Paper review · November 10, 2026
Functional Dependency Beyond Similarity: A Hierarchical Decomposition of Training Data Attribution in Music Generation Models
Functional Dependency beyond Similarity: Hierarchical Decomposition of Training Data Attribution in Music Generative Models
By decomposing TDA scores into three levels — global, group and individual — the paper showed that in music generation models, a large share of training data influence is spread across the whole model or style groups rather than tied to specific outputs.
Problem
Copyright judgments focus on the similarity between two works. Generative AI, however, uses training data through functional relationships that go beyond similarity. TDA (Training Data Attribution) has been put forward as a possible basis for distributing compensation, but a global influence phenomenon is known in which a small number of training samples rank among the most influential for almost every generated output. If TDA scores are used directly as the basis for compensation, the same samples keep getting paid regardless of what was generated.
Method
The method standardizes TDA scores for each generated output and then splits them exactly into three levels. The global level is, for each training sample, the average of its scores across all generated outputs. The group level is obtained by clustering the score vectors with the global level subtracted using k-means and averaging within each cluster. The individual level is what remains. The share of total variance accounted for by each level (summing to 1) is also computed. MusicGen-S/L and InspireMusic-Base/1.5B were fine-tuned on 30,000 segments from MTG-Jamendo. The authors generated 480 outputs across 12 genres and applied 6 TDA methods and 3 Trak variants. In deletion tests, they removed the top 10% of samples at each level, retrained, and compared the results with random deletion.
Results
- Across every combination of the 4 models and the 6 TDA methods plus 3 variants, global- and group-level influence appeared at a non-negligible size.
- The authors reported that influence unique to individual generated outputs is layered beneath shared influence at the group and global levels.
- In deletion tests with GradDot and Trak (λ=1), they reported that removing the top samples at each level changed model behavior within the corresponding scope more than removing the same number of samples at random.
- Based on these observations, they proposed the concept of 'functional dependency,' which separates by scope how a model and its generated outputs depend on the training data.
Limitations
The experiments are limited to two families of autoregressive music generation models and one dataset, MTG-Jamendo. Deletion tests were applied to only two TDA methods. The group level depends on the k-means clustering result, and the groups do not match real music genres; they are styles defined by the model itself. The provided text is cut off in the experimental setup, so the per-level share figures could not be checked. The link to compensation schemes is at the proposal stage, intended for legal, economic and ethical discussion.
Why it matters
Discussions about compensating for generative AI training data require a transparent account of 'what this data contributed to, and by how much.' This decomposition method can be attached to any TDA method. Because it shows contribution to the model as a whole separately from contribution to specific generated outputs, it provides a practical framework for designing copyright and compensation policy.
Key terms
- TDA(Training Data Attribution)
- A technique that estimates how much each training sample influenced a particular output. It is usually computed by comparing the gradients of training samples and outputs.
- Global influence
- A phenomenon in which a small number of training samples rank among the most influential for almost every generated output. It is known to arise mainly from outlier samples with large gradient magnitudes.
- Functional dependency
- A concept proposed in this paper for the relationship in which a trained model or its generated outputs depend on training data. It treats this relationship by scope: the whole model, style groups, and individual outputs.
- Deletion test
- A validation method that removes a set of high-scoring training samples, retrains, and checks whether the model changes more than when samples are removed at random.
Original
Authors: Changheon Han, Hugh Xuechen Liu, Ashkan Panahi, Kıvanç Tatar · Posted 2026-11-06 · License CC BY 4.0 · Based on the full text
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