Source-linked AI summary
ARIA: A Diagnostic Framework for Music Training Data Attribution
Changheon Han, Ashkan Panahi, Kıvanç Tatar
TL;DR
Music attribution must identify which training songs influence an output and along which musical aspects, needs that scalar scores do not meet. ARIA decomposes attribution by musical aspect and diagnoses score-matrix reliability; its diagnostics matched symbolic ground truth and flagged query-independent collapse in audio attribution.
Problem
Music attribution needs to identify influential training songs and the musical aspects involved, while scalar scores do not reveal which aspects dominate.
Source: §1 · pp. 1–2Method
ARIA measures musical homogeneity among top-K attributed tracks against random training-pool groups and diagnoses score-matrix reliability using spectral and column statistics.
Source: §1 · p. 2, §3 · p. 3, §3.2 · p. 4Results
Takeaways & Limitations
Abstract
from arXiv · showhide
Training data attribution (TDA) for music generation must answer two questions that copyright analysis requires, namely which training songs influence a generated output and along which musical aspects the influence operates. Existing methods reduce influence to a single scalar, without revealing which musical aspects are dominant in that influence. We propose ARIA, a framework that decomposes attribution along musical aspects (five for symbolic music, three for audio) and pairs the decomposition with reliability diagnostics computed from the segment-level score matrix. It measures within-group similarity among the top-K attributed tracks against random reference groups drawn from the training pool, and diagnoses the score matrix through its singular value decomposition and column statistics. On a symbolic-music model where attribution ground truth is available through counterfactual retraining, the reliability diagnostics rank four attribution methods identically to that ground truth. On an audio music generation model, ARIA reveals attribution behaviors that vary substantially across TDA methods, flags score matrices whose retrieved tracks are nearly identical across queries rather than reflecting per-query attribution, and characterizes embedding-similarity retrieval baselines by the musical aspect each encoder surfaces. Together, ARIA produces per-aspect attribution evidence aligned with the musical aspects considered under the idea-expression distinction in copyright analysis.
1 Introduction
Music attribution must identify both the training songs that influence an output and the musical aspects through which influence operates. ARIA decomposes attribution by aspect and diagnoses score-matrix reliability; its diagnostics match LDS rankings on a symbolic benchmark and expose query-independent collapse in audio settings.
1 Introduction
- Music’s entangled aspects make influence harder to trace than verbatim text or pixel matches, while copyright analysis distinguishes expressive elements from stylistic ideas.Meaningful attribution therefore needs to identify both influential songs and the aspects through which influence operates.Source: §1 · pp. 1–2
- Existing TDA methods reduce each training example’s influence to one scalar, leaving the musical-aspect question unanswered.Embedding retrieval also inherits the aspects represented by its encoder, while attribution-by-design requires provenance that existing generative music models do not support.Source: §1 · p. 2
- ARIA measures top-K attributed-track similarity across musical-aspect channels against random reference groups and diagnoses score matrices using SVD and column statistics.It uses five channels for symbolic music and three for audio.Source: §1 · p. 2
- Per-aspect evidence follows musical aspects used in copyright analysis, unlike scalar scores.The framework is intended to support compensation and infringement analysis.Source: §1 · p. 2
- ARIA identifies aspect imbalance and query-independent score collapse as structural confounds in per-aspect music attribution.Collapse occurs when methods rank training segments nearly identically across queries.Source: §1 · p. 2
- Four reliability diagnostics rank attribution methods identically to LDS on a symbolic music generation model with attribution ground truth.On an audio generation model, ARIA finds method-dependent attribution profiles and flags score matrices whose results reflect query-independent collapse.Source: §1 · p. 2
2 Related Work
Copyright analysis and music similarity both treat music as multi-aspect, while existing attribution evaluations and methods leave important parts of audio attribution unresolved. ARIA addresses this by diagnosing score matrices and characterizing the musical aspects captured by a scoring method.
