PolarBM: Complex Boltzmann Machine Models Audio with Amplitude-Phase Dependencies
New AI method treats audio as complex numbers, capturing phase-amplitude links other models ignore.
A new paper from arXiv introduces PolarBM, a complex-valued Boltzmann machine designed to model audio signals in polar (amplitude-phase) coordinates. Conventional machine learning methods typically discard phase information by treating complex-valued spectra as real vectors, losing critical structural relationships. PolarBM defines a probability density where phase explicitly depends on amplitude, capturing physically important couplings present in audio, wireless, and quantum signals.
To align with human auditory perception, the authors also propose LogPolarBM, which models amplitude on a logarithmic scale. This yields a flexible power-weighted noncentral complex Gaussian distribution, whose marginal amplitude covers Rice, Nakagami, and noncentral chi distributions as special cases. Restricted variants (PolarRBM and LogPolarRBM) are provided for practical use. Experiments demonstrate that explicitly modeling amplitude-phase dependency achieves superior modeling accuracy compared to standard deep neural networks. While tested on audio, the approach extends to any field dealing with complex-valued data.
- PolarBM models complex variables in polar coordinates, preserving amplitude-phase dependencies ignored by real-valued methods.
- LogPolarBM adapts to human auditory perception using log-scale amplitude, with a flexible probability distribution that generalizes Rice, Nakagami, and chi distributions.
- Restricted variants PolarRBM and LogPolarRBM outperform conventional DNNs in modeling accuracy, with potential applications in wireless communications and quantum mechanics.
Why It Matters
This approach could improve audio processing, wireless signal analysis, and quantum simulations by preserving critical phase information.