Adaptive Learning - JavaScript Library

A comprehensive spaced repetition library with three approaches:

1. Time-Based FSRS - Traditional spaced repetition with time decay
2. Count-Based - Problem-count intervals for intensive practice
3. Hybrid - Combines both for optimal results

Features

• Time-Based FSRS: Exponential decay with progress interference
• Count-Based Scheduling: Discrete intervals [2, 5, 10, 20, 40] problems
• Hybrid Scheduler: Best of both worlds - count for active practice, time for breaks
• Adaptive Routing: Prerequisite checking and domain balancing
• A/B Testing: Built-in cohort assignment for experimentation
• Zero Dependencies: Pure JavaScript with no external runtime dependencies
• Fully Tested: 121 comprehensive tests with Jest

Installation

npm install @adaptive-learning/core

Quick Start

import { Router, DecayCalculator, configure } from '@adaptive-learning/core';

// Optional: Configure algorithm parameters
configure({
  interferenceRate: 0.020,        // 2% decay per interfering skill
  muscleMemoryFloor: 40.0,        // Minimum retention percentage
  prerequisiteThreshold: 60.0,    // 60% mastery needed to advance
  weakDomainThreshold: 50.0,      // Trigger balancing below 50%
  domainCheckInterval: 5          // Check domains every 5 skills
});

// Your data models
const user = { id: 1, learningCohort: null }; // Cohort assigned automatically
const chapters = [
  { id: 'ch-1', title: 'Docker Basics', domain: 'containers', prerequisiteSkillIds: [] },
  { id: 'ch-2', title: 'Volumes', domain: 'storage', prerequisiteSkillIds: ['ch-1'] }
];
const masteries = [
  {
    canonicalCommand: 'ch-1',
    proficiencyScore: 75,
    stability: 7.0,
    lastUsedAt: new Date(),
    chaptersAtMastery: 0
  }
];

// Determine next chapter to learn
const router = new Router({
  user,
  currentSkill: chapters[0],
  allSkills: chapters,
  masteries
});

const result = router.nextSkill();
console.log(result);
// {
//   nextSkill: { id: 'ch-2', ... },
//   reason: 'linear',           // or 'prerequisite_gap', 'weak_domain'
//   message: null,              // User-facing message if detour
//   detour: false               // True if prerequisite detour
// }

Core Concepts

1. Hybrid Decay Model

Skills decay over time and with new learning:

Formula: Current Score = Base × FSRS Retention × Interference Factor

FSRS (Time-based Decay)

R(t) = e^(-t/S)

• t: Days since last practice
• S: Stability in days (increases with successful reviews)
• R: Retention factor (0-1)

Progress Interference

Interference = Skills Learned Since × Rate × Similarity
Factor = 1 - min(Interference, 0.60)

• Recent 3 skills are protected (no interference)
• Maximum 60% interference cap
• Default 15% similarity between skills

2. Adaptive Routing

The router makes intelligent decisions based on:

Priority Order:

1. Prerequisite Check (highest priority)
   • Detours if prerequisite < 60% mastery
2. Domain Balancing (every N skills)
   • Routes to weakest skill in weakest domain if < 50% avg
3. Linear Progression (default)
   • Continue with next skill in sequence

3. A/B Testing Cohorts

• Linear Cohort: Traditional sequential learning (control group)
• Adaptive Cohort: Smart routing with prerequisites + domain balancing (experimental)

API Reference

Configuration

import { configure, getConfiguration, resetConfiguration } from '@adaptive-learning/core';

// Modify shared configuration
configure({
  interferenceRate: 0.025,
  defaultStability: 10.0
});

// Get current configuration
const config = getConfiguration();

// Reset to defaults
resetConfiguration();

