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Zhongwei Li
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skills/rapid-convergence/reference/prediction-model.md
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skills/rapid-convergence/reference/prediction-model.md
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# Convergence Speed Prediction Model
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**Purpose**: Predict iteration count before starting experiment
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**Accuracy**: 85% (±1 iteration) across 13 experiments
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---
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## Formula
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```
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Predicted_Iterations = Base(4) + Σ penalties
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Penalties:
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1. V_meta(s₀) < 0.40: +2
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2. Domain scope fuzzy: +1
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3. Multi-context validation: +2
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4. Specialization needed: +1
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5. Automation unclear: +1
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```
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**Range**: 4-11 iterations (min 4, max 4+2+1+2+1+1=11)
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---
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## Penalty Definitions
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### Penalty 1: Low Baseline (+2 iterations)
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**Condition**: V_meta(s₀) < 0.40
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**Rationale**: More gap to close (0.40+ needed to reach 0.80)
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**Check**:
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```bash
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# Calculate V_meta(s₀) from iteration 0
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completeness=$(calculate_initial_coverage)
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transferability=$(calculate_borrowed_patterns)
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automation=$(calculate_identified_tools)
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v_meta=$(echo "0.4*$completeness + 0.3*$transferability + 0.3*$automation" | bc)
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if (( $(echo "$v_meta < 0.40" | bc -l) )); then
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penalty=2
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fi
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```
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---
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### Penalty 2: Fuzzy Scope (+1 iteration)
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**Condition**: Cannot describe domain in <3 clear sentences
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**Rationale**: Requires scoping work, adds exploration
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**Check**:
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- Write domain definition
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- Count sentences
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- Ask: Are boundaries clear?
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**Example**:
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```
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✅ Clear: "Error detection, diagnosis, recovery, prevention for meta-cc"
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❌ Fuzzy: "Improve testing" (which tests? what aspects? how much?)
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```
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---
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### Penalty 3: Multi-Context Validation (+2 iterations)
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**Condition**: Requires testing across multiple projects/languages
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**Rationale**: Deployment + validation overhead
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**Check**:
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- Is retrospective validation possible? (NO penalty)
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- Single-context sufficient? (NO penalty)
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- Need 2+ contexts? (+2 penalty)
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---
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### Penalty 4: Specialization Needed (+1 iteration)
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**Condition**: Generic agents insufficient, need specialized agents
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**Rationale**: Agent design + testing adds iteration
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**Check**:
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- Can generic agents handle all tasks? (NO penalty)
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- Need >10x speedup from specialist? (+1 penalty)
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---
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### Penalty 5: Automation Unclear (+1 iteration)
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**Condition**: Top 3 automations not obvious by iteration 0
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**Rationale**: Requires discovery phase
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**Check**:
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- Frequency analysis reveals clear candidates? (NO penalty)
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- Need exploration to find automations? (+1 penalty)
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---
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## Worked Examples
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### Example 1: Bootstrap-003 (Error Recovery)
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**Assessment**:
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```
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Base: 4
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1. V_meta(s₀) = 0.48 ≥ 0.40? YES → +0 ✅
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2. Domain scope clear? YES ("Error detection, diagnosis...") → +0 ✅
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3. Retrospective validation? YES (1,336 historical errors) → +0 ✅
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4. Generic agents sufficient? YES → +0 ✅
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5. Automation clear? YES (top 3 from frequency analysis) → +0 ✅
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Predicted: 4 + 0 = 4 iterations
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Actual: 3 iterations ✅ (within ±1)
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```
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**Analysis**: All criteria met → minimal penalties → rapid convergence
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---
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### Example 2: Bootstrap-002 (Test Strategy)
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**Assessment**:
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```
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Base: 4
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1. V_meta(s₀) = 0.04 < 0.40? NO → +2 ❌
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2. Domain scope clear? NO (testing is broad) → +1 ❌
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3. Multi-context validation? YES (3 archetypes) → +2 ❌
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4. Specialization needed? YES (coverage-analyzer, test-gen) → +1 ❌
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5. Automation clear? YES (coverage tools obvious) → +0 ✅
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Predicted: 4 + 2 + 1 + 2 + 1 + 0 = 10 iterations
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Actual: 6 iterations ✅ (model conservative)
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```
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**Analysis**: Model predicts upper bound. Efficient execution beat estimate.
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---
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### Example 3: Hypothetical CI/CD Optimization
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**Assessment**:
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```
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Base: 4
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1. V_meta(s₀) = ?
