Amplitude-Phase Reconstruct Network (APRNet)

• The paper introduces APRNet as an umbrella term for methods that use amplitude-phase recombination to improve model robustness through frequency-domain augmentations.
• Key implementations include APNet for neural vocoding and TimeAPN for forecasting, demonstrating practical applications in audio synthesis and non-stationary signal normalization.
• The framework enhances performance by explicitly modeling amplitude and phase, enabling effective handling of noise and distortions in complex data.

Searching arXiv for the cited papers and closely related terminology. “Amplitude-Phase Reconstruct Network” (APRNet) is not introduced as a canonical method name in the cited arXiv literature. The closest faithful usages span several distinct amplitude–phase formulations: a Fourier-domain data augmentation strategy for CNN robustness, namely Amplitude-Phase Recombination (APR) (Chen et al., 2021); a neural vocoder, APNet, that predicts amplitude and phase spectra and reconstructs waveforms by ISTFT (Ai et al., 2023); a phase–amplitude network reconstruction framework for electrophysiological dynamics (Yeldesbay et al., 2024); and TimeAPN, a forecasting normalization framework that models amplitude- and phase-related non-stationarity (Hu et al., 18 Mar 2026). Accordingly, “APRNet” is best treated as an umbrella label for architectures or training schemes that reconstruct, recombine, or explicitly model amplitude and phase, rather than as a single standardized architecture.

1. Terminological scope and definitional boundaries

In the vision paper “Amplitude-Phase Recombination: Rethinking Robustness of Convolutional Neural Networks in Frequency Domain” (Chen et al., 2021), there is no specialized backbone named APRNet. The method is a training-time data augmentation strategy called Amplitude-Phase Recombination (APR), with two concrete schemes, APR-P and APR-S, and their combination APR-SP. A faithful interpretation of an informal “APRNet” in that context is therefore a standard CNN trained with APR augmentation, rather than a newly defined network architecture.

In the speech paper “APNet: An All-Frame-Level Neural Vocoder Incorporating Direct Prediction of Amplitude and Phase Spectra” (Ai et al., 2023), APNet is explicitly a neural vocoder that reconstructs speech waveforms by separately predicting amplitude and phase spectra and combining them through inverse short-time Fourier transform. This is closer to the literal reading of an “amplitude-phase reconstruction network,” but the formal method name is APNet, not APRNet.

In electrophysiology, “Reconstruction of phase-amplitude dynamics from electrophysiological signals” (Yeldesbay et al., 2024) develops a data-driven reconstruction of interacting oscillatory systems in phase–amplitude coordinates. Here the relevant object is a network of phase-amplitude oscillators whose interactions are represented by coupling functions in reduced coordinates. This is a network in the dynamical-systems sense, not a neural network architecture.

In forecasting, “TimeAPN: Adaptive Amplitude-Phase Non-Stationarity Normalization for Time Series Forecasting” (Hu et al., 18 Mar 2026) is a model-agnostic wrapper around forecasting backbones. It explicitly extracts, predicts, and reintegrates amplitude-, phase-, and mean-related non-stationary factors. This suggests that later uses of “APRNet” may sometimes denote amplitude-phase-aware reconstruction or de-normalization modules rather than a single family of models.

2. Frequency-domain recombination for robust vision

The APR framework in (Chen et al., 2021) begins from the frequency-domain representation of an image $x$: $$\mathcal{F}_x = \mathcal{A}_x \otimes e^{i \cdot \mathcal{P}_x},$$ where $\mathcal{A}_x$ is the amplitude spectrum and $\mathcal{P}_x$ is the phase spectrum. Training samples are reconstructed by the inverse transform,

$$iDFT(\mathcal{A}_x \otimes e^{i \cdot \mathcal{P}_x}).$$

The paper also defines a transfer function

$$\hat{z} = \left\{ \begin{array}{ll} 1, & z = 0 \ z, & otherwise. \end{array} \right.$$

to avoid zero entries suppressing phase information when filtered subbands are combined.

The central claim is that CNNs tend to overuse amplitude cues even though amplitude is “easily disturbed such as noises or common corruptions,” whereas phase carries structured information that better supports robust recognition (Chen et al., 2021). The paper states that CNNs “tends to converge at the local optimum which is closely related to the high-frequency components of the training images,” and contrasts this with empirical observations that “humans rely on more phase components to achieve robust recognition.” The resulting training objective is to alter amplitude while preserving the phase donor’s semantics, so that the label is inherited from the phase source.

The pairwise scheme APR-P takes two samples $(x_i,y_i)$ and $(x_j,y_j)$ and constructs

$$APR_P(x_i,x_j) = iDFT(\mathcal{A}_{x_j} \otimes e^{i \cdot \mathcal{P}_{x_i}}),$$

with training pairs $(APR_P(x_i,x_j), y_i)$ and $$\mathcal{F}_x = \mathcal{A}_x \otimes e^{i \cdot \mathcal{P}_x},$$0. The label follows the phase donor image. The single-image scheme APR-S recombines a sample with a transformed version of itself using a transformation set $$\mathcal{F}_x = \mathcal{A}_x \otimes e^{i \cdot \mathcal{P}_x},$$1, keeping the phase of one transformed view and replacing its amplitude