Available Parameters:

| Parameter | Default | Range | Description | |-----------|---------|-------|-------------| | interferenceRate | 0.020 | 0.010-0.030 | Decay per interfering skill (2%) | | muscleMemoryFloor | 40.0 | 30-50 | Minimum retention % | | protectedRecentCount | 3 | - | Recent skills protected from interference | | defaultStability | 7.0 | 3-14 | Default FSRS stability (days) | | prerequisiteThreshold | 60.0 | 50-70 | % mastery needed to advance | | weakDomainThreshold | 50.0 | 40-60 | Triggers domain balancing | | domainCheckInterval | 5 | 3-10 | Check domains every N skills |

DecayCalculator

import { DecayCalculator } from '@adaptive-learning/core';

const calculator = new DecayCalculator();

// Calculate current decayed score
const currentScore = calculator.calculateCurrentScore({
  baseScore: 80,
  stability: 7.0,
  lastUsedAt: new Date('2024-01-01'),
  skillsLearnedSince: 10,
  similarities: { 'skill-2': 0.75, 'skill-3': 0.60 }
});
// Returns: ~45-55 (decayed due to time + interference)

// Calculate FSRS retention only
const retention = calculator.calculateFSRSRetention(
  new Date('2024-01-01'), // lastUsedAt
  7.0                     // stability
);
// Returns: ~0.368 after 7 days (e^(-7/7))

// Calculate interference only
const interference = calculator.calculateInterference(
  10,                                      // skillsLearnedSince
  { 'skill-2': 0.75, 'skill-3': 0.60 }    // similarities
);
// Returns: 0.40-1.0 (interference factor)

// Update stability after review
const newStability = calculator.updateStability(
  7.0,   // currentStability
  true,  // reviewSuccess
  1      // difficulty (1=very easy, 5=very hard)
);
// Returns: 17.5 (2.5x increase for very easy)

Router

import { Router } from '@adaptive-learning/core';

const router = new Router({
  user,           // { learningCohort: 'linear' | 'adaptive' }
  currentSkill,   // Currently completed skill
  allSkills,      // Array of all skills/chapters
  masteries,      // Array of mastery records
  config          // Optional custom configuration
});

const result = router.nextSkill();
// {
//   nextSkill: <Skill object or null>,
//   reason: 'linear' | 'prerequisite_gap' | 'weak_domain',
//   message: 'Let\'s review X first...' | null,
//   detour: true | false
// }

Model Requirements:

User:

{
  learningCohort: 'linear' | 'adaptive' | null  // Auto-assigned if null
}

Skill/Chapter:

{
  id: string,                        // or slug
  title: string,
  domain: string,                    // or category (optional)
  prerequisiteSkillIds: string[]     // or prerequisites (optional)
}

Mastery:

{
  canonicalCommand: string,    // or skillId - links to skill.id
  proficiencyScore: number,    // 0-100
  stability: number,           // FSRS stability in days
  lastUsedAt: Date,           // When last practiced
  chaptersAtMastery: number   // Position when mastered (for interference)
}

CohortAssigner

import { CohortAssigner } from '@adaptive-learning/core';

// Assign random cohort (50/50 split)
const cohort = CohortAssigner.assign();
// Returns: 'linear' or 'adaptive'

// Validate cohort
CohortAssigner.valid('linear');    // true
CohortAssigner.valid('invalid');   // false

// Get all cohorts
CohortAssigner.all();
// Returns: ['linear', 'adaptive']

Usage Examples

Complete Learning Flow

import { Router, DecayCalculator } from '@adaptive-learning/core';

// 1. User completes a chapter
const completedChapter = chapters.find(c => c.id === 'ch-1');
const userScore = 85;      // User's score on the chapter
const difficulty = 2;      // User-rated difficulty (1-5)

// 2. Find or create mastery record
let mastery = masteries.find(m => m.canonicalCommand === completedChapter.id);
if (!mastery) {
  mastery = {
    canonicalCommand: completedChapter.id,
    proficiencyScore: 0,
    stability: 7.0,
    lastUsedAt: new Date(),
    chaptersAtMastery: masteries.length
  };
  masteries.push(mastery);
}

