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.

利用 APOLLO 多项式复数网络，在语音合成中自然地整合了复数值的时频表示，并通过标准张量分解来实现不同的结构，实现更丰富的相关性建模，同时提高 SC09 数据集上的音频生成性能。

利用复数多项式网络的对抗性音频合成