LUMINA Technical Paper
Gradient-Based Influence Attribution for AI Music Generators
1Introduction
When an AI music generator produces audio, rightsholders need answers to three critical questions:
- Which training songs influenced the output?
- How much did each song contribute?
- How confident are we in these attributions?
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.
From generation to influence share — how we find who really taught the model what it used.
2Mathematical Foundations
Gradient Embedding per Sample
For each training sample xi and for the generated output xgen, the gradient extractor runs a forward pass of the trained model and accumulates per-token gradients with respect to the weights θT of the selected transformer layers. Gradients are computed only for transformer-layer weights — non-transformer components (input preprocessing, output rendering) are excluded. The summed gradient is then L2-normalized, producing one gradient embedding per sample:
The same accumulation and L2 normalization is applied to xgen to obtain φgen. L2 normalization bounds the Gram-matrix entries and renders embeddings comparable across samples regardless of generation length.
Training-time gradients tell you what the model learned. Generation-time gradients tell you what the model used. Differentiating through the actual sampling process captures which transformer-layer weights shaped this specific output — without modifying training or requiring any instrumentation of the training procedure.
Johnson-Lindenstrauss Random Projection
Because gradient embeddings are very high-dimensional, a random projection matrix P is constructed in accordance with the Johnson–Lindenstrauss lemma and applied consistently to every gradient embedding:
The projected dimension d′ is chosen to preserve pairwise inner products with bounded distortion (ε = 0.15), quantized to the nearest 512 multiple for GPU efficiency. Channel C and R each project from ~50M parameters to approximately 6,656D; the full-transformer baseline from ~805M to approximately 7,680D — on the order of 10³–10⁴.
The same matrix P is applied to every embedding — training samples and generated content alike — so inner products in the projected space remain comparable across all samples. JL theory guarantees the distortion is bounded in expectation, making the downstream linear solve well-founded at practical projected dimensions.
Gradient Matrix and Regularized Linear Solve
The projected training embeddings are stacked into Φ̃train ∈ ℝn×d′. The gradient-matrix assembler constructs M and the similarity-vector constructor constructs b:
The regularized linear solver solves for u, then projects back to produce influence scores s ∈ ℝn:
λ = 10.0 is a Tikhonov-type ridge term ensuring numerical conditioning. Each s[i] estimates training sample i's contribution to the generated content — positive values indicate alignment with the generated output; negative values indicate the model diverged from that training direction.
If two training songs shaped the model in the same direction, they share credit rather than both receiving full attribution. The regularized solve decorrelates overlapping gradient embeddings — songs whose projections are nearly collinear receive proportionally lower individual scores, preventing double-counting.
Dual-Channel Combination
Kernel regression is run independently on Channel C and Channel R projections. The combined influence score weights composition more heavily than production:
The 0.7 / 0.3 split reflects the primacy of compositional influence in music copyright — melody, harmony, and structure outweigh timbral and production characteristics when attributing creative debt.
3Influence Quantification
Kernel regression returns a raw influence score for each training song — positive scores indicate the song pushed the model toward producing this output; negative scores indicate it pushed away. Scores are ranked by absolute value and expressed as a percentage of total absolute influence across the corpus:
This is computed on the combined score (0.7 × C + 0.3 × R). Attribution reports the top-K songs by absolute influence (default K = 10), along with their direction (positive = influence toward, negative = influence away).
Unlike cosine similarity, kernel regression scores can be negative. A negative score means the training song's gradient signature actively pointed away from the generated output — the model learned something from it that it deliberately did not use here. Both positive and negative influence are real causal signals worth reporting.
4Dual-Channel Attribution
Gradient accumulation runs three parallel maps during each generation. Two form the dual-channel attribution system; the third is a full-transformer baseline used for comparison:
| Channel | Layers | Params | Projected dim | Captures |
|---|---|---|---|---|
| C — Composition | 42–47 | ~50M (attention only) | ~6,656D | Melody, Harmony, Structure |
| R — Recording | 12–17 | ~50M (FFN only) | ~6,656D | Timbre, Texture, Sound Design |
| Full (baseline) | 0–47 | ~805M (all) | ~7,680D | Validation baseline |
Channel C tensors (per layer): self_attn.in_proj_weight, self_attn.out_proj.weight, cross_attention.in_proj_weight, cross_attention.out_proj.weight — 4 tensors × 6 layers = 24 tensors.
Channel R tensors (per layer): linear1.weight, linear2.weight — 2 tensors × 6 layers = 12 tensors.
Each channel is independently JL-projected with a different seed offset before the linear solve.
6Validation
LUMINA-TRAK has been validated across three experimental regimes:
- Controlled 5-pair test (Exp 1): 5 music genre pairs, fine-tuned on 2 songs each, 3 seeds — 14/15 correct (93.3%) top-1 attribution using Channel C scoring.
- 487-song multi-style (Exp 2): Full catalog across 8 genres, 18 generation prompts — 77.8% top-1 genre attribution (14/18 correct). Top-10 ranked lists are highly reliable; top-1 is sensitive to prompt vocabulary.
- Negative controls (Exp 3): 8 adversarial out-of-distribution prompts — the system correctly withholds high-confidence attribution when no matching training data exists. Adversarial scores (0.17–0.28) remain below in-distribution scores (0.25–0.40), confirming attribution is not hallucinated.
- Reproducibility: 100% deterministic — seeded JL projection (seed=42) and deterministic generation environment produce identical gradient projections for identical inputs across runs.
7Verifiable Attribution
For each generated output, LUMINA commits the attribution result to an append-only cryptographically chained ledger. This enables third-party verification of influence scores without disclosing the training data, the gradient embeddings themselves, or the model's weights.
Each ledger entry comprises: (a) a content identifier — preferably a cryptographic hash of the generated content; (b) cryptographic commitments (Hash/Merkle) to the projected gradient embeddings φ̃ for the top-ranked training samples and for the generated content; (c) the influence scores s; and (d) the projection and regularization parameters (P, λ) used.
A verifier possessing the generated content can recompute the content identifier, retrieve the corresponding ledger entry, and check the zero-knowledge proof — confirming that the published scores are the genuine result of the regularized linear solve on the committed embeddings, without access to the training data, gradient embeddings, or model weights.
Publishing influence scores without proof of computation creates a trust problem: scores could be fabricated or selectively reported. The zk-SNARK proof anchors every ledger entry to the actual linear solve, making the attribution auditable by any third party — rightsholder, regulator, or DSP — using only the public ledger and the generated content hash.
8Version History
Intellectual Property Notice
This document contains proprietary and confidential information belonging to Fold Artists Research. The methods, algorithms, and technical implementations described herein are protected intellectual property. Unauthorized reproduction, distribution, or disclosure of this document or its contents is strictly prohibited and may violate applicable trade secret and intellectual property laws.