dag-convergence-monitor

1. Progress Tracking

• Monitor quality scores over iterations
• Track improvement rates
• Measure goal proximity
• Record iteration history

2. Trend Analysis

• Detect improvement trajectories
• Identify plateauing patterns
• Predict future convergence
• Calculate confidence in predictions

3. Stopping Criteria

• Apply convergence thresholds
• Detect diminishing returns
• Enforce budget limits
• Recommend optimal stopping points

4. Goal Achievement Assessment

• Compare current state to goals
• Identify remaining gaps
• Estimate completion likelihood
• Report achievement status

```typescript

interface ConvergenceStatus {

taskId: string;

currentIteration: number;

analyzedAt: Date;

qualityHistory: QualityPoint[];

trend: TrendAnalysis;

convergence: ConvergenceAssessment;

recommendation: ConvergenceRecommendation;

}

interface QualityPoint {

iteration: number;

timestamp: Date;

qualityScore: number;

confidenceScore: number;

validationScore: number;

improvementsResolved: number;

improvementsRemaining: number;

}

interface TrendAnalysis {

direction: 'improving' | 'stable' | 'declining';

slope: number; // Rate of change

acceleration: number; // Change in rate

isPlateauing: boolean;

plateauStartIteration?: number;

predictedConvergenceIteration?: number;

}

interface ConvergenceAssessment {

isConverged: boolean;

convergenceScore: number; // 0-1, how close to goal

confidenceInConvergence: number;

estimatedIterationsToGoal: number;

goalAchievable: boolean;

}

```

```typescript

interface ProgressTracker {

taskId: string;

goal: ConvergenceGoal;

history: QualityPoint[];

budgetUsed: IterationBudget;

}

interface ConvergenceGoal {

targetQuality: number; // Target quality score

acceptableQuality: number; // Minimum acceptable

maxIterations: number;

requiredImprovements: string[]; // Must-fix items

}

function trackProgress(

tracker: ProgressTracker,

iterationResult: IterationResult

): QualityPoint {

const point: QualityPoint = {

iteration: tracker.history.length + 1,

timestamp: new Date(),

qualityScore: iterationResult.qualityScore,

confidenceScore: iterationResult.confidence,

validationScore: iterationResult.validationPassed ? 1 : 0,

improvementsResolved: countResolved(

tracker.history[tracker.history.length - 1]?.improvementsRemaining ?? 0,

iterationResult.improvements

),

improvementsRemaining: iterationResult.improvements.filter(

i => i.priority === 'critical' || i.priority === 'high'

).length,

};

tracker.history.push(point);

return point;

}

function calculateGoalProximity(

current: QualityPoint,

goal: ConvergenceGoal

): number {

const qualityProgress = current.qualityScore / goal.targetQuality;

const improvementProgress = 1 - (

current.improvementsRemaining /

Math.max(1, current.improvementsRemaining + current.improvementsResolved)

);

return Math.min(1, (qualityProgress 0.7 + improvementProgress 0.3));

}