2.1 Musical Similarity in Copyright Analysis
- Copyright analysis separates musical aspects such as melody, harmony, and rhythm, while music information retrieval also studies rhythm, harmony, and timbre as distinct axes.Audio melody is omitted from ARIA’s channel set because polyphonic melody extraction from full-mix audio remains unresolved.Source: §2.1 · p. 2
2.2 Training Data Attribution
- Existing TDA evaluation is difficult at scale because LDS requires retraining models on corpus subsets, and music lacks the single-concept or verbatim proxies used in other modalities.Music-specific approaches use distinct references, including MIDI-rendered metrics, encoder similarity, parameter updates, or built-in provenance, but none identifies the musical aspects of influence.Source: §2.2 · p. 3
- ARIA diagnoses attribution quality directly from score matrices without retraining or ground-truth labels, while revealing which musical aspects a scoring method captures.A single scalar score cannot expose those aspects.Source: §2.2 · p. 3
3 ARIA: A Diagnostic Framework for Music Attribution
ARIA evaluates score-matrix reliability and attributed-group musical homogeneity without ground-truth attribution labels. Its setup scores training segments or tracks against generated-output queries, then applies structural diagnostics and modality-specific aspect channels.
3 ARIA: A Diagnostic Framework for Music Attribution
- ARIA combines score-matrix reliability diagnostics with musical homogeneity analysis, and evaluates symbolic and audio models where attribution ground truth is respectively available and intractable at scale.The diagnostics use score-matrix structure; homogeneity analysis uses modality-specific evidence channels.Source: §3 · p. 3
3.1 Problem Setting
- A scoring method assigns each training segment a real-valued score for each query derived from a generated output; embedding baselines instead use cosine similarity between audio embeddings.For group homogeneity, segment scores are normalized per query and averaged within tracks; symbolic instances are already segment-indexed, while embedding baselines score tracks directly.Source: §3.1 · pp. 3–4
3.2 Score-Matrix Reliability Diagnostics
- Three score-matrix diagnostics capture different departures from query-dependent rankings: inter-query column correlation, singular-value energy concentration, and mean column concentration.High inter-query correlation indicates similar score profiles; r1 measures single-axis energy, while p near 1 means columns are nearly constant across segments.Source: §3.2 · p. 4
3.3 Evidence Channels
- Evidence channels group features probing a single musical aspect, with channel and feature choices adapted to the modality.Symbolic channels are melody, harmony, rhythm, dynamic, and texture; audio channels are rhythm, harmony, and timbre.Source: §3.3 · p. 5
3.4 Within-Group Musical Homogeneity
- ARIA compares top-K attributed tracks’ within-group pairwise similarity with random reference groups sampled from the training pool.Positive channel z-scores indicate greater internal homogeneity than same-size random groups; the query-level scores are aggregated into channel summary metrics.Source: §3.4 · p. 5
- On the symbolic benchmark, Table 1 reports reliability diagnostics and within-group homogeneity at K=300 across five jSymbolic channels, with LDS as attribution ground truth.The table’s caption establishes its scope and measures, not the comparative values.Source: Table 1 · p. 6
4 Experiments
The experiments validate ARIA’s reliability diagnostics against symbolic attribution ground truth and apply its aspect-wise analyses to audio attribution and embedding retrieval. The results distinguish query-dependent aspect profiles from score-matrix collapse and show that removing the dominant rank-1 component can change apparent homogeneity.
4 Experiments
- The symbolic experiment uses a benchmark with LDS ground truth and five jSymbolic channels, while the audio experiment applies ARIA to three stages and 7,148 queries per stage.The symbolic score matrices are 5000 × 178; LDS is computationally infeasible for the audio model, where the study also evaluates FACTGRASS and LOGRA.Source: §4 · p. 6
4.1 Symbolic Ground-Truth Validation
- All four reliability metrics rank the four symbolic attribution methods identically to LDS, with TRAK strongest and GradDot weakest.The larger gaps in p and κ than in r1 are consistent with r1 missing multi-axis redundancy.Source: §4.1 · p. 6
4.2 Audio Attribution Method Results
- At K=300, GRAD-COS coarse collapses (r1=1.000, p=1.000), while query-dependent settings show aspect-specific profiles; only TRAK fine is positive across all three channels.TRAK coarse and FACTGRASS fine are also collapsed and yield uniformly negative z-scores.Source: Table 2 · p. 7, §4.2 · p. 7
4.3 Embedding Retrieval Method Results
- The shared retrieval rule yields distinct encoder profiles: MERT has strongest harmonic alignment (αreg=0.680) and near-complete timbral alignment (0.896), whereas CLEWS is weak across channels.The authors relate these profiles to the encoders’ different pretraining objectives; retrieval reflects encoder sensitivity, not generative-model training-data influence.Source: Table 3 · p. 8, §4.3 · p. 8
4.4 Residual Analysis
- Removing rank-1 reverses GRAD-COS coarse’s extreme homogeneity (+29.56 timbral, +8.56 harmonic), showing its original scores reflect a static group, not attribution.Settings without query-dependent signal must be excluded from homogeneity-based method ranking.Source: Figure 1 · p. 9, §4.4 · p. 9
5 Conclusions and Limitations
ARIA decomposes music attribution by musical aspect and diagnoses score-matrix quality without ground truth, addressing constraints on evaluating attribution at audio-model scale. Its diagnostics align with symbolic ground truth and expose misleading or encoder-dependent patterns in audio attribution.
