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

arXiv: https://arxiv.org/abs/2601.18829 · HTML: https://mlsanity.com/paper/2601.18829/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 21 references that are in the map.
- First posted on arXiv 25 Jan 2026.

## Builds on (most cited first, 14 of 14)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [Instance-aware Dynamic Prompt Tuning for Pre-trained Point Cloud Models](https://mlsanity.com/paper/2304.07221/) (2023)
- [Patch-wise Structural Loss for Time Series Forecasting](https://mlsanity.com/paper/2503.00877/) (2025)
- [Adaptive Multi-Scale Decomposition Framework for Time Series Forecasting](https://mlsanity.com/paper/2406.03751/) (2024)
- [LCM: Locally Constrained Compact Point Cloud Model for Masked Point Modeling](https://mlsanity.com/paper/2405.17149/) (2024)
- [TILDE-Q: A Transformation Invariant Loss Function for Time-Series Forecasting](https://mlsanity.com/paper/2210.15050/) (2022)
- [CASL: Curvature-Augmented Self-supervised Learning for 3D Anomaly Detection](https://mlsanity.com/paper/2511.12909/) (2025)

## Abstract (arXiv)

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.