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

Impact

Supporting the time series research community. Built on and evaluated by leading research teams.

Community adoption

39,197

Hugging Face downloads

All-time cumulative downloads

Across the Kairos model family

As of Sep 29, 2026

Method reuse

MIT · Ai2 · QRTMIT · Allen Institute for AI · Qube Research & Technologies

Reverso

“Spike Process Generation, adapted from Kairos”

Reverso adapts Kairos's spike-process generation method for synthetic training data. Its appendix explicitly credits Kairos in Algorithm 2.

Read Algorithm 2

Efficiency evaluation

Salesforce AI Research

Moirai 2.0

“Among baseline models, Kairos-50M emerges as the fastest”

The authors identify Kairos-50M as the fastest baseline in their inference-efficiency comparison.

The same comparison reports lower benchmark accuracy and nearly five times the parameter count relative to Moirai 2.0.

Read Section 5.2

Independent benchmark

Datadog · Squirrel Ai

It’s TIME

Coauthored by researchers affiliated with Datadog and Squirrel Ai, TIME evaluates Kairos among 12 time series foundation models across 50 datasets and 98 forecasting tasks.

Read the evaluation setup

Cloud-resource evaluation

State Street Technology · Richoo AI

CloudCons

Researchers from Zhejiang University, State Street Technology (Zhejiang), and Richoo AI include Kairos-50M in an end-to-end benchmark for cloud workload forecasting and resource consolidation.

A coauthor lists Datadog AI Research as their affiliation and notes that the work was completed before joining Datadog.

Read the benchmark

Framework integration

Simulacrum

TempusBench

The open-source evaluation framework integrates Kairos 10M, 23M, and 50M with dedicated model adapters and configurations that load the public checkpoints.

View integration Paper

Independent benchmark

IBM Research

FlowState

The FlowState study includes Kairos among state-of-the-art zero-shot models with publicly available verification code in its GIFT-Eval comparison.

Read Section 6.1

Financial-domain evaluation

LG AI Research

EXAONE Finance 1.0

Kairos 10M, 23M, and 50M are evaluated on FinVerse as part of a comparison of 44 models for financial time series forecasting.

View Table 7

Selected citations

Datadog · Nankai University · Academic collaborators
EIDOS: Latent-Space Predictive Learning for Time Series Foundation Models
Cites Kairos in its discussion of encoder–decoder architectures and time series pretraining data curation.
Indian Institute of Science (IISc) · BITS Pilani
Air Quality Arena: A Large-Scale Multi-Region Ground Monitoring Dataset and Benchmark for Air Quality Forecasting with Time-Series Foundation Models
Includes Kairos-50M in a multi-region air quality forecasting benchmark using a 168-hour input window.
Xiaomi · Sun Yat-sen University · National University of Singapore
WaveMoE: A Wavelet-Enhanced Mixture-of-Experts Foundation Model for Time Series Forecasting
Cites Kairos as an encoder–decoder foundation model in its related-work discussion.
Nokia · FAU Erlangen–Nürnberg
Time-Series Foundation Model Embeddings for Remaining Useful Life Estimation
Includes Kairos in the introduction’s overview of time series foundation models.
Netze BW · Karlsruhe Institute of Technology (KIT)
Probabilistic Low-Voltage Peak Load Forecasting with Time Series Foundation Models Evaluated on Application-Oriented Metrics
Lists Kairos in its model survey and selection tables; Kairos is not included in the final forecasting experiments.
University College London (UCL) · University of Manchester · Shanghai University
Re(Visiting) Time Series Foundation Models in Finance
Evaluates Kairos 10M, 23M, and 50M in an expanded zero-shot financial forecasting comparison.
Technical University of Munich (TUM) · HKUST (Guangzhou) · University of Strasbourg
Adaptive Patching Is Harder Than It Looks for Time-Series Forecasting
Cites Kairos in its discussion of multi-granularity routing and mixing methods for time-series forecasting.

Overview

Kairos achieves superior performance with fewer parameters on zero-shot forecasting benchmarks.

GIFT-Eval performance versus model size, temporal information density, and adaptive tokenization. — **Figure 1.** (a) Comparison on the GIFT-Eval benchmark demonstrates that Kairos achieves superior zero-shot forecasting performance (lower normalized MASE) while requiring significantly fewer parameters than existing TSFMs. (b)(c) Significant variation exists in information density (signal complexity) across and within different time series datasets. (d) Unlike existing TSFMs that use point-wise or fixed-size patching, Kairos uses Mixture-of-Size Tokenization to dynamically adapt to information density.

