Timer-M1: A Multivariate Time Series Foundation Model via Learning Primitives

Haoran Zhang; Haixuan Liu; Xingjian Su; Yong Liu; Zhi Chen; Yuxuan Wang; Jianmin Wang; Mingsheng Long

cs.LGOct 8, 2026

Timer-M1: A Multivariate Time Series Foundation Model via Learning Primitives

Authors: Haoran Zhang, Haixuan Liu, Xingjian Su, Yong Liu, Zhi Chen, Yuxuan Wang, Jianmin Wang, Mingsheng Long

Organizations: School of Software, BNRist, Tsinghua University · ByteDance, Beijing, China

Abstract

We introduce Timer-M1, a pretrained multivariate time series foundation model that learns with primitives for zero-shot forecasting. Across domains, time series share elementary temporal and relational patterns, termed primitives, yet differ in how these primitives manifest and evolve across different contexts. Despite progress in zero-shot and task-general forecasting, existing foundation models may still struggle to generalize to complex real-world scenarios. To this end, we develop a primitive-based data synthesis and pretraining pipeline. The synthesis pipeline generates series with temporal primitives shared across domains and then assembles real and generated series into multivariate samples using relational primitives. Afterwards, samples are organized into episodes by assigning distinct channel roles as target variates, past-only covariates, and known-future covariates, ensuring that the model is optimized on predictable variates using available exogenous information. Technically, Timer-M1 further adapts gated two-dimensional Transformer blocks that dynamically allocate cross-variate attention across layers. Across three large-scale forecasting benchmarks, Timer-M1 ranks first on both FEV and TIME and second on GIFT-Eval among most recent time series foundation models. These results support effective primitive-based pretraining as a route to robust general forecasting technique across domains and task settings.

Figures & tables

Figure 1: Learning with primitives. Temporal and relational patterns observed in real series are composed into diverse samples; episodes vary what is observed and predicted while introducing noise and interference to improve robustness, linking to generalization to new forecasting scenarios.

Figure 2: Timer-M1 overview. (a) Temporal and relational primitives combine real and synthetic sources into multivariate samples through synthesis and augmentation. (b) Forecasting episodes specify variate roles and observation availability, with masks controlling forecasting and within-episode attention. (c) Gated two-dimensional Transformer blocks integrate temporal and cross-variate information, with learned layer-wise gates regulating cross-variate updates.

Figure 3: Persisted records and scalar positions by generation route, before sampling. Real–synthetic joint generation includes corpus-derived and mixed-source generation routes.

Figure 4: Evaluation overview. Public benchmarks assess forecasting across settings, while primitive evaluations examine temporal extrapolation, relational forecasting, and input reliability. Rankings are among compared methods.

Figure 5: Forecasting results on FEV across 100 matched configurations. Top: aggregate MASE and SQL for 12 methods, normalized by Seasonal Naive. Bottom: SQL across five task types with different variate roles and observation availability. Timer-M1 achieves the lowest aggregate errors. Colors denote forecasting interfaces above and individual models below.

Figure 6: Comparison on TIME across 98 matched configurations. Timer-M1 achieves state-of-the-art aggregate performance, attaining the lowest normalized MASE and CRPS among the compared methods across diverse forecasting task settings. Colors distinguish forecasting interfaces.

Figure 7: Point and probabilistic forecasting performance on GIFT-Eval across 97 matched configurations. Timer-M1 ranks second among 12 compared pretrained models on both MASE and CRPS, demonstrating competitive generalization across diverse domains and forecast horizons.

Figure 8: Primitive evaluation. Top: predefined temporal groups, seven relational mechanisms, and six reliability categories, measured by MSE (lower is better). Unsupported interfaces are omitted; detailed results for the displayed groups appear in Appendix C.3 . Bottom: six strength cases spanning distinct mechanisms, not an estimate of their frequency. Shading denotes M1’s marginal 10–90% quantiles.

\dagger

marks unavailable squared-error archives for some baseline.

