PHALAR: Phasors for Learned Musical Audio Representations

Stem retrieval, the task of matching missing stems to a given audio submix, is a key challenge currently limited by models that discard temporal information. We introduce PHALAR, a contrastive framework achieving a relative accuracy increase of up to $\approx 70$% over the state-of-the-art while requiring $<50$% of the parameters and a 7$\times$ training speedup. By utilizing a Learned Spectral Pooling layer and a complex-valued head, PHALAR enforces pitch-invariant and phase-equivariant biases. PHALAR establishes new retrieval state-of-the-art across MoisesDB, Slakh, and ChocoChorales, correlating significantly higher with human coherence judgment than semantic baselines. Finally, zero-shot beat tracking and linear chord probing confirm that PHALAR captures robust musical structures beyond the retrieval task.

When music is mixed, every instrument must lock together in time. A drummer even slightly off-beat with the bassist makes the whole track feel wrong. Current AI models are blind to this: designed to recognize what is in a recording, they discard the timing information needed to judge whether those parts actually fit together. We introduce PHALAR, a model that fixes this by exploiting a mathematical property of sound. Shifting audio in time rotates its frequency-domain representation by a proportional angle, and rather than throwing this rotation away like standard models do, PHALAR is built to preserve it, encoding rhythmic alignment as a geometric angle in a complex-valued space. The result is a model that judges musical coherence up to 70% more accurately than the previous best approach, using half the parameters and training seven times faster, while aligning significantly closer with how human listeners perceive whether stems belong together.