Abstract

Inherent temporal heterogeneity, such as varying sampling densities and periodic structures, has posed substantial challenges in zero-shot generalization for Time Series Foundation Models (TSFMs). Existing TSFMs predominantly rely on massive parameterization to absorb such heterogeneity, as their static tokenization and positional encoding schemes entangle diverse temporal patterns into a fixed representation space, encouraging memorization rather than adaptation. To address this limitation, we propose Kairos, a flexible and parameter-efficient TSFM that decouples temporal heterogeneity from model capacity through a novel tokenization perspective. Kairos introduces a dynamic patching tokenizer and a mixture-of-size encoding that adapt observational granularity to local information density, enabling fine-grained temporal abstraction without increasing model width or depth. In addition, we design a multi-granularity positional embedding based on dynamic rotary encodings, which conditions on instance-level spectral features and temporal structure induced by dynamic patching tokenization, allowing robust modeling of diverse temporal dependencies. Trained on a novel Predictability-Stratified Time-Series (PreSTS) corpus, Kairos achieves superior zero-shot performance with substantially fewer parameters on two mainstream benchmarks, GIFT-Eval and Time-Series-Library.

Methodology

Three complementary components adapt to temporal heterogeneity without relying on massive parameterization.

Adaptive tokenization

Mixture-of-Size Encoder

A dynamic patching tokenizer that adaptively models time series at multiple granularities. It uses a Top-K Granularity Router with null experts to sparsely select optimal patch sizes based on local information density.

Temporal modeling

Heterogeneity-Aware Transformer

The encoder output is processed by a Transformer equipped with Dynamic Rotary Position Embedding (DRoPE). Unlike standard RoPE, DRoPE modulates temporal scales using instance-level spectral features (via FFT) and calibrates positions to account for the varying physical durations of dynamic patches.

Parallel forecasting

Multi-Patch Decoder

To mitigate error accumulation in autoregressive generation, the decoder uses learnable forecast tokens to predict multiple future patches in parallel, offering flexibility for variable-length prediction horizons.

Results

GIFT-Eval Benchmark

Performance evaluation on the GIFT-Eval benchmark using normalized MASE and CRPS metrics, where lower values indicate higher forecasting accuracy. The baseline models fall into three categories: statistical methods, deep learning (DL) models, and Time Series Foundation Models (TSFMs). TSFMs are further subdivided based on whether the training set included test data (TestData Leakage).

GIFT-Eval normalized MASE and CRPS, with model parameter counts. Lower scores are better.
Type	Statistical	DL (Full-Shot)		TSFMs (TestData Leakage)				TSFMs (Zero-Shot)
Type	Seasonal Naïve	DLinear	PTST.	TTM	Chronos	Chronos Bolt	TimesFM	Moirai	VisionTS	Ying.	Toto	Sundial	Kairos_s (Ours)	Kairos_b (Ours)
#Params	-	-	-	5M	709M	205M	500M	311M	112M	300M	151M	128M	23M	53M
MASE ↓	1.000	1.061	0.849	1.020	0.870	0.808	0.758	0.875	0.863	0.798	0.750	0.750	0.748	0.738
CRPS ↓	1.000	0.846	0.587	0.873	0.574	0.574	0.550	0.599	0.755	0.548	0.517	0.559	0.554	0.548

Baselines results officially reported by GIFT-Eval. Best results are bolded, second best are underlined.

TSLib Benchmark

Kairos demonstrates remarkable zero-shot forecasting capabilities, outperforming both recent advanced TSFMs and the majority of full-shot deep learning models on the TSLib benchmark. The charts below show the aggregate average Mean Absolute Error (MAE) and Mean Squared Error (MSE), where lower values indicate better performance.

TSLib zero-shot forecasting results comparing average MAE and MSE across models. — **Figure 3.** Zero-shot performance on TSLib averaged over prediction lengths {96, 192, 336, 720}. Lower AVG MAE and MSE indicate better performance.

Citation

If you find Kairos useful in your research, please cite our paper.

@inproceedings{feng2026kairos,
  title={Kairos: Toward Adaptive and Parameter-Efficient Time Series Foundation Models},
  author={Feng, Kun and Lan, Shaocheng and Fang, Yuchen and He, Wenchao and Lu, Sihan and Gu, Shuqi and Lu, Xingyu and Ma, Lintao and Ren, Kan},
  booktitle={Advances in Neural Information Processing Systems},
  year={2026},
  url={https://arxiv.org/abs/2509.25826}
}