# PHALAR: Phasors for Learned Musical Audio Representations

arXiv: https://arxiv.org/abs/2605.03929 · HTML: https://mlsanity.com/paper/2605.03929/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 56 references that are in the map.
- First posted on arXiv 5 May 2026.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [HuBERT: Self-Supervised Speech Representation Learning by Masked Prediction of Hidden Units](https://mlsanity.com/paper/2106.07447/) (2021)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Large-scale Contrastive Language-Audio Pretraining with Feature Fusion and Keyword-to-Caption Augmentation](https://mlsanity.com/paper/2211.06687/) (2022)
- [CNN Architectures for Large-Scale Audio Classification](https://mlsanity.com/paper/1609.09430/) (2016)
- [High Fidelity Neural Audio Compression](https://mlsanity.com/paper/2210.13438/) (2022)
- [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://mlsanity.com/paper/2301.12503/) (2023)
- [High-Fidelity Audio Compression with Improved RVQGAN](https://mlsanity.com/paper/2306.06546/) (2023)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Stable Audio Open](https://mlsanity.com/paper/2407.14358/) (2024)
- [MERT: Acoustic Music Understanding Model with Large-Scale Self-supervised Training](https://mlsanity.com/paper/2306.00107/) (2023)
- [Contrastive Learning of General-Purpose Audio Representations](https://mlsanity.com/paper/2010.10915/) (2020)
- [Meta Audiobox Aesthetics: Unified Automatic Quality Assessment for Speech, Music, and Sound](https://mlsanity.com/paper/2502.05139/) (2025)
- [Adapting Frechet Audio Distance for Generative Music Evaluation](https://mlsanity.com/paper/2311.01616/) (2023)
- [Cutting Music Source Separation Some Slakh: A Dataset to Study the Impact of Training Data Quality and Quantity](https://mlsanity.com/paper/1909.08494/) (2019)
- [Contrastive Learning of Musical Representations](https://mlsanity.com/paper/2103.09410/) (2021)
- [Spectral Representations for Convolutional Neural Networks](https://mlsanity.com/paper/1506.03767/) (2015)
- [ViSQOL v3: An Open Source Production Ready Objective Speech and Audio Metric](https://mlsanity.com/paper/2004.09584/) (2020)
- [Phase-aware Speech Enhancement with Deep Complex U-Net](https://mlsanity.com/paper/1903.03107/) (2019)
- [CDPAM: Contrastive learning for perceptual audio similarity](https://mlsanity.com/paper/2102.05109/) (2021)

## Built on by (most cited first, 1 of 1)

- [Capturing Cardiac Cyclicity through Phase-Equivariant Self-Supervised Learning](https://mlsanity.com/paper/2608.21147/) (2026)

## Abstract (arXiv)

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 ≈ 70% over the state-of-the-art while requiring <50% of the parameters and a 7× training speedup. By utilizing a Learned Spectral Pooling layer and a complex-valued head, PHALAR enforces pitch-equivariant 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.