```

```typescript

function analyzeTrend(history: QualityPoint[]): TrendAnalysis {

if (history.length < 2) {

return {

direction: 'stable',

slope: 0,

acceleration: 0,

isPlateauing: false,

};

}

// Calculate slope using linear regression

const scores = history.map(p => p.qualityScore);

const slope = calculateSlope(scores);

// Calculate acceleration (change in slope)

const recentScores = scores.slice(-3);

const olderScores = scores.slice(-6, -3);

const recentSlope = calculateSlope(recentScores);

const olderSlope = calculateSlope(olderScores);

const acceleration = recentSlope - olderSlope;

// Detect plateauing

const { isPlateauing, plateauStart } = detectPlateau(history);

// Predict convergence

const predictedIteration = predictConvergence(history, slope);

return {

direction: slope > 0.02 ? 'improving' :

slope < -0.02 ? 'declining' : 'stable',

slope,

acceleration,

isPlateauing,

plateauStartIteration: plateauStart,

predictedConvergenceIteration: predictedIteration,

};

}

function calculateSlope(values: number[]): number {

if (values.length < 2) return 0;

const n = values.length;

const sumX = (n * (n - 1)) / 2;

const sumY = values.reduce((a, b) => a + b, 0);

const sumXY = values.reduce((sum, y, x) => sum + x * y, 0);

const sumXX = (n (n - 1) (2 * n - 1)) / 6;

return (n sumXY - sumX sumY) / (n sumXX - sumX sumX);

}

function detectPlateau(history: QualityPoint[]): {

isPlateauing: boolean;

plateauStart?: number;

} {

if (history.length < 3) {

return { isPlateauing: false };

}

// Check last 3 iterations for plateau

const recent = history.slice(-3);

const scores = recent.map(p => p.qualityScore);

const variance = calculateVariance(scores);

// Plateau if variance is very low

if (variance < 0.01) {

return {

isPlateauing: true,

plateauStart: history.length - 3,

};

}

return { isPlateauing: false };

}

function calculateVariance(values: number[]): number {

const mean = values.reduce((a, b) => a + b, 0) / values.length;

const squaredDiffs = values.map(v => Math.pow(v - mean, 2));

return squaredDiffs.reduce((a, b) => a + b, 0) / values.length;

}

function predictConvergence(

history: QualityPoint[],

currentSlope: number

): number | undefined {

if (history.length < 2 || currentSlope <= 0) {

return undefined;

}

const currentScore = history[history.length - 1].qualityScore;

const targetScore = 0.85; // Acceptable threshold

if (currentScore >= targetScore) {

return history.length; // Already converged

}

const iterationsNeeded = (targetScore - currentScore) / currentSlope;

if (iterationsNeeded > 20) {

return undefined; // Too far to predict

}

return Math.ceil(history.length + iterationsNeeded);

}

```

```typescript

function assessConvergence(

tracker: ProgressTracker,

trend: TrendAnalysis

): ConvergenceAssessment {

const current = tracker.history[tracker.history.length - 1];

const goal = tracker.goal;

// Check if we've reached the goal

const meetsTarget = current.qualityScore >= goal.targetQuality;

const meetsAcceptable = current.qualityScore >= goal.acceptableQuality;

const noBlockingIssues = current.improvementsRemaining === 0;

const isConverged = meetsTarget && noBlockingIssues;

// Calculate convergence score

const convergenceScore = calculateGoalProximity(current, goal);

// Estimate iterations to goal

const estimatedIterations = trend.predictedConvergenceIteration

? trend.predictedConvergenceIteration - tracker.history.length

: Infinity;

// Assess if goal is achievable

const budgetRemaining = goal.maxIterations - tracker.history.length;

const goalAchievable =

!trend.isPlateauing &&

trend.direction !== 'declining' &&

(isConverged || estimatedIterations <= budgetRemaining);

// Calculate confidence in assessment

const confidence = calculateConfidence(tracker.history, trend);

return {

isConverged,

convergenceScore,

confidenceInConvergence: confidence,

estimatedIterationsToGoal: estimatedIterations,

goalAchievable,

};

}

function calculateConfidence(

history: QualityPoint[],

trend: TrendAnalysis

): number {

let confidence = 0.5; // Base confidence

// More history = more confidence

if (history.length >= 3) confidence += 0.1;

if (history.length >= 5) confidence += 0.1;

// Consistent improvement = more confidence

if (trend.direction === 'improving' && trend.acceleration >= 0) {

confidence += 0.15;

}

// Low variance = more confidence

const recentVariance = calculateVariance(

history.slice(-3).map(p => p.qualityScore)

);

if (recentVariance < 0.05) confidence += 0.1;

// Plateau reduces confidence in further improvement

if (trend.isPlateauing) confidence -= 0.2;

return Math.max(0, Math.min(1, confidence));

}