5 Conclusions and Limitations
- ARIA combines musical-aspect decomposition with score-matrix diagnostics, addressing the difficulty of constructing per-aspect ground truth and the infeasibility of counterfactual retraining at audio-model scale.The authors connect this need to copyright analysis under the idea-expression distinction.Source: §5 · p. 9
- On the symbolic benchmark, all four reliability diagnostics rank methods identically to LDS, while audio analyses reveal collapsed matrices and encoder-dependent retrieval patterns.The authors say per-track causal influence remains future work.Source: §5 · p. 9
- ARIA diagnoses score-matrix structure and top-K retrieval homogeneity, but establishing causal influence per track remains future work.The authors identify controlled synthetic data as a possible route to that future work.Source: §5 · p. 9
- The authors frame ARIA as a foundation for richer evidentiary tools relevant to music compensation and copyright frameworks.This is presented as a direction for the field as music-generation models scale.Source: §5 · p. 9
A The Definitions and Formulations of Methods in ARIA
The appendix formulates attribution scores using projected gradients or fixed audio embeddings, and describes per-query normalization and musical-feature similarity used in ARIA.
A.1 Attribution Method Formulations
- TRAK approximates leave-one-out influence using projected gradients and a regularized projected empirical Fisher score.It uses a dense random projection with m=4096; λ is selected on the validation set and was 0.01 in the experiments.Source: §A.1 · p. 13
- GRAD-COS computes cosine similarity between projected gradients, whereas TracIn accumulates projected-gradient inner products across training checkpoints.TracIn was used only in the symbolic experiment.Source: §A.1 · p. 13
- GradDot is the unnormalized single-checkpoint counterpart of GRAD-COS and was used only in the symbolic experiment.The implementation used dattri’s TracInAttributor with normalized_grad=False.Source: §A.1 · p. 13
- LOGRA uses a Kronecker-factored projection and a KFAC-approximated empirical Fisher, with damping scaled by the projected layer’s mean eigenvalue.The damping multiplier c was 0.1 in the experiments.Source: §A.1 · p. 13
- FACTGRASS replaces the dense projection with sparse SJLT factors after masking small gradient entries, without a Hessian preconditioner in the projection.Regularization is applied only in the final solve.Source: §A.1 · p. 13
- CLAP, CLEWS, and MERT rank tracks by cosine similarity between fixed audio embeddings produced by their respective encoders.The encoder output embedding is the representation used for scoring.Source: §A.1 · p. 14
A.2 Per-query normalization
- Audio per-query normalization uses z-scores for bounded, near-symmetric TRAK and GRAD-COS columns, and ranks for heavy-tailed LOGRA and FACTGRASS scores.TracIn and GradDot were used only in the symbolic experiment and require no per-query normalization.Source: §A.2 · p. 14
A.3 Feature Extraction and Similarity Definitions
- The experiments use five symbolic and three audio evidence channels; feature tables list extraction parameters, while feature similarities use standardized Euclidean distance mapped to [0, 1].The symbolic channels use jSymbolic 2.2 features decoded from MIDI; the audio feature table specifies 48 kHz mono audio.Source: §A.3 · p. 14, Table 4 · p. 14, Table 5 · p. 15
B.1 Symbolic Experimental Details
The symbolic experiment uses a pretrained MusicTransformer benchmark with published LDS attribution ground truth and no additional training.