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

Family	Primitive	Representative construction
Temporal	Periodicity	Oscillatory components and their superposition
	Trend	Gradual growth, decline, and shared drift
	Stochastic dependence	Noise and autoregressive dynamics
	Regime changes	Piecewise changes in level or evolution
Relational	Signed responses	Positive and negative source mixing
	Delayed responses	Temporal offsets between source and response

Appendix

Table 2: Operator families in primitive-based data construction. The taxonomy follows the temporal and relational primitives introduced in the main text. Examples describe mechanisms rather than a fixed generation recipe.

Component	Configuration
Parameters	120,998,412 (approximately 121M)
Transformer layers	12
Representation / feed-forward width	768 / 3072
Attention heads / head dimension	12 / 64
Patch length	16 observations
Prediction quantiles	$0.1,0.2,\ldots,0.9$

Appendix

Table 3: Model configuration. The gate contributes one learned scalar per layer; the total parameter count includes the embedding and prediction head.

Figure 10: Layer-wise allocation of cross-variate interaction. The learned coefficients generally rise with depth, while local deviations allow different layers to assign different weights to variate-attention updates. The dashed line marks the earlier stable-model mean used by the fixed-

0.202

control, not the mean of the displayed curve. Together with the gate ablation, the profile motivates adaptive allocation rather than a uniform residual scale.

Capability	Group	Controlled pattern or observation condition
Temporal	Periodic	Period, waveform, modulation, and gradual frequency change
	Trend	Direction, growth shape, and observed slope change
	Shift	Observed level change and unannounced boundary changes
Relational	Sign; scale	Shared dynamics with opposite signs or different scales
	Lag; phase	Delayed responses and phase-shifted periodic targets
	Cointegration	Multiple responses sharing a nonstationary source

Appendix

Table 4: Displayed primitive evaluation groups and their controlled conditions. The counts of scoring records and model-specific results appear in Tables 8 – 10 . All groups report MSE; NMAE additionally supports the comparisons discussed in the text.

Model	FEV MASE	FEV SQL	TIME MASE	TIME CRPS	GIFT MASE	GIFT CRPS
Timer-M1	0.3771	0.4887	0.6372	0.5363	0.6806	0.4688
TimesFM-3	0.3742	0.4866	0.6398	0.5363	0.6668	0.4557
Chronos-2	0.3550	0.4728	0.6620	0.5563	0.6978	0.4854
TiRex-2	0.3374	0.4550	–	–	0.6973	0.4781
Toto 2.0 (2.5B)	0.3254	0.4442	0.6419	0.5394	0.6956	0.4759
TimesFM-2.5	0.3562	0.4668	0.6686	0.5674	0.7050	0.4903

Appendix

Table 5: Aggregate benchmark results. FEV reports skill (

\uparrow

); TIME and GIFT-Eval report normalized errors (

\downarrow

). Red bold and blue underline mark the best and second-best displayed scores per column. Dashes indicate unavailable matched results. Training exposure differs across methods (Appendix B.4 ).

Task type	$n$	Timer-M1	TimesFM-3	Chronos-2	TiRex-2	Toto 2.0
Univariate	32	0.2968	0.2998	0.2799	0.2629	0.2653
Multivariate	26	0.4266	0.4252	0.4017	0.3889	0.4366
Past-only	12	0.4256	0.3933	0.3655	0.3969	0.3426
Known-future	18	0.4481	0.4549	0.4323	0.3979	0.3332
Known + past	12	0.2988	0.2923	0.3029	0.2465	0.1710

Appendix

Table 6: FEV MASE skill by task type. Groups are mutually exclusive and include all 100 configurations; higher is better. Best and second-best values are marked within each row.

Task type	$n$	Timer-M1	TimesFM-3	Chronos-2	TiRex-2	Toto 2.0
Univariate	32	0.3828	0.3847	0.3703	0.3538	0.3563
Multivariate	26	0.5954	0.5953	0.5795	0.5668	0.6033
Past-only	12	0.4668	0.4382	0.4239	0.4387	0.3950
Known-future	18	0.5363	0.5458	0.5257	0.4971	0.4344
Known + past	12	0.4295	0.4171	0.4254	0.3765	0.3022

Appendix

Table 7: FEV SQL skill by task type. Groups are mutually exclusive and include all 100 configurations; higher is better. Best and second-best values are marked within each row.

