Reverso: Efficient Time Series Foundation Models for Zero-shot Forecasting

Xinghong Fu; Yanhong Li; Georgios Papaioannou; Yoon Kim

cs.LGFeb 19, 2026

Reverso: Efficient Time Series Foundation Models for Zero-shot Forecasting

Authors: Xinghong Fu, Yanhong Li, Georgios Papaioannou, Yoon Kim

Organizations: Massachusetts Institute of Technology · Allen Institute for AI · Qube Research & Technologies

Abstract

Learning time series foundation models has been shown to be a promising approach for zero-shot time series forecasting across diverse time series domains. Insofar as scaling has been a critical driver of performance of foundation models in other modalities such as language and vision, much recent work on time series foundation modeling has focused on scaling. This has resulted in time series foundation models with hundreds of millions of parameters that are, while performant, inefficient and expensive to use in practice. This paper describes a simple recipe for learning efficient foundation models for zero-shot time series forecasting that are orders of magnitude smaller. We show that large-scale transformers are not necessary: small hybrid models that interleave long convolution and linear RNN layers (in particular DeltaNet layers) can match the performance of larger transformer-based models while being more than a hundred times smaller. We also describe several data augmentation and inference strategies that further improve performance. This recipe results in Reverso, a family of efficient time series foundation models for zero-shot forecasting that significantly push the performance-efficiency Pareto frontier.

Figures & tables

Figure 1: Reverso architecture. Given a sequence of length $S$ , we turn it into a length- $L$ input $t\in\mathbb{R}^{L\times C}$ by taking the $L,2L,\dots,2^{C-1}L$ most recent data points and downsampling by $\times 1,\times 2,\dots,\times 2^{C-1}$ . The input $t$ is passed through a single projection layer to obtain embedding representations $x\in\mathbb{R}^{L\times d}$ . Then, $n_{layers}$ of sequence-mixing and channel-mixing blocks operates on $x$ , where we alternate between long convolutions and DeltaNet for sequence mixing across length $L$ , and use MLP layers for channel mixing across dimension $d$ . The final output head (based on an attention-based transformation) obtains the predictions $\hat{y}\in\mathbb{R}^{p}$ .

Model	Params	Layers	Dim.
Reverso-Nano	200K	2	32
Reverso-Small	550K	4	64
Reverso	2.6M	8	128

Table 1: Architecture configurations.

Model	Params	Short	Medium	Long	Average
		MASE
Xihe-Max	1.5B	0.623	0.718	0.763	0.701
TimesFM-2.5	200M	0.626	0.724	0.751	0.700
PatchTST-FM	260M	0.616	0.722	0.745	0.694
Flowstate-r1.1	18M	0.633	0.720	0.736	0.696
Reverso	2.6M	0.634	0.699	0.741	0.691

Table 2: Model MASE scores across forecast horizons, averaged across the 21 long sequence datasets in Gift-Eval with all three horizons available.

Panel of Figure 3 — Figure 3: Inference efficiency on Gift-Eval. Reverso variants achieve lower latency and lower peak memory usage than larger time series foundation models while having the lowest parameters.

Appendix figures & tables21 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4: Our data augmentation (left) and synthetic data generation (right) pipeline. For data augmentation we apply: downsampling, amplitude modulation, vertical flip, horizontal flip, censor, mixup. For synthetic data generation, we generate data from Gaussian process with randomly selected kernels from a kernel bank, and combine this with spike/trapezoidal patterns as well as processes sampled with trend, seasonality and irregularity.

Model	Size	UCR	Multivariate UEA
Reverso	2.6M	81%	74%
TiRex	30M	81%	74%
Chronos-Bolt	205M	79%	74%
TIC	–	80%	–
Moirai-Large	311M	80%	70%
TimesFM-2.0	500M	79%	70%

Appendix

Table 3: Classification accuracy on UCR and multivariate UEA benchmarks. Higher is better.

