Research map / Time series / Long-term forecasting
Rethinking Time Encoding via Learnable Transformation Functions
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Proposes LeTE, a time encoding whose non-linear transformations (Fourier series or B-splines) are learnable, generalizing functional time encodings, and evaluates it on sequential MNIST, time series forecasting, dynamic graph link prediction, and a financial risk control task.
Problem
Existing time encodings (hand-crafted and functional) rely on fixed pre-defined non-linearities such as sine, so they capture only specific periodic patterns and struggle with non-periodic and mixed time patterns.
Approach
Parameterize the non-linear transformation in time encoding with deep function learning (Fourier series expansion and B-splines, KAN-style) so that the activation is learnable jointly with the model; a combined variant splits dimensions between the two. Previous functional time encodings are shown to be special cases.
Key results
- LeTE applied to the Transformer reduces average MAE and MSE across time series datasets by 25.1% and 46.5% respectively, with an overall 98% win rate on MAE versus HCTE.
- On dynamic graph link prediction, LeTE outperforms FTE for all four baselines (TGAT, TGN, TCL, DyGFormer) on Wikipedia, Reddit, MOOC, and LastFM in transductive and inductive settings.
- LeTE with 2, 8, or 16 dimensions outperforms the 100-dimensional FTE on dynamic graph link prediction.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace HCTE with LeTE | Transformer · Time-series forecasting across datasets and prediction lengths | MAE: average MAE and MSE across all datasets by 25.1% and 46.5% | Helped |
| Replace FTE with LeTE | Time-series forecasting baselines · ETT, Electricity, Exchange, and Weather | MAE: 98% | Helped |
| Replace FTE with LeTE | Dynamic graph link prediction baselines · Wikipedia, Reddit, MOOC, and LastFM; transductive and inductive | AP | Helped |
| Replace FTE with LeTE | TGAT · Wikipedia transductive | AP: 96.95 ± 0.24 -> 97.82 ± 0.09 | Helped |
| Replace FTE with LeTE | TGN · Reddit inductive | AP: 97.50 ± 0.07 -> 97.65 ± 0.04 | Helped |
| Replace FTE with LeTE | TCL · MOOC inductive | AP: 80.60 ± 0.22 -> 82.72 ± 0.12 | Helped |
| Replace FTE with LeTE | DyGFormer · LastFM inductive | AP: 94.23 ± 0.09 -> 94.69 ± 0.12 | Helped |
| Use LeTE instead of no time encoding | Financial risk-control model · Tencent Mobile Payment | classification performance | Helped |
| Use LeTE instead of FTE at lower time-encoding dimensions | Dynamic graph link prediction models · Wikipedia/TGN and MOOC/TGN | AP: 2, 8 or 16; 100-dimensional | Helped |
Surprising findings
- Models using LeTE with very low dimensions (2, 8, or 16) outperform 100-dimensional FTE on dynamic graph link prediction.
Limitations
- Real-world financial risk control dataset is proprietary and not released, limiting reproducibility.
- Time series experiments use only absolute timestamps and dynamic graph experiments use relative time, with the design choices for p and spline basis left as hyperparameters.
Experimental setup
Datasets: sequential MNIST ETT Electricity Exchange Weather Wikipedia Reddit MOOC LastFM Tencent Mobile Payment risk control data
Benchmarks: sequential MNIST ETT Electricity Exchange Weather Wikipedia Reddit MOOC LastFM
Metrics: MAE MSE AP AUC-ROC accuracy win rate
Baselines: HCTE FTE Transformer Pyraformer Non-stationary Transformer MICN TimesNet TGAT TGN TCL DyGFormer
Builds on: Functional Time Representation Time2Vec KAN TGAT DyGFormer
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