tree-of-thoughts

# Tree of Thoughts Reasoning Methodology **Purpose**: Systematic parallel exploration of solution spaces through recursive branching, self-reflection, and rigorous evaluation. Use this methodology when facing complex problems with multiple viable solution paths. ## When to Use Tree of Thoughts **✅ Use ToT when:** - Problem has multiple viable solution approaches (3+ fundamentally different paths) - Need to find optimal solution, not just any solution - Can define clear evaluation criteria - Complexity justifies systematic exploration - Trade-offs exist between competing approaches - Strategic or architectural decisions with long-term impact **❌ Don't use ToT when:** - Problem has obvious single solution path - Time-critical decisions with simple trade-offs - Problem is well-defined with standard solution - Exploratory work where breadth matters more than depth **Examples**: - "Should we use REST, GraphQL, or gRPC?" (3 paths, clear trade-offs) ✅ - "Design distributed caching system balancing latency, consistency, cost" (multi-dimensional) ✅ - "Fix this syntax error" (single path) ❌ - "Research all available databases" (breadth-of-thought better) ❌ --- ## Core Methodology: 5-Step Process ### Step 1: Problem Decomposition (5+ Branches) **Objective**: Identify 5+ fundamentally different approaches to explore **Actions**: 1. Analyze problem to identify key dimensions (technical, organizational, risk, cost, timeline) 2. Brainstorm 5-10 distinct approaches (**not variations** of same approach) 3. Define evaluation criteria from problem constraints 4. Validate diversity: Each branch explores different solution philosophy **Example** (Distributed Caching): ``` Branch A: Write-through consistency (strong consistency, higher latency) Branch B: Eventual consistency (performance, weaker guarantees) Branch C: Hybrid tiered (hot data write-through, cold data eventual) Branch D: Edge-centric (CDN-style, geography-aware) Branch E: Cost-optimized minimal (single region, no replication) ``` **Deliverable**: 5+ distinct approach definitions --- ### Step 2: Parallel Branch Exploration **Objective**: Explore each branch systematically with self-reflection **For each branch**: 1. Analyze approach against problem requirements 2. Consider strengths, weaknesses, trade-offs 3. Identify assumptions and constraints 4. End with self-reflection (see template below) **Self-Reflection Template** (REQUIRED for each branch): ```markdown ## Branch [X]: [Approach Name] [Analysis of this approach: 2-4 paragraphs covering requirements, strengths, weaknesses, trade-offs] ### Self-Reflection - **Confidence**: [0-100]/100 - **Strengths**: [What makes this approach compelling] - **Weaknesses**: [Gaps, assumptions, limitations] - **Trade-offs**: [What you gain vs what you lose] - **Recommendation**: [Continue deeper exploration? Prune? Why?] ``` **Execution Options**: - **With Task tool**: Spawn 5+ parallel tasks for independent exploration - **Without Task tool**: Explore branches sequentially using TodoWrite to track progress - **Hybrid**: Use Task for complex branches, sequential for simple ones **Deliverable**: 5+ explored branches with self-reflections --- ### Step 3: Branch Evaluation (Scoring) **Objective**: Systematically evaluate all branches against criteria **Evaluation Criteria** (100 points total, 5 categories × 20 points): 1. **Novelty** (0-20): Does it explore new solution space vs obvious approaches? - 18-20: Innovative approach, fresh perspective - 12-17: Good approach with some novel elements - 6-11: Standard approach, minor tweaks - 0-5: Obvious/conventional approach 2. **Feasibility** (0-20): Practically implementable with reasonable resources? - 18-20: Proven technology, clear implementation path - 12-17: Feasible with moderate effort/risk - 6-11: Significant technical challenges - 0-5: Impractical or resource-intensive 3. **Completeness** (0-20): Addresses all stated requirements? - 18-20: Covers all requirements comprehensively - 12-17: Covers most requirements, minor gaps - 6-11: Missing key requirements - 0-5: Incomplete solution 4. **Confidence** (0-20): Branch's self-reflection confidence score? - 18-20: High confidence (80-100%) with justification - 12-17: Medium confidence (60-79%) - 6-11: Low confidence (40-59%) - 0-5: Very low confidence (<40%) 