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Do Audio Representations Compose Additively?

Chenhao Xue, Zhijin Guo, Joyraj Chakraborty, Martin Reed, Nikolaos Thomos

arXiv:2609.27187v1cs.SDcs.MM

TL;DR

It remains unclear whether pre-trained audio representations encode additive structure without compositional supervision, independently of text grounding. The paper tests frozen representations with label-alignment and held-out-combination reconstruction diagnostics. All three models align with source labels and reconstruct better than permutation baselines, while CLAP shows the clearest additive evidence, including gains over label-overlap baselines on FSD50K.

  • Problem

    It remains unclear whether pre-trained audio representations encode additive structure without compositional supervision, independently of text grounding.

    Source: §I · p. 1

  • Method

    The study evaluates frozen audio representations with canonical correlation analysis for label alignment and leave-one-combination-out reconstruction from fitted source contributions.

    Source: §I · p. 1, §V · p. 4

  • Results

    All three models show linear source-label correlation and better leave-one-combination-out reconstruction than permutation baselines, while CLAP also beats label overlap on FSD50K.

    Source: B. Quantifying Linear Alignment · p. 3, §V · p. 4, C. Quantifying Additive Generalization · p. 4

  • Takeaways & Limitations

    Unseen mean representations are additively predictable from source contributions, most clearly for CLAP.

    Source: §V · p. 4

    All three models fall short of ideal reconstruction, indicating residual limits to additive compositionality.

    Source: §V · p. 4

Abstract

from arXiv · show

Compositionality, the ability to represent complex acoustic scenes as combinations of simpler sound sources, is central to auditory perception and classical additive signal models. Still, it remains unclear whether modern pre-trained audio representations internalize additive structure without compositional supervision. Existing evaluation frameworks of audio compositional reasoning largely focus on cross-modal audio-text alignment, leaving open whether audio representations themselves exhibit additive compositional structure independent of text grounding, analogous to vector arithmetic in word representations. To investigate this, we adopt a two-step diagnostic for frozen audio representations. First, we quantify linear alignment between representations and sound source labels using canonical correlation analysis. Second, we test additive compositional generalization via leave-one-combination-out reconstruction, grouping clips by exact source-label set, averaging their representations, and predicting held-out means from per-source contributions fitted only on training combinations. With larger combination holdouts, CLAP outperforms the permuted and label-overlap baselines on FSD50K, while the speech models do not outperform the label-overlap baseline. We examine representations generated by Wav2Vec2, HuBERT, and CLAP on FSD50K and CHiME-Home datasets. All three models show consistently higher linear correlation and more accurate leave-one-combination-out reconstructions than the permuted baselines. However, only CLAP shows large cosine similarity gains, which could be associated with its training on many kinds of audio and text. Finally, we note that all three models exhibit reconstruction residuals, revealing limits of additive compositionality such as nonlinear or non-compositional audio structure.

I. INTRODUCTION

Compositionality is central to auditory perception and classical audio models, but it is unclear whether modern pre-trained audio representations encode additive structure without compositional supervision. This work evaluates frozen representations on real recordings to test linear alignment with sound-source labels and reconstruction of unseen source combinations.

I. INTRODUCTION

  • Compositionality describes representing complex structure through simpler components, a principle used in classical audio models such as non-negative matrix factorization and sparse coding.Human auditory perception also organizes complex scenes into constituent sources, temporal patterns, and semantic attributes.Source: §I · p. 1
  • Modern pre-trained audio models learn without explicit supervision of how constituent sounds compose, leaving their multi-source structure difficult to interpret.The open question is whether that structure is reflected in the representation space or arises mainly from statistical associations.Source: §I · p. 1
  • Prior audio compositionality evaluations emphasize audio–text alignment, leaving additive structure within audio representations independent of text grounding less systematically evaluated.The study instead asks whether unseen source combinations can be reconstructed from contributions estimated using other combinations.Source: §I · p. 1
  • The study evaluates Wav2Vec2, HuBERT, and CLAP on real recordings from FSD50K and CHiME-Home using semantic multi-hot source labels.It tests linear alignment and reconstruction of unseen source combinations in frozen audio representations.Source: §I · p. 1
  • The proposed repeated-holdout evaluation uses permutation and label-overlap baselines to reveal when reconstruction success does not extend beyond source-label overlap.Estimating source contributions from known combinations could allow an unseen mixture to be approximated without recording that exact mixture or fine-tuning the encoder.Source: §I · p. 1

