Adversarial Audio Synthesis with Complex-valued Polynomial Networks
This work addresses the challenge of modeling complex-valued audio representations for researchers in audio synthesis, offering a novel method that improves performance on specific benchmarks.
The paper tackled the problem of suboptimal performance in audio synthesis due to overlooking the complex-valued nature of time-frequency representations by introducing APOLLO, a complex-valued polynomial network, which achieved a 17.5% improvement over adversarial methods and 8.2% over state-of-the-art diffusion models on the SC09 dataset.
Time-frequency (TF) representations in audio synthesis have been increasingly modeled with real-valued networks. However, overlooking the complex-valued nature of TF representations can result in suboptimal performance and require additional modules (e.g., for modeling the phase). To this end, we introduce complex-valued polynomial networks, called APOLLO, that integrate such complex-valued representations in a natural way. Concretely, APOLLO captures high-order correlations of the input elements using high-order tensors as scaling parameters. By leveraging standard tensor decompositions, we derive different architectures and enable modeling richer correlations. We outline such architectures and showcase their performance in audio generation across four benchmarks. As a highlight, APOLLO results in $17.5\%$ improvement over adversarial methods and $8.2\%$ over the state-of-the-art diffusion models on SC09 dataset in audio generation. Our models can encourage the systematic design of other efficient architectures on the complex field.