Group	$n$	Timer-M1	TimesFM-3	Chronos-2	TiRex-2	Toto 2.0
Shift	6	6.4278	7.4830	6.8490	6.9092	6.4418
Periodic	13	0.0271	0.6803	0.0919	0.0735	0.2300
Trend	10	0.1312	0.0299	0.4522	0.4512	0.0083

Appendix

Table 8: Temporal extrapolation groups corresponding to Figure 8 . Mean squared error is averaged over the complete records of each displayed group; lower is better.

Group	$n$	Timer-M1	TimesFM-3	Chronos-2	TiRex-2	Toto 2.0
Sign	2	0.0021	0.0036	0.0077	0.0100	0.0073
Cointegration	2	0.2477	0.3953	2.2627	1.3930	4.7848
Promotion	2	0.3008	0.3042	1.0424	0.5567	–
Lag	2	0.0012	0.0005	0.0185	0.0074	0.0049
Phase	2	0.000053	0.000043	0.0002	0.0087	0.0010
Scale	2	0.0688	0.0955	0.8690	2.2971	4.7189

Appendix

Table 9: Relational forecasting groups corresponding to Figure 8 . Mean squared error is averaged over the complete records of each displayed group; lower is better.

Group	$n$	Timer-M1	TimesFM-3	Chronos-2	TiRex-2	Toto 2.0
Irrelevant context	7	0.3681	0.2588	0.2554	0.2585	0.2451
Irrelevant targets	3	0.0035	–	0.0167	0.0633	0.0055
Missing event inputs	7	5.7917	5.7594	3.9130	2.2120	–
Target corruption	21	12.0938	2.6081	23.9802	0.2260	3.8370
Target missingness	21	0.1957	0.1477	0.7231	0.2184	0.3595
Variate order	7	0.0034	–	0.0221	0.0623	0.0055

Appendix

Table 10: Input reliability groups corresponding to Figure 8 . Mean squared error is averaged over the complete records of each displayed group; lower is better.

Gate	Overall	Univariate	Multivariate	Past-only	Known-future	Known + past
MASE Skill $\uparrow$
Adaptive	0.3771	0.2968	0.4266	0.4256	0.4481	0.2988
Fixed 0.202	0.3714	0.2969	0.4299	0.4266	0.4084	0.3081
Fixed 1.0	0.3680	0.2963	0.4260	0.4238	0.3979	0.3104
SQL Skill $\uparrow$
Adaptive	0.4887	0.3828	0.5954	0.4668	0.5363	0.4295

Appendix

Table 11: Gate ablation on FEV overall and five task types. Both metrics report skill scores. Red bold and underline indicate the best and second-best results within each column and metric. Adaptive gates achieve the highest overall skill, with the clearest advantage in known-future forecasting.

Recipe	FEV MASE $\uparrow$	FEV SQL $\uparrow$	TIME MASE $\downarrow$	TIME CRPS $\downarrow$	GIFT MASE $\downarrow$	GIFT CRPS $\downarrow$
Real Only	0.3196	0.4431	0.6579	0.5526	0.6998	0.4850
Synthetic Only	0.3568	0.4710	0.6438	0.5456	0.6884	0.4741
No-Joint	0.3578	0.4725	0.6379	0.5359	0.6819	0.4722
Full Recipe	0.3771	0.4887	0.6372	0.5363	0.6806	0.4688

Appendix

Table 12: Data-construction ablations across three benchmarks. Recipe names refer to the source-generation routes under comparison; shared benchmark-associated training data are unchanged across variants.

Figure 11: Temporal extrapolation across periodicity, modulation, frequency drift, and observed regime changes. Lower strips show Timer-M1’s absolute forecast error. Each panel uses its own value scale.

Figure 12: Relational forecasting with shared, signed, delayed, phase-shifted, cointegrated, and event-driven dynamics. Lower strips show available related inputs or target histories; they are not additional forecast targets unless specified by the task.

Figure 13: Input reliability under missing histories, imperfect event information, irrelevant inputs, and historical outliers. Lower strips show Timer-M1’s absolute forecast error.

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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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