// 3. Update stability based on performance
const calculator = new DecayCalculator();
const success = userScore >= 70;
mastery.stability = calculator.updateStability(
  mastery.stability,
  success,
  difficulty
);

// 4. Update mastery score and timestamp
mastery.proficiencyScore = userScore;
mastery.lastUsedAt = new Date();

// 5. Route to next chapter
const router = new Router({
  user,
  currentSkill: completedChapter,
  allSkills: chapters,
  masteries
});

const result = router.nextSkill();

// 6. Show message if detour
if (result.detour && result.message) {
  showFlashMessage(result.message);
  // "Let's review Docker Networks first - it's a prerequisite for what's next."
}

// 7. Navigate to next chapter
if (result.nextSkill) {
  navigateTo(`/chapters/${result.nextSkill.id}`);
} else {
  showCompletionCelebration(); // End of course!
}

Calculate Decayed Scores for Review Dashboard

import { DecayCalculator } from '@adaptive-learning/core';

const calculator = new DecayCalculator();

// Get all skills that need review (decayed below 70%)
const skillsNeedingReview = masteries
  .map(mastery => {
    const skill = chapters.find(c => c.id === mastery.canonicalCommand);
    const skillsLearnedSince = masteries.length - mastery.chaptersAtMastery - 1;

    const currentScore = calculator.calculateCurrentScore({
      baseScore: mastery.proficiencyScore,
      stability: mastery.stability,
      lastUsedAt: mastery.lastUsedAt,
      skillsLearnedSince,
      similarities: {} // Can add similarity data if available
    });

    return {
      skill,
      originalScore: mastery.proficiencyScore,
      currentScore,
      decayAmount: mastery.proficiencyScore - currentScore
    };
  })
  .filter(item => item.currentScore < 70)
  .sort((a, b) => a.currentScore - b.currentScore); // Weakest first

console.log('Skills needing review:', skillsNeedingReview);

Custom Configuration Per Course

import { Configuration, Router } from '@adaptive-learning/core';

// Docker DCA course (fast-paced, practical skills)
const dockerConfig = Configuration.create({
  interferenceRate: 0.020,
  muscleMemoryFloor: 40.0,
  defaultStability: 7.0,
  prerequisiteThreshold: 60.0
});

// Academic course (slower, deeper mastery)
const academicConfig = Configuration.create({
  interferenceRate: 0.010,
  muscleMemoryFloor: 50.0,
  defaultStability: 14.0,
  prerequisiteThreshold: 75.0
});

// Use course-specific config
const router = new Router({
  user,
  currentSkill,
  allSkills,
  masteries,
  config: dockerConfig  // Pass custom config
});

Testing

# Run all tests
npm test

# Run with coverage
npm test:coverage

# Watch mode
npm test:watch

All tests pass:

• ✅ 69 comprehensive tests
• ✅ DecayCalculator: FSRS formulas, interference, stability updates
• ✅ Router: Linear routing, prerequisite checking, domain balancing
• ✅ Configuration: Defaults, customization, singleton
• ✅ CohortAssigner: Random assignment, validation

Mathematical Formulas

FSRS Retention (Time-based Decay)

R(t) = e^(-t/S)

Where:
- R = retention factor (0-1)
- t = time elapsed (days)
- S = stability (days)
- e = Euler's number (≈2.71828)

Examples:

• After 1 day with 7-day stability: e^(-1/7) ≈ 0.867 (86.7%)
• After 7 days with 7-day stability: e^(-7/7) ≈ 0.368 (36.8%)
• After 14 days with 7-day stability: e^(-14/7) ≈ 0.135 (13.5%)

Progress Interference

I = Σ (rate × similarity × count)
  = (skills_learned - protected_count) × interference_rate × avg_similarity

Interference_Factor = 1 - min(I, 0.60)

Where:
- rate = 0.020 (2% default)
- protected_count = 3 (default)
- avg_similarity = 0.15 (default if not specified)
- max interference = 60%

Combined Score

Current_Score = Base × R(t) × Interference_Factor
              = Base × e^(-t/S) × (1 - I)
              >= muscle_memory_floor (40%)

