# Beyond Magnitude and Shape: A Direction-Aware Loss for Time Series Forecasting

arXiv: https://arxiv.org/abs/2608.01857 · HTML: https://mlsanity.com/paper/2608.01857/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [Fast Differentiable Sorting and Ranking](https://mlsanity.com/paper/2002.08871/) (2020)
- [Less Is More: Fast Multivariate Time Series Forecasting with Light Sampling-oriented MLP Structures](https://mlsanity.com/paper/2207.01186/) (2022)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [Shape and Time Distortion Loss for Training Deep Time Series Forecasting Models](https://mlsanity.com/paper/1909.09020/) (2019)
- [Applications of deep learning in stock market prediction: recent progress](https://mlsanity.com/paper/2003.01859/) (2020)
- [Mean Absolute Directional Loss as a New Loss Function for Machine Learning Problems in Algorithmic Investment Strategies](https://mlsanity.com/paper/2309.10546/) (2023)

## Built on by (most cited first, 4 of 4)

- [EXAONE Finance 1.0: An Attention-free Time Series Foundation Model for Financial Time Series](https://mlsanity.com/paper/2609.04239/) (2026)
- [Explaining Time Series Forecasting with Horizon-Resolved Attribution](https://mlsanity.com/paper/2609.12639/) (2026)
- [EXAONE Demand 1.0: A Time Series Foundation Model for Demand Forecasting](https://mlsanity.com/paper/2609.30880/) (2026)
- [DPAL: A Test-Time Adaptation Loss for Financial Time Series Forecasting](https://mlsanity.com/paper/2610.14376/) (2026)

## Abstract (arXiv)

The direction of change --- whether a series will move up or down --- is often as important as its exact value in decisiondriven applications such as risk management and financial forecasting. However, most forecasting losses optimize either point magnitude or shape and frequency structure, and none explicitly targets the direction of change. In this paper, we find that MSE-trained forecasters fail on the direction of small moves. To address this, we propose CosDir, a simple yet effective direction-aware loss that aligns the difference vectors of the prediction and the target via cosine similarity. Being scale-invariant, CosDir keeps a directional gradient on small moves, re-injecting learning signal exactly where MSE neglects it. CosDir is a lightweight, plug-in term that attaches to any backbone without architectural modification. Since the best ratio for mixing the directional and magnitude terms differs across datasets, we further propose CosDir-UW, an extension that makes this ratio adaptive by learning it during training, matching a per-dataset tuned weight with no hyperparameter. We conduct over 100K experiments, demonstrating that our method consistently and significantly improves directional accuracy while preserving magnitude accuracy, and that it outperforms various loss functions. Code is available at: https://github.com/seunghan96/cosdir.