B.1 Symbolic Experimental Details
- The benchmark supplies 5,000 training segments and 178 test queries per method, with each segment a fixed-length tokenized MIDI block.The model is a pretrained MusicTransformer on MAESTRO; the experiment performs no additional training.Source: §B.1 · p. 15
- TRAK, TracIn, GRAD-COS, and GradDot use dattri implementations with library defaults, and reproduced LDS values match the benchmark within 10^-3.The benchmark provides the published LDS ground truth.Source: §B.1 · p. 15
B.2 Audio Experimental Details
The audio experiment applies a three-stage MusicLM-style model to filtered FMA Large tracks and evaluates attribution methods and retrieval baselines. The appendix also reports method costs and TRAK sensitivity to projection dimension and regularization.
B.2 Audio Experimental Details
- The semantic, coarse, and fine stages share a transformer architecture, while their input duration, prediction target, output rate, quantizers, and conditioner vary by stage.Table 6 summarizes the per-stage model configuration.Source: §B.2 · p. 15, Table 6 · p. 15
- The filtered FMA Large dataset contains 67,219 training tracks and 7,148 held-out evaluation tracks, split into stage-specific segments of 10, 4, and 2 seconds.Tracks with more than 15 seconds of silence and specified low-engagement Experimental-genre tracks were removed.Source: §B.2 · p. 16
- CLAP, CLEWS, and MERT baselines use public checkpoints, with each track represented by an embedding averaged across time.The model uses AdamW with cosine learning-rate decay and weight decay 0.01; Table 7 lists stage-specific training hyperparameters.Source: §B.2 · pp. 15–16, Table 7 · p. 15
- Attribution hyperparameters are summarized in Table 8; published defaults are used when available, while FACTGRASS damping is set to 10^-2 × ¯λ within the searched grid.The appendix also reports end-to-end compute and storage costs for the four attribution methods in Table 9.Source: §B.2 · p. 16, Table 8 · p. 16, Table 9 · p. 16
B.3 TRAK Hyperparameter Sensitivity
- With λ=0, TRAK’s fine harmonic score is −5.52 at projection dimension 2048 and −5.70 at 4096; λ in [10^-2, 10^2] recovers it to +1.25 to +1.31.Table 10 reports ¯z at K=300 across projection dimensions and λ; the selected configuration is marked in the table.Source: §B.3 · p. 17, Table 10 · p. 17
B.4 Full K-Sweep results
The symbolic K-sweep shows stable channel rankings and contrasting TracIn harmony and GradDot dynamics signals. The K=300 residual table reports per-channel homogeneity and reliability values across 15 settings.
B.4 Full K-Sweep results
- Across K=20–500, TracIn’s harmony rises +1.09 to +2.43, while GradDot’s dynamics falls −0.10 to −0.78; all four methods retain channel rankings.For all four MusicTransformer methods, r1<0.15 and r2:5<0.25, keeping residual homogeneity close to the original across channels and K.Source: Figure 2 · p. 17, §B.4 · p. 17
- The audio sweeps add eight attribution stage-method settings and three embedding retrieval baselines, plotting homogeneity across K.Figures 3–4 use the same dashed-original and solid-rank-1-residual curve conventions.Source: Figure 2 · p. 17, Figure 3 · p. 18, Figure 4 · p. 18
B.5 Residual Homogeneity at K=300
- At K=300, Table 11 reports per-channel residual homogeneity, Pos, and Sig for all 15 settings, alongside reliability diagnostics.The table covers Ntest=7,148; its caption defines S, C, and F as semantic, coarse, and fine stages.Source: Table 11 · p. 19, §B.5 · p. 19
B.6 Genre Confound Analysis
The genre breakdown tests whether positive fine-stage harmonic homogeneity for canonical TRAK is driven by a dominant genre. The positive signal is consistent across the 13 genres examined.
B.6 Genre Confound Analysis
- Across 13 genres, mean z is positive and Pos is at least 87% in each; the SD of 0.11 is inconsistent with a single-dominant-genre explanation.The analysis covers 3,605 genre-labelled queries and uses B=200 random reference groups.Source: Table 12 · p. 19, §B.6 · p. 19