Model	Reverso	Reverso-Small	Reverso-Nano	Sundial-L	Super-Linear	Timer-XL	TiRex	Chronos-2
Params	2.6M	550K	200K	444M	2.6M	85M	30M	120M
ETTm1	0.367	0.376	0.382	0.369	0.389	0.392	0.365	0.359
ETTm2	0.304	0.309	0.311	0.315	0.325	0.336	0.302	0.291
ETTh1	0.404	0.404	0.416	0.420	0.416	0.417	0.417	0.405
ETTh2	0.365	0.370	0.384	0.387	0.386	0.388	0.362	0.367
Electricity	0.238	0.241	0.249	0.262	0.267	0.268	0.240	0.237

Appendix

Table 4: Zero-shot forecasting performance (MAE) on LTSF datasets: ETTm1, ETTm2, ETTh1, ETTh2, Electricity and Weather, comparing between Reverso variants against state-of-the-art foundation models. Results represent the averaged MAE across prediction lengths

\{96,192,336,720\}

. Best results are in bold , and second-best are underlined . A full set of results are shown in Table 13

Figure 5: LTSF performance vs. Parameter Count. MAE is averaged over the horizons of $\{96,192,336,720\}$ for the datasets ETTh1, ETTh2, ETTm1, ETTm2, Electricity and Weather. For models which are not evaluated on all the datasets (e.g. YingLong did not report results for Electricity), we impute with the other best existing model on that dataset.

Threshold	Reverso	Timer	Anomaly Transformer	TimesNet
Detected@1%	88 (35%)	51	51	31
Detected@3%	126 (50%)	110	98	61
Detected@10%	188 (75%)	172	129	109

Appendix

Table 5: Zero-shot anomaly detection on UCR. Higher detected counts are better. Percentages in parentheses indicate the fraction of UCR anomalies detected by Reverso.

Model	ETTh1	ETTh2	ETTm1	ETTm2	Weather	Traffic	ECL
Reverso	0.285	0.147	0.149	0.084	0.081	0.433	0.151
Timer	0.312	0.209	0.413	0.158	0.158	0.477	0.152
TimesNet	0.289	0.253	0.373	0.112	0.127	0.624	0.209

Appendix

Table 6: Imputation MSE on standard time-series benchmarks. Lower is better.

Run Setting	Seed 1	Seed 2	Seed 3	Seed 4	Mean $\pm$ Std.
20% training run	0.720	0.722	0.719	0.723	$0.7210\pm 0.0018$
Full training run	0.711	0.712	0.713	0.710	$0.7115\pm 0.0013$

Appendix

Table 8: Gift-Eval MASE across random seeds. Lower is better.

Kernel	Formula $\kappa(x,x^{\prime})$	Hyperparameters
Constant	$C$	$C=1$
Linear	$\sigma^{2}+x\cdot x^{\prime}$	$\sigma\in\{0,1,10\}$
RBF	$\exp\left(-\frac{\\|x-x^{\prime}\\|^{2}}{2l^{2}}\right)$	$l\in\{0.1,1,10\}$
Rational Quadratic	$\left(1+\frac{\\|x-x^{\prime}\\|^{2}}{2\alpha}\right)^{-\alpha}$	$\alpha\in\{0.1,1,10\}$
Matérn	$\frac{2^{1-\nu}}{\Gamma(\nu)}\left(\sqrt{2\nu}\frac{\\|x-x^{\prime}\\|}{l}\right)^{\nu}K_{\nu}\left(\sqrt{2\nu}\frac{\\|x-x^{\prime}\\|}{l}\right)$	$\nu\in\{0.5,1.5,2.5\},l\in\{0.1,1,10\}$
Periodic	$\exp\left(-2\sin^{2}(\pi\\|x-x^{\prime}\\|/p)\right)$	$p\in\mathcal{P}$

Appendix

Table 9: Kernel Bank

\mathcal{K}

used for Synthetic Data Generation

Family	Model	Params	MASE
TimesFM	TimesFM-2.5	200M	0.705
	TimesFM-2.0	500M	0.758
PatchTST-FM-r1	PatchTST-FM	260M	0.707
Xihe	Xihe-Max	1.5B	0.711
	Xihe-Base	700M	0.718
	Xihe-Flash	300M	0.726

Appendix

Table 11: MASE scores versus parameter size breakdowns for models compared in the Gift-Eval benchmark in Figure 2 . Note that the data leaked version of Chronos-2 has been trained on datasets within Gift-Eval and hence is not included within Figure 2 for fair zero-shot comparison, but is still a strong frame of reference for SOTA foundation models.