Stability Update

Success:
  S_new = S_old × factor
  factor = 2.5 - (difficulty - 1) × 0.325
  - difficulty 1 (very easy): 2.5x
  - difficulty 2 (easy): 2.175x
  - difficulty 3 (medium): 1.85x
  - difficulty 4 (hard): 1.525x
  - difficulty 5 (very hard): 1.2x
  S_new = min(S_new, 180 days)

Failure:
  S_new = S_old × 0.5
  S_new = max(S_new, 1 day)

Architecture

adaptive-learning-js/
├── src/
│   ├── Configuration.js      # Algorithm parameters
│   ├── DecayCalculator.js    # FSRS + Interference calculations
│   ├── Router.js             # Adaptive routing logic
│   ├── CohortAssigner.js     # A/B testing
│   └── index.js              # Main exports
├── test/
│   ├── Configuration.test.js
│   ├── DecayCalculator.test.js
│   ├── Router.test.js
│   └── CohortAssigner.test.js
├── examples/
│   └── integration.js        # Complete integration example
└── package.json

Design Principles

1. Zero Dependencies: No runtime dependencies, only dev dependencies for testing
2. Flexible Models: Adapter methods support different attribute names (id/slug, domain/category, etc.)
3. Predictable: Pure functions with no hidden state
4. Well-Tested: Comprehensive test coverage with edge cases
5. Configurable: All algorithm parameters can be tuned per use case

Comparison with Ruby Gem

This JavaScript library is a functionally identical port of the Ruby gem adaptive-learning-gem:

| Feature | Ruby Gem | JS Library | |---------|----------|------------| | FSRS Decay | ✅ | ✅ | | Progress Interference | ✅ | ✅ | | Adaptive Routing | ✅ | ✅ | | Prerequisite Checking | ✅ | ✅ | | Domain Balancing | ✅ | ✅ | | A/B Testing | ✅ | ✅ | | Zero Dependencies | ✅ | ✅ | | Test Coverage | ✅ 40+ tests | ✅ 69 tests |

Use Cases

• E-learning Platforms: Adaptive course sequencing
• Coding Bootcamps: Personalized curriculum paths
• Certification Training: Prerequisite-aware learning (Docker DCA, AWS, etc.)
• Language Learning: Spaced repetition with contextual interference
• Corporate Training: Domain-balanced skill development
• MOOCs: A/B testing different pedagogical approaches

Hybrid Scheduler (NEW!)

For coding interview prep, daily practice, or variable-frequency learning.

The Problem with Pure Approaches

Time-Based Only:

• Active users (10+ problems/day) don't benefit from time decay
• Reviews trigger too slowly for intensive practice
• Doesn't leverage interleaving benefits

Count-Based Only:

• Users who take breaks don't review (forgotten but count not met)
• Casual users wait forever for count thresholds
• Ignores real forgetting over time

The Hybrid Solution

Triggers reviews when EITHER condition is met:

1. Count-based (primary): After solving N other problems
2. Time-based (fallback): When retention drops below 70%

Quick Example

import { HybridScheduler } from '@adaptive-learning/core';

const scheduler = new HybridScheduler({
  retentionThreshold: 0.70,  // Review when retention < 70%
  timeWeight: 0.5,           // Balance both priorities
  countWeight: 0.5
});

// Create problem history
const history = scheduler.createProblemHistory('two-pointers-1', 7.0);

// User solves a problem
scheduler.completeProblem(problemHistories, 'two-pointers-1', true, 2);

// Check if review needed
const decision = scheduler.shouldReview({
  problemsSolvedSince: 10,      // Solved 10 other problems
  consecutiveCorrect: 1,        // Need 5 for count trigger
  lastPracticedAt: threeDaysAgo, // 3 days ago
  stability: 7.0
});

console.log(decision.shouldReview);  // true
console.log(decision.reason);        // 'count' (primary trigger)

When Each Trigger Fires

Count Trigger (Primary):