5. **Alignment** (0-20): Matches problem constraints and context? - 18-20: Perfect fit for constraints - 12-17: Good fit, minor misalignment - 6-11: Notable misalignment - 0-5: Poor fit for context **Scoring Process**: 1. Review each branch's analysis and self-reflection 2. Score each branch on all 5 criteria (0-20 per criterion) 3. Calculate total score (0-100) for each branch 4. Rank branches by total score 5. Select highest-scoring branch for deeper exploration **Deliverable**: Scored ranking of all branches, winner selected --- ### Step 4: Recursive Depth Exploration (Level 1+) **Objective**: Recursively expand the best branch **Actions**: 1. Take highest-scoring branch from Step 3 2. Decompose that branch into 5+ sub-approaches or refinements 3. Repeat Steps 2-3 for the new level (explore → evaluate → select) 4. Continue recursion until stopping criteria met **Minimum Depth**: 4 levels (Level 0 → 1 → 2 → 3) **Level Transition Example**: ``` Level 0: "Distributed caching system" (5 approaches) → Winner: Branch B (Eventual consistency) Level 1: "Eventual consistency variants" (5 refinements) - B.1: Last-write-wins - B.2: Version vectors - B.3: CRDTs - B.4: Causal consistency - B.5: Session consistency → Winner: Branch B.3 (CRDTs) Level 2: "CRDT implementations" (5 options) - B.3.1: G-Counter - B.3.2: PN-Counter - B.3.3: LWW-Element-Set - B.3.4: OR-Set - B.3.5: RGA (Replicated Growable Array) → Winner: Branch B.3.4 (OR-Set) Level 3: "OR-Set optimizations" (5 variants) [Explore specific implementation strategies] → Winner: Branch B.3.4.2 (Tombstone compaction) ``` **Deliverable**: Recursive tree with minimum 4 levels explored --- ### Step 5: Final Synthesis **Objective**: Synthesize insights into final recommendation **Actions**: 1. **Trace winning path**: Document Level 0 → Level 1 → Level 2 → Level 3+ 2. **Extract key insights**: What was learned at each level? 3. **Document pruned branches**: Why were alternatives discarded? 4. **Calculate confidence**: Final confidence score (see Bayesian formula below) 5. **State assumptions**: What assumptions underpin the recommendation? 6. **Provide recommendation**: Clear, actionable guidance **Synthesis Template**: ```markdown ## Tree of Thoughts Analysis Complete ### Winning Path - **Level 0**: [Chosen approach] (Score: X/100) - **Level 1**: [Refinement] (Score: X/100) - **Level 2**: [Sub-refinement] (Score: X/100) - **Level 3**: [Implementation] (Score: X/100) ### Key Insights 1. [Insight from Level 0] 2. [Insight from Level 1] 3. [Insight from Level 2] 4. [Insight from Level 3] ### Alternatives Considered - [Branch A]: Pruned because [reason] - [Branch C]: Pruned because [reason] - [Branch D]: Pruned because [reason] ### Final Confidence: [X]% **Justification**: [Why this confidence level based on exploration depth, evidence, and remaining uncertainties] ### Recommendation [Clear, actionable recommendation with next steps] ### Remaining Uncertainties - [Assumption 1] - [Assumption 2] ``` **Deliverable**: Comprehensive synthesis with traced path and confidence score --- ## Stopping Criteria **Stop exploration when ANY of:** 1. ✅ Reached 4+ levels AND best branch confidence >80% 2. ✅ Reached 6 levels (maximum recommended depth) 3. ✅ All branches converge to same solution across multiple levels 4. ✅ Diminishing returns (Level N scores similar to Level N-1) **Warning signs** (don't stop yet): - ❌ Only 2-3 levels explored - ❌ Confidence <80% without clear reason - ❌ Winner not clearly superior to alternatives --- ## Bayesian Confidence Scoring **Purpose**: Quantify confidence based on accumulated evidence **Formula**: ``` Prior Odds = P(correct) / (1 - P(correct)) Likelihood Ratio = Evidence strength (from scores) Posterior Odds = Prior Odds × Likelihood Ratio Final Confidence = Posterior Odds / (1 + Posterior Odds) ``` **Practical Calculation**: 1. Start with prior confidence: 50% (neutral) 2. For each evaluation criterion score (0-20): - Convert to likelihood ratio: `LR = 0.25 + (score/20) * 3.75` - Update odds: `Odds = Odds × LR` 3. Convert back to probability: `Conf = Odds / (1 + Odds)` 4. Cap at 95% (Bayesian humility for unknown unknowns) **Example**: - Branch scores: Novelty 18/20, Feasibility 19/20, Completeness 17/20, Confidence 18/20, Alignment 19/20 - Likelihood ratios: 3.62, 3.81, 3.44, 3.62, 3.81 - Final