TempoPFN: Synthetic Pre-training of Linear RNNs for Zero-shot Time Series Forecasting

Vladyslav Moroshan; Julien Siems; Arber Zela; Timur Carstensen; Frank Hutter

cs.LGOct 29, 2025

TempoPFN: Synthetic Pre-training of Linear RNNs for Zero-shot Time Series Forecasting

Authors: Vladyslav Moroshan, Julien Siems, Arber Zela, Timur Carstensen, Frank Hutter

Organizations: University of Freiburg · ELLIS Institute Tübingen · Prior Labs

Abstract

Foundation models for zero-shot time series forecasting face challenges in efficient long-horizon prediction and reproducibility, with existing synthetic-only approaches underperforming on challenging benchmarks. This paper presents TempoPFN, a univariate time series foundation model based on linear Recurrent Neural Networks (RNNs) pre-trained exclusively on synthetic data. The model uses a GatedDeltaProduct architecture with state-weaving for fully parallelizable training across sequence lengths, eliminating the need for windowing or summarization techniques while maintaining robust temporal state-tracking. Our comprehensive synthetic data pipeline unifies diverse generators, including stochastic differential equations, Gaussian processes, and audio synthesis, with novel augmentations. In zero-shot evaluations on the Gift-Eval, fev-bench and Chronos-ZS benchmarks, TempoPFN achieves top-tier competitive performance, surpassing the majority of models trained on real-world data, while leveraging fully parallelizable training and inference. We open-source our complete data generation pipeline and training code, providing a reproducible foundation for future research.

Figures & tables

Criterion	TiRex	TabPFN-TS	Mamba4Cast	Chronos	TempoPFN
Fully open-source data pipeline	✗	✗	✓	✗	✓
Open-source training code	✗	✗	✓	✓	✓
Competitive with SOTA performance	✓	✓	✗	✓	✓
Fast training and inference	✓	✗	(✓)	(✓)	✓
Purely synthetic pretraining	✗	(✓)	✓	✗	✓

Table 1: Contributions of TempoPFN: the first fully open-source time series forecasting foundation model with competitive performance; with fully synthetic pretraining and fast training and inference.

Figure 1: (Left) Synthetic Data Generation pipeline containing a mix of novel and existing time-series generators are augmented with a diverse set of augmentations to produce the time-series used for training. (Middle) The TempoPFN architecture produces coherent quantile predictions for all future time-stamps in parallel. (Right) TempoPFN obtains competitive performance on Gift-Eval despite being trained only on synthetic time-series.

Panel of Figure 2 — Figure 2: The TempoPFN architecture (3 blocks) uses stacked GatedDeltaProduct blocks, learnable initial states ${\bm{H}}_{0}^{i}$ and state-weaving.

Panel of Figure 3 — Figure 3: Synthetic data augmentation pipeline. Synthetic time-series undergo probabilistic transformations across six categorical groups (Invariances, Structure, Seasonality, Analytic, Discrete, Artifacts), with optional TS-Mixup combinations and stochastic convolution filtering. Competitive selection based on change scores ensures meaningful augmentations. Example outputs demonstrate the diversity of generated temporal patterns.

Panel of Figure 4 — Figure 4: Comparison of TempoPFN (3M iterations with a per-GPU batch size of 40) against other models on GiftEval benchmark. We compute both normalized and average ranks for CRPS and MASE. Colors represent the class of time series model.

Figure 5: Qualitative comparison between TempoPFN, TiRex and TabPFN-TS on two series from the GIFT-Eval Benchmark. (Left) Total context with prediction window in dashed grey box. (Right) Predictions between TempoPFN, TiRex, and TabPFN-TS.

Figure 6: Normalized CRPS of TempoPFN and TiRex as a function of missing values (NaN) in the data.