II. PROBLEM FORMULATION

The paper asks whether pre-trained audio representations encode complex scenes as additive combinations of their constituent sound sources. It tests this by fitting source contributions to grouped real-world clips and predicting combinations absent from fitting.

II. PROBLEM FORMULATION

  • The central question is whether pre-trained audio representations encode compositional structure in which complex acoustic scenes decompose into additive combinations of constituent sources.The formulation uses real-world clips that may contain co-occurring sound sources, with a set of labeled source types.Source: §II · pp. 1–2
  • For reconstruction, clips with identical source labels are grouped and their representations averaged, yielding one representation row per unique source combination.A multi-hot matrix records which source types occur in each combination.Source: §II · p. 2
  • The additive hypothesis assigns each source a contribution vector, so a combination’s mean representation is approximated by summing the contributions of its constituent sources.The contribution matrix is fitted to predict combination representations from their source labels.Source: §II · p. 2
  • The formulation assumes each source’s representation contribution is context-independent, motivated by additive superposition of acoustic signals and power from uncorrelated sources.For example, the contribution of a dog bark should be similar whether it co-occurs with traffic or bird chirps.Source: §II · p. 2
  • Unlike CompA, which evaluates audio–text compositional alignment, this approach evaluates additive structure within frozen audio representations independently of text grounding.Human labels construct the source matrix and fit contributions; the encoders remain frozen.Source: §II · p. 2

III. METHODOLOGY

The paper adapts a two-step diagnostic to evaluate compositional structure in audio representations. It assesses both linear alignment and whether representations generalize additively to unseen source combinations.

III. METHODOLOGY

  • The adapted two-step diagnostic evaluates compositional structure in audio representations through linear alignment and additive generalization.The framework is illustrated in Fig. 1.Source: §III · p. 2
  • Linear alignment tests whether audio representations correlate with sound-source labels.This is one of the two diagnostic targets.Source: §III · p. 2
  • Additive generalization tests whether representations support reconstruction of unseen source combinations.This is the second diagnostic target.Source: §III · p. 2

A. Compositional Diagnostic

The diagnostic separates linear label alignment from additive prediction on held-out source combinations. Permutation and overlap-based predictors provide comparison baselines for the tests.

A. Compositional Diagnostic

  • Canonical correlation analysis measures linear correlation between source labels and clip representations using clip-level rows and projection pairs.The additive test instead groups exact label combinations, fits source contributions without the held-out combination, and predicts its representation.Source: A. Compositional Diagnostic · p. 2
  • A row-permuted baseline shuffles source-label rows to disrupt row-label alignment while preserving label co-occurrence statistics.The method uses 100 permutations; for repeated holdouts, only training pairings are permuted and predictions are evaluated against true held-out representations.Source: A. Compositional Diagnostic · p. 2
  • For repeated holdouts, overlap predictors either copy the representation of the most Jaccard-similar training combination or average training representations using Jaccard weights.Jaccard overlap is the intersection-to-union ratio for source-label sets, and the better predictor is reported per metric.Source: A. Compositional Diagnostic · p. 2

B. Ridge Regularization for Hierarchical Audio Labels

Hierarchical and co-occurring audio labels create correlated columns that can destabilize the standard pseudoinverse. Ridge regularization shrinks unstable directions while retaining the additive-structure test.