odds: 1.0 × 3.62 × 3.81 × 3.44 × 3.62 × 3.81 = 1,782 - Confidence: 1782 / 1783 = 99.9% → **Capped at 95%** **Confidence Interpretation**: - **90-95%**: Exceptional evidence, suitable for critical decisions - **80-89%**: High confidence, suitable for important decisions - **70-79%**: Medium confidence, consider additional validation - **60-69%**: Low confidence, recommend further investigation - **<60%**: Very low confidence, gather more information --- ## Self-Critique Checklist After applying ToT methodology, verify: - [ ] **Branch Diversity**: Are all 5+ branches fundamentally different (not variations)? - [ ] **Self-Reflection Quality**: Does each branch have genuine self-reflection (not boilerplate)? - [ ] **Evaluation Rigor**: Did I systematically score all 5 criteria for each branch? - [ ] **Depth Achievement**: Did I reach minimum 4 levels of exploration? - [ ] **Confidence Validity**: Is final confidence score justified by exploration depth? - [ ] **Pruning Rationale**: Can I explain why each non-selected branch was discarded? - [ ] **Path Traceability**: Can I clearly trace the winning path from root to leaf? - [ ] **Synthesis Clarity**: Does final output provide actionable recommendation? - [ ] **Stopping Appropriateness**: Did I stop for valid reasons per criteria? --- ## Common Mistakes to Avoid 1. **Too Few Branches**: Using <5 branches reduces exploration quality 2. **Variation vs Diversity**: Creating 5 variations of same approach instead of 5 different approaches 3. **Shallow Depth**: Stopping at 1-2 levels instead of minimum 4 4. **Biased Evaluation**: Favoring familiar approaches without systematic scoring 5. **Missing Self-Reflection**: Skipping confidence assessment in branches 6. **Premature Convergence**: Selecting winner before thorough evaluation 7. **Over-Recursion**: Going beyond 6 levels without clear benefit 8. **Poor Synthesis**: Not clearly documenting winning path and rationale --- ## Reference Documentation **Detailed Templates**: `~/.claude/skills/tree-of-thoughts/references/tree-of-thoughts-patterns.md` Includes: - Branch exploration template (detailed prompts) - Self-reflection rubric (confidence scoring guide) - Evaluation matrix (scoring examples per criterion) - Level transition logic (when/how to deepen) - Edge case handling (convergence, insufficient diversity) --- ## Quick Start Examples ### Example 1: Simple Decision (3 levels) **Problem**: Choose between Redis, Memcached, or Hazelcast for caching **Level 0** (3 branches): - Branch A: Redis (rich data structures) - Branch B: Memcached (pure speed) - Branch C: Hazelcast (distributed computing) → Winner: Branch A (Redis) - 85/100 **Level 1** (Redis deployment options): - A.1: Single instance - A.2: Sentinel (high availability) - A.3: Cluster (horizontal scaling) - A.4: Redis Enterprise - A.5: Managed service (AWS ElastiCache) → Winner: Branch A.3 (Cluster) - 88/100 **Level 2** (Cluster configuration): - A.3.1: 3 masters, no replicas - A.3.2: 3 masters, 3 replicas - A.3.3: 6 masters, 6 replicas - A.3.4: Auto-scaling cluster - A.3.5: Hybrid (critical data replicated) → Winner: Branch A.3.2 (3+3) - 91/100 **Confidence**: 88% (3 levels, clear winner at each level) ### Example 2: Complex Architecture (5 levels) **Problem**: Design microservices communication strategy **Level 0**: REST, gRPC, Message Queue, Event Sourcing, GraphQL (5 approaches) **Level 1**: [Winner] expanded into 5 sub-approaches **Level 2**: [Winner] expanded into 5 implementation variants **Level 3**: [Winner] expanded into 5 technology choices **Level 4**: [Winner] expanded into 5 deployment patterns **Confidence**: 93% (5 levels, 25+ branches explored total) --- ## Summary Tree of Thoughts is a **systematic methodology** for exploring complex problem spaces through: 1. **Parallel branching** (5+ approaches per level) 2. **Self-reflection** (confidence scoring for each branch) 3. **Rigorous evaluation** (5 criteria, 0-100 scoring) 4. **Recursive depth** (minimum 4 levels) 5. **Bayesian confidence** (evidence-based scoring) Use it for strategic decisions, architectural choices, and optimization problems where systematic exploration yields better outcomes than intuition alone. **Remember**: Quality over speed. ToT trades time for rigor. The goal is high-confidence optimal solutions, not quick answers.