Rank	Model	Avg. Win Rate (%)	Skill Score (%)	Median Runtime (s)	Leakage (%)	Organization	Zero-shot
1	Chronos-2	87.7	35.5	2.69	0	AWS	✓
2	TiRex	76.5	30.0	1.40	1	NX-AI	✓
3	TimesFM 2.5	74.8	30.2	16.92	10	Google	✓
4	Toto 1.0	66.6	28.2	90.74	8	Datadog	✓
5	TempoPFN	62.4	25.7	20.67	0	Uni Freiburg / ELLIS	✓
6	Moirai 2.0	60.4	27.3	2.46	28	Salesforce	✓

Table 2: fev-bench leaderboard based on MASE. Models are ranked by Win Rate and Skill Score. TempoPFN is evaluated with a sign-flip and context-length ensemble at a maximum context of 3072.

	Gift-ZS Overall		Gift-ZS Short		Gift-ZS Medium		Gift-ZS Long
Model	CRPS	MASE	CRPS	MASE	CRPS	MASE	CRPS	MASE
TempoPFN (Linear RNN, 40M)	0.577	0.842	0.563	0.763	0.566	0.900	0.631	1.019
chronos-2-small (Transformer, 28M)	0.581	0.849	0.578	0.784	0.571	0.913	0.619	1.001
seasonal_naive	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000

Table 3: Backbone swap. Both models are pre-trained from scratch on the same univariate synthetic corpus for the matched 500k-iteration ablation budget (as in Table 4 ). TempoPFN uses our GatedDeltaProduct linear-RNN backbone (40M parameters); chronos-2-small ( AutoGluon Team, 2025 ) is a 28M-parameter Transformer. Lower is better.

		Gift-ZS Overall		Gift-ZS Short		Gift-ZS Medium		Gift-ZS Long
Ablation	Source	CRPS	MASE	CRPS	MASE	CRPS	MASE	CRPS	MASE
Base Model	–	$0.577$	$0.842$	$0.563$	$0.763$	$0.566$	$0.900$	$0.631$	$1.019$
- GP	A	$0.591$	$0.830$	$0.576$	$0.749$	$0.605$	$0.924$	$0.618$	$0.981$
- Kernel	A	$0.611$	$0.885$	$0.589$	$0.796$	$0.637$	$0.981$	$0.648$	$1.056$
- ForecastPFN	A	$0.617$	$0.885$	$0.588$	$0.791$	$0.643$	$0.981$	$0.674$	$1.075$
- Sawtooth	N	$0.628$	$0.900$	$0.597$	$0.800$	$0.661$	$1.012$	$0.684$	$1.091$

Table 4: Ablation study of synthetic data priors using a leave-one-out methodology (500k iterations). The ’Ablation’ column indicates the single prior excluded from the training mixture. Performance is measured by CRPS and MASE (lower is better). Rows are colored to indicate the performance impact on the overall CRPS when a prior is removed: High Impact (

>25\%

increase) and Medium Impact (

>10\%

increase). N = Novel prior (our contribution), A = Adapted from open-source.

	Gift-ZS Overall		Gift-ZS Short		Gift-ZS Medium		Gift-ZS Long
Model	CRPS	MASE	CRPS	MASE	CRPS	MASE	CRPS	MASE
w/ Aug	0.577	0.842	0.563	0.763	0.566	0.900	0.631	1.019
w/o Aug	0.610	0.875	0.582	0.783	0.617	0.963	0.643	1.059
seasonal_naive	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000

Table 5: The impact of data augmentation on model performance, shown by normalized performance values (500k iterations). Individual augmentation effects and probability tuning were not exhaustively explored due to resource constraints.

Appendix figures & tables34 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Example time series generated by CauKer

