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FITS: Modeling Time Series with $10k$ Parameters
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Proposes FITS, a ~10k-parameter time series model that performs interpolation in the complex frequency domain (rFFT, complex linear layer, low-pass filter, irFFT) for forecasting and anomaly detection via reconstruction.
Problem
Time series analysis (forecasting, anomaly detection) typically requires large compute-heavy models unsuitable for resource-constrained edge devices; existing frequency-aware methods do not exploit complex-valued amplitude and phase representations compactly.
Approach
Reinterpret forecasting and reconstruction as interpolation of the rFFT spectrum: a single complex-valued linear layer learns amplitude scaling and phase shift, combined with a low-pass filter whose cutoff is set by harmonics of the dominant frequency, then irFFT maps back to time domain for time-domain supervision.
Key results
- FITS achieves MSE comparable to or better than PatchTST, DLinear, FEDformer and TimesNet on most ETT, Weather and Electricity horizons while using about 4.5K–16K parameters versus 139.7K for DLinear and 1.5M for PatchTST.
- On anomaly detection, FITS reaches F1 of 99.95 on SMD and 98.9 on SWaT, but lags on SMAP (70.74) and MSL (78.12) compared with Anomaly Transformer and others.
- On M4, FITS underperforms TimesNet (e.g., yearly SMAPE 14.00 vs 13.38), which the authors attribute to short look-back windows and limited capacity.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FITS instead of the strongest listed baseline | Long-term forecasting · ETTh1, ETTh2, ETTm1, ETTm2, Weather, Electricity, and Traffic (horizon 96) | MSE: ETTh1: 0.375 -> 0.372; ETTh2: 0.274 -> 0.271; ETTm1: 0.292 -> 0.303; ETTm2: 0.163 -> 0.162; Weather: 0.151 -> 0.143; Ele | Mixed |
| Use FITS instead of the strongest listed baseline | Anomaly detection · SMD and SWaT | F1-score: SMD: 92.33 -> 99.95; SWaT: 94.07 -> 98.9 | Helped |
| Use FITS instead of the strongest listed baseline | Anomaly detection · PSM, SMAP, and MSL | F1-score: PSM: 98.54 -> 93.96; SMAP: 96.69 -> 70.74; MSL: 94.08 -> 78.12 | Hurt |
| Add backcasting supervision to forecasting supervision (ablation) | FITS · ETTh2, horizon 96; look-back 720; COF harmonic 6 | MSE: 0.271312 -> 0.271028 | Helped |
| Increase look-back window from 360 to 720 (ablation) | FITS · ETTh2 forecasting | MSE: 0.275930 -> 0.271312 | Helped |
| Increase cutoff frequency from harmonic 2 to harmonic 6 (ablation) | FITS · ETTh2, horizon 96; look-back 720; forecasting-only | MSE: 0.275600 -> 0.271312 | Helped |
| Increase look-back window from 360 to 720 (ablation) | FITS · ETTh1 forecasting | MSE: 0.372101 -> 0.379216 | Hurt |
| Use longer look-back windows (ablation) | FITS · ETTm1 forecasting | MSE | Mixed |
| Use a low cutoff frequency rather than a higher cutoff frequency (ablation) | FITS · ETTh2 forecasting | MSE | No clear effect |
| Use FITS rather than TimesNet, N-Hits, or N-Beats | Short-term forecasting · M4 yearly, quarterly, and monthly | SMAPE: Yearly: 13.38 -> 14.00; Quarterly: 10.1 -> 10.72; Monthly: 12.67 -> 13.49 | Mixed |
Surprising findings
- Increasing the cutoff frequency yields only marginal gains, while longer look-back windows generally help.
- On ETTh1 and ETTm1, longer look-back windows (720) do not help, which the authors attribute to distribution shift.
Limitations
- Underperforms on SMAP and MSL anomaly detection datasets, attributed to binary event data not captured well in frequency domain.
- Suboptimal on M4 short-term forecasting due to short look-back windows and limited capacity.
- Cutoff frequency selection is a hyperparameter requiring grid search; longer look-back windows increase parameter count.
Experimental setup
Datasets: Traffic Electricity Weather ETTh1 ETTh2 ETTm1 ETTm2 M4 SMD PSM SWaT MSL
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Weather Electricity Traffic M4 SMD PSM SWaT MSL
Metrics: MSE SMAPE Precision Recall F1-score parameter count MACs
Baselines: PatchTST TimesNet FEDformer DLinear Anomaly Transformer THOC OmniAnomaly N-BEATS N-HiTS
Builds on: DLinear RIN TimesNet
Closest papers by meaning
- MOMENT: A Family of Open Time-series Foundation Models (ICML 2024 · similarity 0.85)
- TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis (ICLR 2025 · similarity 0.85)
- Retrieval Over Training: Similarity search-based Model Selection for Time Series Anomaly Detection (NeurIPS 2026 · similarity 0.84)
- Detect, Explain, Interpret: An End-to-End Benchmark for Time Series Anomaly Detection, Explainability and Interpretability. (NeurIPS 2026 · similarity 0.84)
- Parsimony or Capability? Decomposition Delivers Both in Long-term Time Series Forecasting (NeurIPS 2024 · similarity 0.84)
- The Elephant in the Room: Towards A Reliable Time-Series Anomaly Detection Benchmark (NeurIPS 2024 · similarity 0.84)
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