```

```typescript

type ConvergenceRecommendation =

| { action: 'continue'; reason: string; priority: string }

| { action: 'accept'; reason: string; qualityLevel: string }

| { action: 'escalate'; reason: string; blockers: string[] }

| { action: 'abort'; reason: string };

function recommendAction(

tracker: ProgressTracker,

trend: TrendAnalysis,

convergence: ConvergenceAssessment

): ConvergenceRecommendation {

const current = tracker.history[tracker.history.length - 1];

const budgetRemaining = tracker.goal.maxIterations - tracker.history.length;

// Case 1: Goal achieved

if (convergence.isConverged) {

return {

action: 'accept',

reason: 'Target quality achieved with no blocking issues',

qualityLevel: 'target',

};

}

// Case 2: Acceptable quality, close to budget limit

if (

current.qualityScore >= tracker.goal.acceptableQuality &&

budgetRemaining <= 1

) {

return {

action: 'accept',

reason: 'Acceptable quality reached, iteration budget nearly exhausted',

qualityLevel: 'acceptable',

};

}

// Case 3: No budget remaining

if (budgetRemaining <= 0) {

if (current.qualityScore >= tracker.goal.acceptableQuality) {

return {

action: 'accept',

reason: 'Budget exhausted, quality is acceptable',

qualityLevel: 'acceptable',

};

}

return {

action: 'escalate',

reason: 'Budget exhausted without reaching acceptable quality',

blockers: extractBlockers(tracker),

};

}

// Case 4: Plateaued below acceptable

if (

trend.isPlateauing &&

current.qualityScore < tracker.goal.acceptableQuality

) {

return {

action: 'escalate',

reason: 'Quality plateaued below acceptable threshold',

blockers: extractBlockers(tracker),

};

}

// Case 5: Declining quality

if (trend.direction === 'declining' && tracker.history.length >= 3) {

return {

action: 'escalate',

reason: 'Quality declining over multiple iterations',

blockers: ['Iterations making things worse, not better'],

};

}

// Case 6: Goal not achievable within budget

if (!convergence.goalAchievable) {

return {

action: 'escalate',

reason: 'Target quality unlikely to be achieved within remaining budget',

blockers: extractBlockers(tracker),

};

}

// Case 7: Continue improving

return {

action: 'continue',

reason: 'Progress being made, goal achievable within budget',

priority: current.improvementsRemaining > 0 ? 'high' : 'medium',

};

}

function extractBlockers(tracker: ProgressTracker): string[] {

const current = tracker.history[tracker.history.length - 1];

const blockers: string[] = [];

if (current.qualityScore < tracker.goal.acceptableQuality) {

blockers.push(Quality score ${(current.qualityScore 100).toFixed(0)}% below acceptable ${(tracker.goal.acceptableQuality 100).toFixed(0)}%);

}

if (current.improvementsRemaining > 0) {

blockers.push(${current.improvementsRemaining} critical/high improvements unresolved);

}

if (current.validationScore < 1) {

blockers.push('Validation still failing');

}

return blockers;

}

```

```yaml

convergenceReport:

taskId: code-review-task

currentIteration: 4

analyzedAt: "2024-01-15T10:45:00Z"

goal:

targetQuality: 0.85

acceptableQuality: 0.70

maxIterations: 5

requiredImprovements:

- "Security analysis section"

- "Performance metrics"

qualityHistory:

- iteration: 1

qualityScore: 0.52

confidenceScore: 0.55

improvementsRemaining: 5

- iteration: 2

qualityScore: 0.58

confidenceScore: 0.62

improvementsRemaining: 4

- iteration: 3

qualityScore: 0.68

confidenceScore: 0.70

improvementsRemaining: 2

- iteration: 4

qualityScore: 0.75

confidenceScore: 0.73

improvementsRemaining: 1

trend:

direction: improving

slope: 0.077

acceleration: 0.02

isPlateauing: false

predictedConvergenceIteration: 5

convergence:

isConverged: false

convergenceScore: 0.88

confidenceInConvergence: 0.72

estimatedIterationsToGoal: 1

goalAchievable: true

recommendation:

action: continue

reason: "Progress being made, target quality likely achievable in next iteration"

priority: high

progressVisualization: |

Iteration Quality Target

1 ████░░░░ 52%

2 █████░░░ 58%

3 ██████░░ 68%

4 ███████░ 75% ← Current

5 (est) ████████ 85% ← Target

nextIterationFocus:

- "Resolve remaining high-priority improvement"

- "Improve confidence through better sourcing"

- "Verify all validation criteria pass"

```

• Input: Iteration results from dag-iteration-detector and dag-feedback-synthesizer
• Output: Recommendations to dag-dynamic-replanner
• History: Stores patterns for dag-pattern-learner
• Metrics: Reports to dag-performance-profiler

1. Sufficient History: Wait for 3+ iterations before trend analysis
2. Budget Awareness: Always consider remaining iterations
3. Early Detection: Catch plateaus before wasting iterations
4. Clear Thresholds: Define target and acceptable levels upfront
5. Confidence Calibration: Trust predictions more with more data

---

Track progress. Detect plateaus. Know when to stop.