PolarBM: Complex-valued Boltzmann Machine for Modeling Audio Signals in Polar and Log-polar Coordinates

arXiv:2607.12417 · cs.LG, cs.SD, eess.AS, stat.ML · Submitted 2026-07-14 · Read on arXiv

Toru Nakashika, Kohei Yatabe

cs.LG, cs.SD, eess.AS, stat.ML

Submitted: 2026-07-14

Comments: Submitted to IEEE Trans. ASLP

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Boltzmann Machine — 22× in this paper
• Generalization — 3× in this paper · explained in 14 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Adam — 2× in this paper · explained in 3 episodes
• Decoder — 2× in this paper · explained in 2 episodes
• Computational Efficiency — 1× in this paper · explained in 2 episodes
• Conditional Independence — 1× in this paper · explained in 2 episodes
• Downstream Tasks — 1× in this paper · explained in 2 episodes
• Editor — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Latent Representation — 1× in this paper · explained in 2 episodes
• Latent Representations — 1× in this paper · explained in 3 episodes
• Latent Variables — 1× in this paper · explained in 2 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Parameterization — 1× in this paper · explained in 2 episodes
• Power Distribution — 1× in this paper · explained in 2 episodes
• Representation Learning — 1× in this paper · explained in 3 episodes
• Training Objective — 1× in this paper · explained in 3 episodes
• Training Objectives — 1× in this paper · explained in 2 episodes

Sources

• A Survey of Complex-Valued Neural Networks
• Complex Amplitude-Phase Boltzmann Machines
• A Power-Weighted Noncentral Complex Gaussian Distribution
• The Complex Gradient Operator and the CR-Calculus

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