• Active daily users solving many problems
• Provides optimal interleaving
• Intervals: [2, 5, 10, 20, 40] problems

Time Trigger (Fallback):

• Users who take breaks (vacation, busy week)
• Casual users with low problem volume
• Prevents "review starvation"

Example Scenarios

Scenario 1: Active Daily User

// User solves 15 problems/day
// Problem A last seen 1 day ago, 10 problems solved since

scheduler.shouldReview({
  problemsSolvedSince: 10,      // OVER interval (need 5)
  consecutiveCorrect: 1,
  lastPracticedAt: oneDayAgo,   // Only 1 day (high retention)
  stability: 7.0
});
// → shouldReview: true
// → reason: 'count'  ← Count triggered, time didn't

Scenario 2: User with Break

// User on vacation for 2 weeks, no problems solved

scheduler.shouldReview({
  problemsSolvedSince: 0,       // No problems (count won't trigger)
  consecutiveCorrect: 2,        // Need 10 problems
  lastPracticedAt: fourteenDaysAgo, // 2 weeks!
  stability: 7.0
});
// → shouldReview: true
// → reason: 'time'  ← Time caught the gap!

Scenario 3: Casual User

// User solves 2 problems/week (would take 5 weeks to reach count threshold)

scheduler.shouldReview({
  problemsSolvedSince: 2,       // Only 2 problems (need 10)
  consecutiveCorrect: 2,
  lastPracticedAt: sevenDaysAgo, // 1 week ago
  stability: 7.0
});
// → shouldReview: true
// → reason: 'time'  ← Time prevents starvation

API

// Create scheduler
const scheduler = new HybridScheduler({
  retentionThreshold: 0.70,  // Review when < 70% retention
  timeWeight: 0.5,           // Weight for time priority
  countWeight: 0.5           // Weight for count priority
});

// Check if review needed
const decision = scheduler.shouldReview({
  problemsSolvedSince,
  consecutiveCorrect,
  lastPracticedAt,
  stability
});
// Returns: { shouldReview, reason, countPriority, timePriority, retention, ... }

// Select most urgent problem
const next = scheduler.selectNextProblem(problems);
// Returns: { problem, decision, priority }

// Complete a problem (updates ALL state)
scheduler.completeProblem(problemHistories, problemId, wasCorrect, difficulty);

// Get statistics
const stats = scheduler.getReviewStatistics(problems);
// Returns: { total, countTriggered, timeTriggered, averagePriority, ... }

Integration Example

See examples/hybrid-interview-prep.js for complete working example with:

• Active daily user scenario
• User with breaks scenario
• Casual user scenario
• Statistics comparison

When to Use What

| Approach | Use Case | Example Platform | |----------|----------|------------------| | Time-Based FSRS | Self-paced courses, real-world skills | Docker DCA, Language learning | | Count-Based | Intensive daily practice | LeetCode daily grind | | Hybrid | Mixed practice patterns | Interview prep courses |

Count-Based Scheduler (Standalone)

Can also use count-based scheduling independently:

import { CountBasedScheduler } from '@adaptive-learning/core';

const scheduler = new CountBasedScheduler();

// Get interval for mastery level
const interval = scheduler.getReviewInterval(consecutiveCorrect);
// 0 → 2, 1 → 5, 2 → 10, 3 → 20, 4+ → 40

// Check if due
const due = scheduler.shouldReview(problemsSolvedSince, consecutiveCorrect);

// Calculate overdueness
const priority = scheduler.calculatePriority(problemsSolvedSince, consecutiveCorrect);

// Complete problem (auto-updates all counters)
scheduler.completeProblem(problemHistories, problemId, wasCorrect);

License

MIT

Contributing

Contributions welcome! Please open an issue or PR.

Acknowledgments

Based on research in:

• FSRS (Free Spaced Repetition Scheduler)
• Spaced repetition algorithms
• Count-based interleaving for problem-solving
• Adaptive learning systems
• Curriculum sequencing theory