# CoRe: Coherency Regularization for Hierarchical Time Series

arXiv: https://arxiv.org/abs/2502.15983 · HTML: https://mlsanity.com/paper/2502.15983/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 36 references that are in the map.
- First posted on arXiv 21 Feb 2025.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [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)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Temporal Latent Auto-Encoder: A Method for Probabilistic Multivariate Time Series Forecasting](https://mlsanity.com/paper/2101.10460/) (2021)
- [Time-Series Forecasting for Out-of-Distribution Generalization Using Invariant Learning](https://mlsanity.com/paper/2406.09130/) (2024)
- [Simultaneously Reconciled Quantile Forecasting of Hierarchically Related Time Series](https://mlsanity.com/paper/2102.12612/) (2021)
- [Probabilistic forecast reconciliation under the Gaussian framework](https://mlsanity.com/paper/2103.11128/) (2021)

## Abstract (arXiv)

Hierarchical time series forecasting presents unique challenges, particularly when dealing with noisy data that may not perfectly adhere to aggregation constraints. This paper introduces a novel approach to soft coherency in hierarchical time series forecasting using neural networks. We present a network coherency regularization method, which we denote as CoRe (Coherency Regularization), a technique that trains neural networks to produce forecasts that are inherently coherent across hierarchies, without strictly enforcing aggregation constraints. Our method offers several key advantages. (1) It provides theoretical guarantees on the coherency of forecasts, even for out-of-sample data. (2) It is adaptable to scenarios where data may contain errors or missing values, making it more robust than strict coherency methods. (3) It can be easily integrated into existing neural network architectures for time series forecasting. We demonstrate the effectiveness of our approach on multiple benchmark datasets, comparing it against state-of-the-art methods in both coherent and noisy data scenarios. Additionally, our method can be used within existing generative probabilistic forecasting frameworks to generate coherent probabilistic forecasts. Our results show improved generalization and forecast accuracy, particularly in the presence of data inconsistencies. On a variety of datasets, including both strictly hierarchically coherent and noisy data, our training method has either equal or better accuracy at all levels of the hierarchy while being strictly more coherent out-of-sample than existing soft-coherency methods.