# C3RL: Rethinking the Combination of Channel-independence and Channel-mixing from Representation Learning

arXiv: https://arxiv.org/abs/2507.17454 · HTML: https://mlsanity.com/paper/2507.17454/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 23 Jul 2025.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)

## Built on by (most cited first, 1 of 1)

- [IBN: An Interpretable Bidirectional-Modeling Network for Multivariate Time Series Forecasting with Variable Missing](https://mlsanity.com/paper/2509.07725/) (2025)

## Abstract (arXiv)

Multivariate time series forecasting has drawn increasing attention due to its practical importance. Existing approaches typically adopt either channel-mixing (CM) or channel-independence (CI) strategies. CM strategy can capture inter-variable dependencies but fails to discern variable-specific temporal patterns. CI strategy improves this aspect but fails to fully exploit cross-variable dependencies like CM. Hybrid strategies based on feature fusion offer limited generalization and interpretability. To address these issues, we propose C3RL, a novel representation learning framework that jointly models both CM and CI strategies. Motivated by contrastive learning in computer vision, C3RL treats the inputs of the two strategies as transposed views and builds a siamese network architecture: one strategy serves as the backbone, while the other complements it. By jointly optimizing contrastive and prediction losses with adaptive weighting, C3RL balances representation and forecasting performance. Extensive experiments on seven models show that C3RL boosts the best-case performance rate to 81.4% for models based on CI strategy and to 76.3% for models based on CM strategy, demonstrating strong generalization and effectiveness.