Figure 8: Example time series generated by KernelSynth

Figure 9: Example time series generated by GP

Figure 10: Example time series generated by ForecastPFN

Figure 11: Example time series generated by Sawtooth Generator

Figure 12: Example time series generated by Step Function

Figure 13: Example time series generated by Anomaly Generator

Figure 14: Example time series generated by Spike Generator

Figure 15: Example time series generated by Sine Wave Generator

Figure 16: Example time series generated by Audio Stochastic Rhythm

Figure 17: Example time series generated by Ornstein–Uhlenbeck process

Parameter	Range / Distribution
Integration step size $dt$	$0.01$
Initial value $y_{0}$	$\mathcal{N}(0,2^{2})$
Regime 0 mean reversion $\theta^{(0)}$	$[1.0,5.0]$
Regime 0 mean $\mu^{(0)}$	$\mathcal{N}(-2.0,1.0^{2})$
Regime 0 volatility $\sigma^{(0)}$	$\log\mathcal{N}(\log 0.3,0.3)$
Regime 0 vol. process $(\kappa_{v},\theta_{v},\xi_{v})$	$[2.0,5.0],[0.2,0.4],[0.1,0.3]$

Appendix

Table 6: Parameter ranges for the Regime-Switching OU generator.

Generator	Source	Length	Series / Sec
Cauker	A	2048	$0.66$
GP	A	2048	$7.04$
Kernel	A	2048	$0.32$
ForecastPFN	A	2048	$35.49$
Sawtooth	N	2048	$242.95$
Sinewave	N	2048	$144.93$

Appendix

Table 7: Profiling results for synthetic data generation throughput. N = Novel prior, A = Adapted from open-source.

Category	Parameter	Value
Model	Total Parameters	40M
	Embedding size ( embed_size )	512
	Encoder layers	10
	Number of heads ( num_heads )	4
	Encoder attention mode	chunk
	Short convolution kernel size	32

Appendix

Table 8: Hyperparameters for main TempoPFN model.

		Gift-ZS Overall		Gift-ZS Short		Gift-ZS Medium		Gift-ZS Long
Ablation	Source	CRPS	MASE	CRPS	MASE	CRPS	MASE	CRPS	MASE
Base Model	–	0.577	0.842	0.563	0.763	0.566	0.900	0.631	1.019
+ Cauker	Adapted	0.600	0.875	0.583	0.789	0.615	0.964	0.631	1.043
+ GP	Adapted	0.632	0.897	0.607	0.812	0.666	0.993	0.666	1.053
+ Kernel	Adapted	0.638	0.926	0.622	0.835	0.656	1.042	0.661	1.082
+ ForecastPFN	Adapted	0.715	1.027	0.695	0.918	0.760	1.172	0.726	1.206

Appendix

Table 9: Ablation study of single synthetic priors (trained for 500k iterations). ’Base Model’ uses all priors and augmentations. Lower values are better. Bold : best, underline : second-best. Novel priors are our contributions; Adapted are modified open-source versions.

Ablating Positional Encoding:
	Gift-ZS Overall		Gift-ZS Short		Gift-ZS Medium		Gift-ZS Long
Configuration	CRPS	MASE	CRPS	MASE	CRPS	MASE	CRPS	MASE
Base Model (Sin. Pos. Enc. Off)	0.561	0.820	0.553	0.751	0.556	0.880	0.590	0.962
Sinusoidal Positional Encoding	0.648	0.937	0.596	0.809	0.731	1.120	0.715	1.152
Ablating Number of Householder Matrices (H):
H=6	0.556	0.823	0.545	0.750	0.552	0.886	0.590	0.972

Appendix

Table 10: Core architectural ablations (trained for 2M iterations with a per-GPU batch size of 40). Base config:

d=512

L=10

, conv size 16,

H=4

, weaving enabled, negative eigenvalues allowed. Sorted by overall CRPS. Bold : best, underline : second-best.

	Gift-ZS Overall		Gift-ZS Short		Gift-ZS Medium		Gift-ZS Long
Configuration	CRPS	MASE	CRPS	MASE	CRPS	MASE	CRPS	MASE
Base Model (d=512, L=10)	0.533	0.788	0.532	0.727	0.523	0.840	0.544	0.912
d=512, L=10, Weaving Off	0.537	0.790	0.532	0.723	0.533	0.862	0.553	0.914
d=384, L=16 (Narrower, Deeper)	0.539	0.792	0.532	0.727	0.533	0.850	0.563	0.921
d=576, L=8 (Wider, Shallower)	0.540	0.794	0.536	0.732	0.529	0.849	0.561	0.921
seasonal_naive	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000

Appendix

Table 11: Ablation of model scale and depth (trained for 3M iterations with a batch size of 40). Base Model:

d=512,L=10

H=4

, conv size 32, weaving/neg eigenvalues on. Compares width vs. depth at constant parameter count. Sorted by overall CRPS. Bold : best, underline : second-best.

