Sound is naturally described by a complex number, where loudness is the wave's strength and phase is its timing. Ordinary neural networks split this into two separate coordinates, like giving directions: 'two blocks east, one block north.' But the connection is lost: loudness and phase change together, like distance and direction.
The model based on Ludwig Boltzmann's ideas about entropy works directly with the 'distance–direction' pair. To handle sound spectra, they added a logarithmic scale — after all, the ear perceives a tenfold power jump as just a doubling of loudness. Thus, LogPolarBM was born, encompassing the well-known Rice and Nakagami distributions as special cases. In audio tests, it even outperformed deep neural networks.
An unexpected twist: the same principle applies in wireless communications and quantum physics. Wave phases are critical for quantum computing, and the machine's 'hearing' helps extract from the signal what older methods missed.
The ear compresses loudness: a 10x power jump feels like a doubling. Engineers have long used the logarithmic decibel scale. LogPolarBM bakes this trait right into the neural network, achieving high accuracy.