CP Loss: Channel-wise Perceptual Loss for Time Series Forecasting

TL;DR

Multi-channel time-series forecasting suffers from channel heterogeneity and the drawbacks of channel-agnostic losses like $\mathcal{L}$, which can blunt dynamics in volatile channels. The authors propose Channel-wise Perceptual Loss (CP Loss), which learns a per-channel perceptual space via a differentiable, channel-specific filter that decomposes each channel into multi-scale representations and drives learning with $\mathcal{L}_{CP\ Loss} = \sum_{k=1}^{K} l(\tau_k, \hat{\tau}_k)$. This loss is optimized jointly with the forecasting model, yielding task-aligned representations that provide sharper gradients for prediction. Empirical results on six real-world datasets across four backbones show consistent improvements over MSE and competitive gains against other perceptual losses, with CP Loss achieving notable MAE reductions on the ETTm1 and Weather datasets. The approach is lightweight (parameter count scales as $C\times k$ with small $k$) and scalable, offering a practical, dynamics-aware alternative for multivariate time-series forecasting.

Abstract

Multi-channel time-series data, prevalent across diverse applications, is characterized by significant heterogeneity in its different channels. However, existing forecasting models are typically guided by channel-agnostic loss functions like MSE, which apply a uniform metric across all channels. This often leads to fail to capture channel-specific dynamics such as sharp fluctuations or trend shifts. To address this, we propose a Channel-wise Perceptual Loss (CP Loss). Its core idea is to learn a unique perceptual space for each channel that is adapted to its characteristics, and to compute the loss within this space. Specifically, we first design a learnable channel-wise filter that decomposes the raw signal into disentangled multi-scale representations, which form the basis of our perceptual space. Crucially, the filter is optimized jointly with the main forecasting model, ensuring that the learned perceptual space is explicitly oriented towards the prediction task. Finally, losses are calculated within these perception spaces to optimize the model. Code is available at https://github.com/zyh16143998882/CP_Loss.

Figures (4)

• Figure 1: The prediction results of different channels.
• Figure 2: The pipeline of our channel-wise perceptual loss.
• Figure 3: The detail of our perceptual filter.
• Figure 4: The effect of different scales.