# EuleroDec: A Complex-Valued RVQ-VAE for Efficient and Robust Audio Coding

arXiv: https://arxiv.org/abs/2601.17517 · HTML: https://mlsanity.com/paper/2601.17517/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 29 references that are in the map.
- First posted on arXiv 24 Jan 2026.

## Builds on (most cited first, 23 of 23)

- [HiFi-GAN: Generative Adversarial Networks for Efficient and High Fidelity Speech Synthesis](https://mlsanity.com/paper/2010.05646/) (2020)
- [Autoregressive Image Generation using Residual Quantization](https://mlsanity.com/paper/2203.01941/) (2022)
- [High Fidelity Neural Audio Compression](https://mlsanity.com/paper/2210.13438/) (2022)
- [High-Fidelity Audio Compression with Improved RVQGAN](https://mlsanity.com/paper/2306.06546/) (2023)
- [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018)
- [Dilated Residual Networks](https://mlsanity.com/paper/1705.09914/) (2017)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [DCCRN: Deep Complex Convolution Recurrent Network for Phase-Aware Speech Enhancement](https://mlsanity.com/paper/2008.00264/) (2020)
- [SoundStorm: Efficient Parallel Audio Generation](https://mlsanity.com/paper/2305.09636/) (2023)
- [LibriTTS-R: A Restored Multi-Speaker Text-to-Speech Corpus](https://mlsanity.com/paper/2305.18802/) (2023)
- [Robust Training of Vector Quantized Bottleneck Models](https://mlsanity.com/paper/2005.08520/) (2020)
- [AudioDec: An Open-source Streaming High-fidelity Neural Audio Codec](https://mlsanity.com/paper/2305.16608/) (2023)
- [FunCodec: A Fundamental, Reproducible and Integrable Open-source Toolkit for Neural Speech Codec](https://mlsanity.com/paper/2309.07405/) (2023)
- [Building Blocks for a Complex-Valued Transformer Architecture](https://mlsanity.com/paper/2306.09827/) (2023)
- [FlowDec: A flow-based full-band general audio codec with high perceptual quality](https://mlsanity.com/paper/2503.01485/) (2025)
- [APCodec: A Neural Audio Codec with Parallel Amplitude and Phase Spectrum Encoding and Decoding](https://mlsanity.com/paper/2402.10533/) (2024)
- [High-Resolution Speech Restoration with Latent Diffusion Model](https://mlsanity.com/paper/2409.11145/) (2024)
- [ScoreDec: A Phase-preserving High-Fidelity Audio Codec with A Generalized Score-based Diffusion Post-filter](https://mlsanity.com/paper/2401.12160/) (2024)
- [Complex-valued Spatial Autoencoders for Multichannel Speech Enhancement](https://mlsanity.com/paper/2108.03130/) (2021)
- [APCodec+: A Spectrum-Coding-Based High-Fidelity and High-Compression-Rate Neural Audio Codec with Staged Training Paradigm](https://mlsanity.com/paper/2410.22807/) (2024)
- [STFTCodec: High-Fidelity Audio Compression through Time-Frequency Domain Representation](https://mlsanity.com/paper/2503.16989/) (2025)
- [ComplexDec: A Domain-robust High-fidelity Neural Audio Codec with Complex Spectrum Modeling](https://mlsanity.com/paper/2502.02019/) (2025)
- [Complex-valued Neural Networks -- Theory and Analysis](https://mlsanity.com/paper/2312.06087/) (2023)

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

- [PHALAR: Phasors for Learned Musical Audio Representations](https://mlsanity.com/paper/2605.03929/) (2026)

## Abstract (arXiv)

Audio codecs power discrete music generative modelling, music streaming and immersive media by shrinking PCM audio to bandwidth-friendly bit-rates. Recent works have gravitated towards processing in the spectral domain; however, spectrogram-domains typically struggle with phase modeling which is naturally complex-valued. Most frequency-domain neural codecs either disregard phase information or encode it as two separate real-valued channels, limiting spatial fidelity. This entails the need to introduce adversarial discriminators at the expense of convergence speed and training stability to compensate for the inadequate representation power of the audio signal. In this work we introduce an end-to-end complex-valued RVQ-VAE audio codec that preserves magnitude-phase coupling across the entire analysis-quantization-synthesis pipeline and removes adversarial discriminators and diffusion post-filters. Without GANs or diffusion we match or surpass much longer-trained baselines in-domain and reach SOTA out-of-domain performance. Compared to standard baselines that train for hundreds of thousands of steps, our model reducing training budget by an order of magnitude is markedly more compute-efficient while preserving high perceptual quality.