	Gift-ZS Overall		Gift-ZS Short		Gift-ZS Medium		Gift-ZS Long
LR Scheduler	CRPS	MASE	CRPS	MASE	CRPS	MASE	CRPS	MASE
WarmupStableDecay	0.554	0.812	0.544	0.740	0.550	0.877	0.584	0.956
CosineWithWarmup	0.559	0.817	0.552	0.751	0.550	0.873	0.588	0.955
CosineWithRestarts	0.559	0.820	0.552	0.755	0.552	0.874	0.585	0.953
Cosine (no warmup)	0.561	0.820	0.553	0.751	0.556	0.880	0.590	0.962
seasonal_naive	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000

Appendix

Table 12: LR scheduler ablation (trained for 2M iterations with a batch size of 40). Base architecture:

d=512,L=10

H=4

, conv size 32, weaving enabled. WarmupStableDecay : warmup (0.3%), plateau (90%), cosine decay (9.7%). CosineWithRestarts : 4 resets. Sorted by overall CRPS. Bold : best, underline : second-best.

Figure 18: Comparison of TempoPFN normalized CRPS and MASE (3M iterations with a batch size of 40) against other models on Chronos-ZS benchmark.

Model	Params (M)	Training Time	Inference Time	Memory	Parallelization
TiRex ( Auer et al., 2025 )	35	Work: $\mathcal{O}(TLd^{2})$ Depth: $\mathcal{O}(L\,T/w)$ (window $w{=}32$ )	AR: $\mathcal{O}(HLd^{2})$ Depth: $\mathcal{O}(L\,T/w)$	$\mathcal{O}(d)$ (streaming)	Low (sequential sLSTM)
TabPFN-TS ( Hoo et al., 2024 )	11	$\mathcal{O}(T^{2}d)$	$\mathcal{O}(T^{2}d)$	$\mathcal{O}(Td)$	Moderate (attention)
TimesFM-2.0 ( Das et al., 2024 )	500	$\mathcal{O}(T^{2}d)$	Direct: $\mathcal{O}(T^{2}d)$	$\mathcal{O}(Td)$	High (transformer)
Chronos ( Ansari et al., 2024 )	9–205	$\mathcal{O}(T^{2}d)$	AR: $\mathcal{O}(H)$	$\mathcal{O}(Td)$	High (transformer)
MOIRAI-MoE ( Liu et al., 2025b )	14–935	$\mathcal{O}(T^{2}d)$	$\mathcal{O}(T^{2}d)$	$\mathcal{O}(Td)$	High (MoE + transformer)
TempoPFN (ours)	40	Work: $\mathcal{O}(TLd^{2})$ Depth: $\mathcal{O}(L\log T)$	Work: $\mathcal{O}(TLd^{2})$ Depth: $\mathcal{O}(L\log T)$ Horizon: $\mathcal{O}(1)$	$\mathcal{O}(d)$ (streaming) or $\mathcal{O}(Td)$ (cached)	Full (sequence-parallel)

Appendix

Table 13: Comparison of time-series foundation models. Complexities are reported with respect to sequence length

T

, horizon

H

, embedding dimension

d

, and layers

L

. We distinguish total work from parallel depth. TempoPFN benefits from scan-accelerated linear recurrences enabling sublinear depth.

Figure 19: CRPS and MASE average rank of TempoPFN (3M iterations with a per-GPU batch size of 40) on Chronos-ZS benchmark.

