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Kairos: Toward Adaptive and Parameter-Efficient Time Series Foundation Models

NeurIPS 2026 · Time series › Foundation models for time series · approach: Time series foundation models

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Proposes Kairos, a parameter-efficient time series foundation model with dynamic patch tokenization (mixture-of-size encoder with null experts), instance-adaptive rotary position embeddings (DRoPE), and a multi-patch decoder, trained on the PreSTS corpus.

Problem

Zero-shot forecasting by time series foundation models is hampered by temporal heterogeneity (varying information density and periodicity); static tokenization and fixed positional encodings force large parameter counts to memorize patterns.

Approach

Segment-level top-K routing over multiple patch-size experts with computation-free null experts yields adaptive granularity; RoPE frequencies are modulated per instance using FFT features in log-space and positions are calibrated by physical patch duration; a multi-patch decoder predicts several patches in parallel.

Key results

• Kairos-Base (53M) achieves normalized MASE 0.738 on GIFT-Eval, the best MASE in the comparison table, versus 0.750 for Toto (151M) and Sundial (128M).
• Kairos-Small (23M) with MASE 0.748 surpasses Toto and Sundial in MASE with 6.6x and 5.6x fewer parameters.
• Shuffling routing decisions at inference raises normalized MASE from 0.738 to 1.205, supporting the learned segment-level routing.

Surprising findings

• Kairos-Base has a higher normalized CRPS (0.548) than Toto (0.517), so probabilistic accuracy lags despite the best MASE.
• Kairos trained on the Chronos corpus (0.761) still outperforms ChronosBolt trained on PreSTS (0.781), suggesting architecture contributes more than data.

Limitations

• Channel-independent modeling; does not explicitly capture inter-variable dependencies.
• Probabilistic forecasting (CRPS) trails Toto.
• Evaluation focused on zero-shot forecasting; anomaly detection and imputation not yet explored.

Experimental setup

Datasets: PreSTS Chronos corpus UCR archive

Benchmarks: GIFT-Eval Time-Series-Library ETT Time-Series-Library Weather Saugeen UCR classification

Metrics: MASE CRPS MSE MAE accuracy

Baselines: Chronos Chronos-Bolt TimesFM Moirai Toto Sundial TTM VisionTS Time-MoE Timer-XL MOMENT ElasTST

Builds on: RoPE Mixture-of-Experts Pathformer Chronos PatchTST

Closest papers by meaning

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