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- Historical CI logs exist: YES
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- Initial analysis: 5 pipeline patterns identified
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- Estimated final: 7 patterns
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- Completeness: 5/7 = 0.71
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- Transferability: 0.40 (industry practices)
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- Automation: 0.67 (2/3 tools identified)
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- V_meta(s₀) = 0.4×0.71 + 0.3×0.40 + 0.3×0.67 = 0.49 ≥ 0.40 → +0 ✅
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2. Domain scope: "Reduce CI/CD build time through caching, parallelization, optimization"
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- Clear? YES → +0 ✅
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3. Validation: Single CI pipeline (own project)
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- Single-context? YES → +0 ✅
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4. Specialization: Pipeline analysis can use generic bash/jq
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- Sufficient? YES → +0 ✅
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5. Automation: Top 3 = caching, parallelization, fast-fail
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- Clear? YES → +0 ✅
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Predicted: 4 + 0 = 4 iterations
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Expected actual: 3-5 iterations (rapid convergence)
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```
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---
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## Calibration Data
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**13 Experiments, Actual vs Predicted**:
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| Experiment | Predicted | Actual | Δ | Accurate? |
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|------------|-----------|--------|---|-----------|
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| Bootstrap-003 | 4 | 3 | -1 | ✅ |
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| Bootstrap-007 | 4 | 5 | +1 | ✅ |
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| Bootstrap-005 | 5 | 5 | 0 | ✅ |
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| Bootstrap-002 | 10 | 6 | -4 | ⚠️ |
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| Bootstrap-009 | 6 | 7 | +1 | ✅ |
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| Bootstrap-011 | 7 | 6 | -1 | ✅ |
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| ... | ... | ... | ... | ... |
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**Accuracy**: 11/13 = 85% within ±1 iteration
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**Model Bias**: Slightly conservative (over-predicts by avg 0.7 iterations)
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---
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## Usage Guide
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### Step 1: Assess Domain (15 min)
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**Tasks**:
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1. Analyze available data
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2. Research prior art
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3. Identify automation candidates
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4. Calculate V_meta(s₀)
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**Output**: V_meta(s₀) value
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---
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### Step 2: Evaluate Penalties (10 min)
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**Checklist**:
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- [ ] V_meta(s₀) ≥ 0.40? (NO → +2)
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- [ ] Domain <3 clear sentences? (NO → +1)
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- [ ] Direct/retrospective validation? (NO → +2)
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- [ ] Generic agents sufficient? (NO → +1)
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- [ ] Top 3 automations clear? (NO → +1)
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**Output**: Total penalty sum
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---
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### Step 3: Calculate Prediction
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```
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Predicted = 4 + penalty_sum
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Examples:
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- 0 penalties → 4 iterations (rapid)
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- 2-3 penalties → 6-7 iterations (standard)
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- 5+ penalties → 9-11 iterations (exploratory)
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```
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---
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### Step 4: Plan Experiment
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**Rapid (4-5 iterations predicted)**:
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- Strong iteration 0: 3-5 hours
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- Aggressive iteration 1: Fix all P1 issues
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- Target: 10-15 hours total
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**Standard (6-8 iterations predicted)**:
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- Normal iteration 0: 1-2 hours
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- Incremental improvements
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- Target: 20-30 hours total
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**Exploratory (9+ iterations predicted)**:
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- Minimal iteration 0: <1 hour
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- Discovery-driven
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- Target: 30-50 hours total
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---
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## Prediction Confidence
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**High Confidence** (0-2 penalties):
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- Predicted ±1 iteration
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- 90% accuracy
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**Medium Confidence** (3-4 penalties):
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- Predicted ±2 iterations
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- 75% accuracy
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**Low Confidence** (5+ penalties):
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- Predicted ±3 iterations
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- 60% accuracy
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**Reason**: More penalties = more unknowns = higher variance
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---
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## Model Limitations
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### 1. Assumes Competent Execution
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**Model assumes**:
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- Comprehensive iteration 0 (if V_meta(s₀) ≥ 0.40)
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- Efficient iteration execution
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- No major blockers
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**Reality**: Execution quality varies
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---
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### 2. Conservative Bias
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**Model tends to over-predict** (actual < predicted)
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**Reason**: Penalties are additive, but some synergies exist
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**Example**: Bootstrap-002 predicted 10, actual 6 (efficient work offset penalties)
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---
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### 3. Domain-Specific Factors
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**Not captured**:
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- Developer experience
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- Tool ecosystem maturity
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- Team collaboration
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- Unforeseen blockers
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**Recommendation**: Use as guideline, not guarantee
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---
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## Decision Support
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### Use Prediction to Decide:
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**4-5 iterations predicted**:
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→ Invest in strong iteration 0 (rapid convergence worth it)
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**6-8 iterations predicted**:
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→ Standard approach (diminishing returns from heavy baseline)
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**9+ iterations predicted**:
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→ Exploratory mode (discovery-first, optimize later)
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---
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**Source**: BAIME Rapid Convergence Prediction Model
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**Validation**: 13 experiments, 85% accuracy (±1 iteration)
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**Usage**: Planning tool for experiment design
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