LUMINA Technical Paper

Gradient-Based Influence Attribution for AI Music Generators

Research Paper Version 7.0 • Jan 2026

1Introduction

When an AI music generator produces audio, rightsholders need answers to three critical questions:

  1. Which training songs influenced the output?
  2. How much did each song contribute?
  3. How confident are we in these attributions?
💡 Core Insight

A model's gradients encode which parameters would change to better fit a sample. By comparing gradient signatures, we can identify which training songs share "influence DNA" with a generated output.

2Mathematical Foundations

Cross-Entropy Teacher Forcing

LUMINA uses teacher forcing with cross-entropy loss to extract gradient signatures. Given audio codes from EnCodec:

Loss Function L = CrossEntropy(logits, codes) = -Σ log P(codet | code<t)

Chunked Processing

Audio is processed in 10-second chunks with gradients averaged across chunks:

Gradient Averaging g = (1/N) × Σ ∇θ L(chunki)

Attribution via Cosine Similarity

Cosine Similarity Score score = (goutput · gsong) / (‖goutput‖ × ‖gsong‖)

Kernel Regression (SpinTrak-Aligned)

To account for correlations between training songs, we use kernel regression:

Kernel Regression Formula scores = (K KT + λI)-1 K · goutput

Where K is the (N×D) training fingerprint matrix and λ=0.01 is the regularization parameter.

3Statistical Confidence

In high-dimensional space (d=512), random vectors have a noise floor of σ ≈ 4.4%. Attribution requires signals significantly above this noise.

Confidence Formula confidence(s) = erf(z / √2), where z = s / σ

Songs must achieve ≥ 95% confidence (~1.65σ) to qualify for attribution.

4Dual-Channel Attribution

LUMINA separates influence into two distinct rights channels:

Attribution Flow
Gradient Extraction
↓
Publishing (Composition)
Master (Production)
Channel Source Captures
Composition (P) Self-Attention (self_attn) Melody, Chord Progression, Structure
Production (M) Output Linears (lm.linears) Timbre, Texture, Sound Design

5Share Allocation

Royalty splits are proportional to Standardized TracIn Score (STS) and LUMINA Influence Potency (LIP).

STS: Standardized TracIn Score

Raw cosine similarities are z-score normalized:

Z-Score Normalization STS = (score - μ) / σ

LIP: Influence Potency via Tanh

STS is mapped to a bounded percentage using hyperbolic tangent:

LIP Score LIP = tanh(k × STS) where k = 0.5
LIP Percentage LIP% = (LIP + 1) / 2 × 100

This maps [-∞, +∞] STS to [0%, 100%] LIP with 50% as baseline.

Gated Weights

Only signals above 1σ contribute to share allocation:

Gated Weight wi = max(0, STSi - 1)²
Share Formula sharei = wi / Σ(wj) for all qualified songs

6Validation

LUMINA has been validated against 10,000 generation cycles.

  • Reproducibility: < 0.1% variance in signatures.
  • Baseline Confidence: > 68% at 1σ qualification gate.
  • Causal Link: 94% accuracy in identifying ground-truth prompts.