Panel of Figure 6 — Figure 6: Zero-shot performance on the Gift-Eval benchmark for (a) long sequences (average length at least 2048) and (b) short sequences.

Dataset	Frequency
bitbrains_fast_storage	5T
bitbrains_rnd	5T
bizitobs_application	10S
bizitobs_l2c	5T
bizitobs_l2c	H
bizitobs_service	10S

Appendix

Table 12: Datasets used for Table 2 , a subset of GiftEval which have all three short/medium/long forecasting horizons.

Panel of Figure 7 — Figure 7: Qualitative results visualizing zero-shot forecasts by Reverso on various tasks within Gift-Eval. Reverso is able to perform long horizon forecasting, accurately capturing patterns at multiple frequency scales. The grey vertical dotted line denotes the length of a single autoregressive prediction.

Figure 8: Downsampling Comparison. In this example, consider an input with period 4000 to a model with context length 2048, tasked with forecasting the next 720 points. In (b), the model does not have enough information to forecast the rising part of the trapezoid. However, through downsampling the input, multiple full periods now fit into the context window and the model can forecast more accurately.

Model	Long MASE	Full MASE
Reverso-Nano	0.766	0.757
w/o. multi-scale input	0.783	0.760
Reverso-Small	0.742	0.722
w/o. multi-scale input	0.754	0.726
Reverso	0.741	0.706
w/o. multi-scale input	0.749	0.711

Appendix

Table 14: Effect of multiscale downsampling on Gift-Eval MASE. Lower is better.

Sequence Module	Long MASE	Short MASE	Overall MASE
DeltaNet	0.706	0.792	0.732
Gated DeltaProduct	0.711	0.793	0.735
Gated DeltaNet	0.708	0.782	0.730
Long Convolution	0.708	0.799	0.735
Gated Linear Attention	0.726	0.817	0.753
Attention ( sin-cos )	0.729	0.840	0.762

Appendix

Table 15: Architectural ablations.

Method	MASE
Baseline	0.738
w/o mixup	0.740
w/o downsample	0.740
w/o temp rev	0.740
w/o flip	0.739
w/o censor	0.738

Appendix

Table 16: Data pipeline ablations.

Method	Short Seq	Long Seq	Short Term	Med Term	Long Term	Overall
Baseline	0.764	0.682	0.696	0.699	0.741	0.706
w/o downsampling	0.764	0.700	0.696	0.723	0.778	0.719
No flip	0.776	0.686	0.705	0.702	0.745	0.713
Flip equivariance	0.764	0.682	0.696	0.699	0.741	0.706

Appendix

Table 17: Inference strategy ablations on Gift-Eval.

Architecture	Layer Sequence	MASE
Reverso	Conv $\to$ DN $\to$ Conv $\to$ DN $\to$ Conv $\to$ DN $\to$ Conv $\to$ DN	0.720
Variant 1	DN $\to$ Conv $\to$ DN $\to$ Conv $\to$ DN $\to$ Conv $\to$ DN $\to$ Conv	0.724
Variant 2	Conv $\to$ DN $\to$ DN $\to$ DN $\to$ DN $\to$ DN $\to$ DN $\to$ DN	0.725
Variant 3	Conv $\to$ Conv $\to$ Conv $\to$ Conv $\to$ DN $\to$ DN $\to$ DN $\to$ DN	0.730

Appendix

Table 18: MASE performance for different architecture variants.

Figure 9: Filter visualizations for the first convolution layer of Reverso-Nano.

	Conv layer 1	Conv layer 2	Conv layer 3	Conv layer 4
Min period	98	293	4	5
Median period	244	293	204	163

Appendix

Table 19: Minimum and median periods across convolutional layers.

Figure 10: State evolution of of the Deltanet states in Reverso-Nano. Across the 4 heads of the $8\times 8$ state matrix $S_{t}$ , we visualize the 32 coordinates with the highest temporal variance.

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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.

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