Rank	Model	Avg. Win Rate (%)	Skill Score (%)	Median Runtime (s)	Leakage (%)	Organization	Zero-shot
1	Chronos-2	90.9	47.3	2.69	0	AWS	✓
2	TiRex	82.1	42.6	1.40	1	NX-AI	✓
3	TimesFM 2.5	77.1	42.2	16.92	10	Google	✓
4	Toto 1.0	69.6	40.7	90.74	8	Datadog	✓
5	TempoPFN	65.3	38.3	20.67	0	Uni Freiburg / ELLIS	✓
6	Moirai 2.0	63.4	39.3	2.46	28	Salesforce	✓

Appendix

Table 14: fev-bench leaderboard based on Scaled Quantile Loss (SQL). Models are ranked by Win Rate and Skill Score. TempoPFN is evaluated with a sign-flip and context-length ensemble at a maximum context of 3072.

Panel of Figure 20 — Figure 20: Head-to-head comparisons on FEV-Bench using Scaled Quantile Loss (SQL). (a) Win Rate: Percentage of tasks where the row model achieves lower error than the column model (ties count as half-wins); values $>$ 50% indicate the row model is more accurate on average. (b) Skill Score: Average relative error reduction of the row model with respect to the column model; positive values indicate error reduction. Brackets indicate 95% confidence intervals estimated via 1000 bootstrap samples.

Panel of Figure 21 — Figure 21: Feature-Space Distribution of Real vs. Synthetic Data. UMAP projections of time-series features extracted via tsfresh . Real-world benchmarks (GIFT-Eval, FEV-Bench, Chronos) are shown in cold colors (Blue/Teal) in the foreground, while our synthetic generators are shown in warm colors (Red/Orange/Yellow) in the background.

Figure 36

Figure 37

Figure 38

Figure 39

Figure 40

Figure 22: Qualitative comparison between TempoPFN, TiRex and TabPFN-TS on the GIFT-Eval Benchmark. (Left) Total context with prediction window in dashed grey box. (Right) Predictions between TempoPFN, TiRex, and TabPFN-TS.

Dataset	TempoPFN	TiRex	FlowState-9.1M	Toto_Open_Base_1.0	TabPFN-TS	YingLong_50m	Chronos Bolt B	TTM-R2-Finetuned	Moirai L 1.1	Moirai B 1.1
bitbrains_fast_storage/5T/long	0.555	0.558	0.701	0.568	0.752	0.586	0.635	0.796	0.608	0.622
bitbrains_fast_storage/5T/medium	0.516	0.516	0.651	0.525	0.792	0.537	0.631	0.690	0.531	0.553
bitbrains_fast_storage/5T/short	0.334	0.334	0.422	0.306	0.547	0.343	0.375	0.465	0.340	0.341
bitbrains_fast_storage/H/short	0.632	0.683	0.684	0.609	0.655	0.610	0.757	1.007	0.632	0.600
bitbrains_rnd/5T/long	0.602	0.541	0.619	0.501	0.697	0.563	0.643	0.648	0.577	0.566
bitbrains_rnd/5T/medium	0.530	0.500	0.619	0.537	0.701	0.546	0.517	0.670	0.508	0.527

Appendix

Table 15: Normalized CRPS (Continuous Ranked Probability Score) for various zero-shot models on the GiftEval benchmark. Scores are normalized against a seasonal naive baseline, with values less than 1.0 signifying superior probabilistic forecasts. The top two performing models are highlighted.

Dataset	TempoPFN	TiRex	FlowState-9.1M	Toto_Open_Base_1.0	TTM-R2-Finetuned	TabPFN-TS	Chronos Bolt B	YingLong_50m	Moirai L 1.1	Moirai B 1.1
bitbrains_fast_storage/5T/long	0.846	0.808	0.913	0.789	0.827	1.014	0.834	0.886	0.840	0.851
bitbrains_fast_storage/5T/medium	0.896	0.815	1.033	0.807	0.876	1.072	0.871	0.889	0.836	0.860
bitbrains_fast_storage/5T/short	0.716	0.609	0.883	0.591	0.648	0.879	0.662	0.719	0.728	0.697
bitbrains_fast_storage/H/short	0.910	0.825	0.851	0.728	0.927	0.912	0.824	0.856	0.839	0.909
bitbrains_rnd/5T/long	1.005	0.954	1.007	0.953	1.001	1.107	0.970	1.002	0.977	0.985
bitbrains_rnd/5T/medium	1.001	0.967	1.009	0.972	0.997	1.064	0.979	1.004	0.982	0.997

Appendix

Table 16: Normalized MASE scores of different zero-shot models on the GiftEval benchmark. Scores are relative to a seasonal naive baseline, where values below 1.0 indicate better performance. The models achieving the best and second-best scores are highlighted.

