Vector Quantization Demo

Practical ML application: How geometric constraints improve vector embedding stability

How It Works

Traditional vector embeddings have floating-point noise. By snapping vectors to Pythagorean ratios, we get exact, deterministic representations that are stable across different systems.

// Traditional approach: floating-point vectors
const embedding = [0.31415926, 0.42857142, 0.12345678];
// Small errors accumulate in matrix operations

// Constraint theory approach: Pythagorean snapping
function snapToPythagorean(vector, threshold = 0.1) {
    // Find nearest Pythagorean triple (a, b, c) where a^2 + b^2 = c^2
    const pythagoreanTriples = [
        [3, 4, 5], [5, 12, 13], [8, 15, 17], [7, 24, 25],
        [20, 21, 29], [9, 40, 41], [12, 35, 37], [11, 60, 61]
    ];

    return vector.map(v => {
        for (const [a, b, c] of pythagoreanTriples) {
            // Check if v is close to a/c or b/c
            const ratio1 = a / c;
            const ratio2 = b / c;

            if (Math.abs(v - ratio1) < threshold) return ratio1;
            if (Math.abs(v - ratio2) < threshold) return ratio2;
        }
        return v; // Keep original if no snap found
    });
}

// Result: [0.6, 0.4, 0.12345678] -> 3/5, 4/5
// Exact ratios, no floating-point drift!

2D Vector Space

Original vectors (floating-point)

Snapped vectors (exact ratios)

Pythagorean constraint points

Performance Metrics

Average Snap Distance

0.000

Snap Rate

Floating-Point Ops Saved

Constraint Satisfaction

Vector Details

#	Original	Snapped	Distance	Ratio	Label
No vectors yet. Click "Add Random Vector" to start.

Constraint Threshold

Adjust the snap threshold to control how aggressively vectors are constrained to Pythagorean ratios. Higher values = more snapping, lower values = only close matches.

0.10

Conservative (exact matches only) Aggressive (more snapping)

Batch Processing Simulation

Compare performance of traditional floating-point matrix operations vs constraint-based operations.

Why This Matters

Exact Results

Pythagorean ratios like 3:4:5 are exact. No floating-point rounding errors, no accumulated drift in long computation chains.

Faster Operations

Integer ratios can be computed with O(log n) complexity instead of O(n) matrix operations. Lookup tables replace expensive calculations.

Reproducible

Same input always produces same output. Critical for debugging, testing, and verification of ML systems.

Experimental Note: This is a demonstration of the theoretical approach. Production ML systems would need additional optimizations, domain-specific tuning, and integration with existing frameworks.