# MoDEx: Mixture of Depth-specific Experts for Multivariate Long-term Time Series Forecasting

arXiv: https://arxiv.org/abs/2602.00624 · HTML: https://mlsanity.com/paper/2602.00624/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 19 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Builds on (most cited first, 8 of 8)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion](https://mlsanity.com/paper/2404.14197/) (2024)

## Abstract (arXiv)

Multivariate long-term time series forecasting (LTSF) supports critical applications such as traffic-flow management, solar-power scheduling, and electricity-transformer monitoring. The existing LTSF paradigms follow a three-stage pipeline of embedding, backbone refinement, and long-horizon prediction. However, the behaviors of individual backbone layers remain underexplored. We introduce layer sensitivity, a gradient-based metric inspired by GradCAM and effective receptive field theory, which quantifies both positive and negative contributions of each time point to a layer's latent features. Applying this metric to a three-layer MLP backbone reveals depth-specific specialization in modeling temporal dynamics in the input sequence. Motivated by these insights, we propose MoDEx, a lightweight Mixture of Depth-specific Experts, which replaces complex backbones with depth-specific MLP experts. MoDEx achieves state-of-the-art accuracy on seven real-world benchmarks, ranking first in 78 percent of cases, while using significantly fewer parameters and computational resources. It also integrates seamlessly into transformer variants, consistently boosting their performance and demonstrating robust generalizability as an efficient and high-performance LTSF framework.