Dataset	TempoPFN	TiRex	FlowState-9.1M	Toto_Open_Base_1.0	Chronos Bolt B	TabPFN-TS	YingLong_50m	TTM-R2-Finetuned	Moirai L 1.1	Moirai B 1.1
bitbrains_fast_storage/5T/long	1.000	2.000	8.000	3.000	7.000	9.000	4.000	10.000	5.000	6.000
bitbrains_fast_storage/5T/medium	1.000	2.000	8.000	3.000	7.000	10.000	5.000	9.000	4.000	6.000
bitbrains_fast_storage/5T/short	2.000	3.000	8.000	1.000	7.000	10.000	6.000	9.000	4.000	5.000
bitbrains_fast_storage/H/short	4.000	7.000	8.000	2.000	9.000	6.000	3.000	11.000	5.000	1.000
bitbrains_rnd/5T/long	6.000	2.000	7.000	1.000	8.000	10.000	3.000	9.000	5.000	4.000
bitbrains_rnd/5T/medium	5.000	1.000	8.000	6.000	3.000	10.000	7.000	9.000	2.000	4.000

Appendix

Table 17: CRPS performance summarized by average rank for zero-shot models on the GiftEval benchmark. A lower rank signifies superior probabilistic forecasting performance. The models achieving the first and second-best overall average ranks are highlighted.

Dataset	TempoPFN	TiRex	FlowState-9.1M	Toto_Open_Base_1.0	Chronos Bolt B	TTM-R2-Finetuned	TabPFN-TS	YingLong_50m	Moirai L 1.1	Moirai B 1.1
bitbrains_fast_storage/5T/long	6.000	2.000	9.000	1.000	4.000	3.000	11.000	8.000	5.000	7.000
bitbrains_fast_storage/5T/medium	8.000	2.000	10.000	1.000	5.000	6.000	11.000	7.000	3.000	4.000
bitbrains_fast_storage/5T/short	6.000	2.000	10.000	1.000	4.000	3.000	9.000	7.000	8.000	5.000
bitbrains_fast_storage/H/short	8.000	3.000	5.000	1.000	2.000	10.000	9.000	6.000	4.000	7.000
bitbrains_rnd/5T/long	9.000	2.000	10.000	1.000	3.000	7.000	11.000	8.000	4.000	5.000
bitbrains_rnd/5T/medium	8.000	1.000	10.000	2.000	3.000	5.000	11.000	9.000	4.000	6.000

Appendix

Table 18: MASE performance presented as average ranks for zero-shot models across the GiftEval benchmark. A lower average rank indicates consistently higher accuracy across datasets. The two models with the best overall average ranks are highlighted.

Zero-Shot Time Series Forecasting

Zero-shot time series forecasting uses pretrained models to predict unseen series or domains without task-specific training.

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Inspired by recent breakthroughs in large language models for natural language processing, foundation models have emerged as a promising paradigm for zero-shot time series forecasting, enabling accurate predictions on datasets never seen during pre-training. Ranging from tens to hundreds of millions of parameters, these models are pre-trained on vast and diverse collections of time series, learning generalizable representations that support both point and probabilistic forecasting. This approach alleviates the need for dataset-specific model design and manual tuning, offering a unified solution across forecasting problems. In this work, we review the main architectures, pre-training strategies, and optimization methods underpinning these models. We further investigate post-pre-training fine-tuning of selected foundation models to enhance their performance on specific datasets. Our empirical results demonstrate that this step consistently improves forecasting accuracy over the zero-shot baseline.

Abstract

Zero-Shot Time Series Forecasting

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