traffic service

### Generated Paths

| Path | Approach | Score |
|------|----------|-------|
| A | REST with caching | 7.5 |
| B | GraphQL with dataloader | 7.2 |
| C | gRPC for internal, REST for external | 8.0 |
| D | Event-driven with CQRS | 6.8 |
| E | Simple REST, optimize later | 6.5 |

### Top Synergies

**A + C**: REST caching + gRPC internal
- Score: 8.7
- Rationale: Best of both protocols

**B + D**: GraphQL + Event sourcing
- Score: 7.8
- Rationale: Real-time + flexible queries

### Combination: A + C (Selected)

### Feedback Loop

**Critique**: "Caching strategy unclear for gRPC"
**Improvement**: Add gRPC response caching
**New Score**: 9.0

### Final Solution

Hybrid architecture:
- REST for external consumers (caching)
- gRPC for internal services (performance)
- Unified API Gateway
- Smart caching at both layers

**Confidence**: 85%

## GoT: Search Algorithm Optimization

**Problem**: Improve search performance for large dataset

### Generated Paths

| Path | Approach | Score |
|------|----------|-------|
| A | Inverted index | 8.2 |
| B | Trie structure | 7.5 |
| C | Vector embeddings | 7.8 |
| D | Simple caching | 6.5 |
| E | Distributed search | 7.0 |

### Synergies Found

**A + C**: Inverted index + Vector similarity
- Score: 9.0
- Hybrid: Keyword + semantic search

**A + D**: Index + Caching
- Score: 8.5
- Fast repeated queries

### Combination: A + C

### Feedback Iterations

1. Critique: "Vector search slow for large scale"
   Fix: Add approximate nearest neighbor
   Score: 9.2

2. Critique: "Memory usage high"
   Fix: Quantize vectors
   Score: 9.3

### Final Solution

Hybrid search with:
- Inverted index (exact)
- ANN vector search (semantic)
- Quantized embeddings (memory)
- Combined ranking

**Confidence**: 88%