Do Audio Representations Compose Additively?

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.