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Hierarchical Classification Auxiliary Network for Time Series Forecasting
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Proposes HCAN, a model-agnostic hierarchical classification auxiliary network that tokenizes time series values into coarse and fine classes with evidential uncertainty-aware classifiers and a hierarchical consistency loss, improving MSE of several forecasting backbones.
Problem
MSE-trained deep time series forecasters produce over-smooth predictions that lack high-entropy feature representations, and discretizing values into classes suffers from boundary effects near class edges.
Approach
Reformulates forecasting as hierarchical classification (1, 2 and 4 classes) trained with evidential (Dirichlet) uncertainty-aware cross-entropy, adds a symmetric KL-based hierarchical consistency loss across levels, and fuses the class-level features with backbone features via a Hierarchy-Aware Attention module.
Key results
- HCAN improves MSE over backbones in 66 of 70 multivariate cases, e.g. Informer on ETTh2 averages 4.779 -> 2.359 MSE.
- Averaged across ETT datasets HCAN reduces MSE by 9.1%, 35.5%, 10.2%, and 22.3% for the reported backbones.
- Univariate results show overall MSE reductions of 23.0%, 35.8%, 7.5%, 12.6%, 2.5%, 22.8%, and 1.5% across the reported settings.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add HCAN to Informer | Informer · ETTh1, ETTh2, ETTm1, ETTm2, Weather, Exchange, ILI, Electricity, Traffic, Solar Wind | MSE: ETTh1: 1.077 -> 0.897; ETTh2: 4.779 -> 2.359; ETTm1: 0.951 -> 0.717; ETTm2: 1.729 -> 0.981; Weather: 0.733 -> 0.370; Exc | Helped |
| add HCAN to forecasting backbones | Informer, Autoformer, PatchTST, SCINet, DLinear, iTransformer, FITS · Multivariate long sequence forecasting | MSE: 66 out of 70 cases | Mixed |
| add HCAN to forecasting backbones | baseline models · Univariate ETT and Solar Wind | MSE: 23.0%, 35.8%, 7.5%, 12.6%, 2.5%, 22.8%, and 1.5% | Helped |
| add fine-grained UAC loss (ablation) | Informer+HCAN · Weather and Solar Wind | MSE: Weather: 0.352 -> 0.349, 0.636 -> 0.509, 0.680 -> 0.613, 1.265 -> 0.993; Solar Wind: 1.710 -> 0.991, 1.991 -> 1.077, 1.9 | Helped |
| add relative regression loss to fine-grained UAC (ablation) | Informer+HCAN · Weather and Solar Wind | MSE: Weather: 0.349 -> 0.300, 0.509 -> 0.515, 0.613 -> 0.579, 0.993 -> 0.999; Solar Wind: 0.991 -> 0.964, 1.077 -> 1.060, 1.1 | Mixed |
| add coarse-grained hierarchy features (ablation) | Informer+HCAN · Weather and Solar Wind | MSE: Weather: 0.300 -> 0.322, 0.515 -> 0.406, 0.579 -> 0.580, 0.999 -> 0.961; Solar Wind: 0.964 -> 0.948, 1.060 -> 1.048, 1.1 | Mixed |
| add hierarchical consistency loss (HCL) (ablation) | Informer+HCAN · Weather and Solar Wind | MSE: Weather: 0.322 -> 0.295, 0.406 -> 0.345, 0.580 -> 0.395, 0.961 -> 0.614; Solar Wind: 0.948 -> 0.935, 1.048 -> 1.038, 1.0 | Helped |
| replace direct concatenation with HAA (ablation) | Informer+HCAN · Weather and Solar Wind | MSE: Weather: 0.295 -> 0.291, 0.345 -> 0.306, 0.395 -> 0.369, 0.614 -> 0.513; Solar Wind: 0.935 -> 0.920, 1.038 -> 1.027, 1.0 | Helped |
Surprising findings
- Reported gains are largest for weaker backbones such as Informer, with smaller gains for strong models like PatchTST and FITS.
Limitations
- Relies on grid-searched loss weights and bin partitions, adding hyperparameters.
- Boundary effects are only mitigated, not eliminated, per the authors' qualitative analysis.
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Weather Exchange-Rate ILI Electricity Traffic Solar Wind
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Weather Exchange-Rate ILI Electricity Traffic Solar Wind
Metrics: MSE MAE
Baselines: Informer Autoformer PatchTST SCINet DLinear iTransformer FITS
Builds on: Evidential Deep Learning Informer PatchTST iTransformer
Closest papers by meaning
- Graph-based Time Series Clustering for End-to-End Hierarchical Forecasting (ICML 2024 · similarity 0.87)
- CATS: Enhancing Multivariate Time Series Forecasting by Constructing Auxiliary Time Series as Exogenous Variables (ICML 2024 · similarity 0.87)
- Hi-Patch: Hierarchical Patch GNN for Irregular Multivariate Time Series (ICML 2025 · similarity 0.86)
- DDN: Dual-domain Dynamic Normalization for Non-stationary Time Series Forecasting (NeurIPS 2024 · similarity 0.86)
- Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts (ICLR 2025 · similarity 0.85)
- Learning Optimal Projection for Forecast Reconciliation of Hierarchical Time Series (ICML 2024 · similarity 0.85)
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