B. Ridge Regularization for Hierarchical Audio Labels

  • Label hierarchies and co-occurrence, such as Animal → Wild animal → Bird and Speech with Music, induce strong correlations among columns of S.Source: B. Ridge Regularization for… · p. 2
  • A ridge-regularized pseudoinverse addresses numerical instability from correlated label columns.Source: B. Ridge Regularization for… · p. 2
  • The estimator shrinks unstable directions, approaches the Moore–Penrose pseudoinverse as λ → 0, and stabilizes the fit without changing the linear-structure hypothesis.CHiME-Home uses centered ridge with validation-selected fixed λ; FSD50K uses the uncentered pseudoinverse.Source: B. Ridge Regularization for… · p. 2

C. Reconstruction Metrics

Five metrics assess complementary aspects of held-out representation reconstruction, from error and direction to distribution, similarity structure, and retrieval.

C. Reconstruction Metrics

  • Relative Frobenius error measures reconstruction error relative to the original signal magnitude, while cosine similarity measures directional alignment.Source: C. Reconstruction Metrics · p. 3
  • KL divergence compares softmax distributions in bits, and CKA assesses whether pairwise similarity structure is preserved.Source: C. Reconstruction Metrics · p. 3
  • Hits@K measures whether the true held-out representation appears among the prediction’s nearest neighbors; repeated holdouts rank only held-out combinations by Euclidean distance.Source: C. Reconstruction Metrics · p. 3

A. Models, Datasets, and Setups

The study compares frozen Wav2Vec2, HuBERT, and CLAP representations on FSD50K and CHiME-Home, using sound-label combinations to evaluate reconstruction.

A. Models, Datasets, and Setups

  • Wav2Vec2 and HuBERT are speech-trained self-supervised models, whereas CLAP learns joint audio-text representations from diverse audio sources.All encoders remain frozen throughout the analysis.Source: A. Models, Datasets, and Setups · p. 3
  • FSD50K provides 51,197 clips labeled across 200 hierarchical sound classes, while CHiME-Home contributes 2,762 four-second chunks analyzed using seven content classes.Source: A. Models, Datasets, and Setups · p. 3
  • The analysis groups clips into source-label combinations; ridge regularization is selected on validation data and held fixed across leave-one-out folds.Repeated holdouts use fixed per-encoder regularization, and retrieval uses K = 5.Source: A. Models, Datasets, and Setups · p. 3

B. Quantifying Linear Alignment

True source-label pairings show higher canonical correlations than permutation baselines across models and datasets, but alignment alone does not establish additive generalization. In reconstruction, all models beat permutation in leave-one-combination-out tests, while CLAP shows the clearest advantage over label overlap on FSD50K.

B. Quantifying Linear Alignment

  • Canonical correlations are higher for true pairings than permutations across all models and datasets, with larger separation on FSD50K and the strongest separation for CLAP.This establishes linear source-label alignment, not additive generalization.Source: B. Quantifying Linear Alignment · p. 3, Figure 2 · p. 4

C. Quantifying Additive Generalization

V. CONCLUSIONS

The conclusions find strong evidence of additive compositionality for CLAP, but only partial evidence for Wav2Vec2 and HuBERT. Across the evaluation, representations align with sound-source labels and support better held-out reconstruction than a permuted baseline, while residuals indicate limits to ideal additivity.

V. CONCLUSIONS

  • CLAP showed strong evidence of additive compositionality, whereas Wav2Vec2 and HuBERT showed only partial evidence.The conclusions characterize unseen mean representations as additively predictable, most clearly for CLAP.Source: §V · p. 4
  • All three models showed linear correlations with sound-source labels and better leave-one-combination-out reconstruction than the permuted baseline.On FSD50K, CLAP also outperformed label overlap in repeated combination holdouts.Source: §V · p. 4
  • All three models had reconstruction residuals, and the analysis treated clips as unordered source sets without modeling temporal arrangement.The authors suggest reverberation, masking, nonlinear encoder processing, and coherent-scene semantics may contribute to the residuals.Source: §V · p. 4
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