TiRex-2: Streaming Multivariate Time Series Model

• TiRex-2 is a recurrent xLSTM-based time series model that extends univariate forecasting to multivariate settings with streaming updates.
• It leverages a memory-centric design with constant per-patch inference cost and strict causality while integrating past and future covariates.
• Synthetic coupling during pretraining enables TiRex-2 to generalize robustly across diverse forecasting tasks and maintain strong performance under deployment stress tests.

Searching arXiv for the exact TiRex-2 paper and closely related work to ground the article. TiRex-2 is a recurrent xLSTM-based time series foundation model that generalizes the univariate TiRex to multivariate forecasting with both past and future covariates. It is designed for settings in which observations arrive continuously, variables evolve jointly, and a subset of covariates is known ahead of time. Its defining combination of properties is a memory-centric recurrent design, strict causality on the target stream, support for future-known covariates, and constant per-patch cost under streaming inference (Podest et al., 1 Jul 2026).

1. Problem setting and model scope

TiRex-2 extends the recurrent TiRex backbone in two orthogonal directions: from univariate to multivariate forecasting, and from batch inference to constant-cost streaming updates. The model operates on three variate types—targets, past covariates, and future covariates—and is explicitly constructed so that future-known covariates can be exploited without allowing future target information to leak into the target representation (Podest et al., 1 Jul 2026).

This design addresses two limitations identified in Transformer-based time series foundation models. First, cross-variate modeling in self-attentive architectures typically incurs quadratic complexity in context length. Second, streaming inference usually requires recomputation over the full history as new observations arrive. TiRex-2 replaces full-history recomputation with a recurrent state carried by xLSTM layers, so that only the newly arrived patch needs to be processed at inference time. A plausible implication is that the model targets operational forecasting regimes in which latency and continuously extending contexts are primary constraints rather than secondary engineering considerations.

2. Architectural organization

After patching each variate into non-overlapping blocks of length $P$, TiRex-2 embeds the resulting sequence into tokens

$\mathbf{H}^{[0]}\in\mathbb{R}^{V\times L\times D},$

where $V=V_{\rm tgt}+V_{\rm pcov}+V_{\rm fcov}$ is the total number of variates and $L=\lceil(T+F)/P\rceil$. Each of the $N$ residual blocks alternates two mixers: a Time Mixer, implemented with xLSTM along the patch axis independently per variate, and a Variate Mixer, implemented as grouped multi-head self-attention along the variate axis independently per patch (Podest et al., 1 Jul 2026).

When only one variate is present, TiRex-2 skips the variate mixer entirely and reverts to the original TiRex with 38.4 M parameters. Activating the grouped variate mixer for multivariate inputs turns on an additional 44.1 M parameters, yielding a total of $\sim 82.5$ M parameters, while only 53.8 M are “active” on average for fev-bench because 65 % of tasks are univariate.

Mode	Activated components	Parameters
Univariate	Time mixer only; variate mixer skipped	38.4 M
Multivariate	Time mixer + grouped variate mixer	$38.4$ M + $44.1$ M $\approx 82.5$ M
fev-bench average active	Task-dependent activation	53.8 M

The time mixer uses xLSTM with mLSTM–sLSTM alternation to carry a hidden state of size $D$. For each variate type $\mathbf{H}^{[0]}\in\mathbb{R}^{V\times L\times D},$0,

$\mathbf{H}^{[0]}\in\mathbb{R}^{V\times L\times D},$1

For future-known covariates, the same weights are also used in reverse,

$\mathbf{H}^{[0]}\in\mathbb{R}^{V\times L\times D},$2

and the forward and reverse states are fused before being written back to the residual stream. This asymmetric treatment is central: targets and past covariates are processed forward only, whereas future covariates receive forward and reverse processing.

3. Causality, cross-variate interaction, and streaming

The grouped-attention Variate Mixer applies a mask

$\mathbf{H}^{[0]}\in\mathbb{R}^{V\times L\times D},$3

which permits $\mathbf{H}^{[0]}\in\mathbb{R}^{V\times L\times D},$4, $\mathbf{H}^{[0]}\in\mathbb{R}^{V\times L\times D},$5, and $\mathbf{H}^{[0]}\in\mathbb{R}^{V\times L\times D},$6 attention within a group, but forbids $\mathbf{H}^{[0]}\in\mathbb{R}^{V\times L\times D},$7 attention (Podest et al., 1 Jul 2026).

Combined with the forward-only time mixer on targets, this mask guarantees that the representation of each target token $\mathbf{H}^{[0]}\in\mathbb{R}^{V\times L\times D},$8 cannot depend on future target inputs $\mathbf{H}^{[0]}\in\mathbb{R}^{V\times L\times D},$9. The model therefore remains strictly causal on the target stream while still using future-known covariates bidirectionally. This is the core formal mechanism by which TiRex-2 reconciles forecasting causality with exogenous look-ahead.

Because xLSTM is recurrent, the time-mixing update is $V=V_{\rm tgt}+V_{\rm pcov}+V_{\rm fcov}$0 per variate and per block rather than $V=V_{\rm tgt}+V_{\rm pcov}+V_{\rm fcov}$1 as in self-attention. At inference time, only the newly arrived patch must be fed into the xLSTM hidden state, which yields constant-time streaming updates per patch. The reported streaming granularity is patch-level rather than step-level; with $V=V_{\rm tgt}+V_{\rm pcov}+V_{\rm fcov}$2, sub-patch updates incur patch-level latency. This suggests that TiRex-2 is optimized for long-sequence online forecasting where patch throughput is more important than single-step reactivity.

4. Synthetic multivariate pretraining and optimization recipe

To support multivariate pretraining without retraining on each downstream dataset, TiRex-2 uses a synthetic coupling pipeline that procedurally composes multivariate samples on the fly from large univariate corpora. Each minibatch samples $V=V_{\rm tgt}+V_{\rm pcov}+V_{\rm fcov}$3 univariate series independently and then applies one of several coupling mechanisms: identity or univariate pass-through, direct functional coupling, linear mixing, cointegration, linear structural causal models on a random DAG, or nonlinear structural causal models (Podest et al., 1 Jul 2026).

After coupling, the pipeline further randomizes variate order, applies per-variate time-warping, contiguous patch masking, partial future covariate hiding, and value/time discretization. The stated purpose is to expose the model to a broad mixture of cross-variate structures and realistic sampling artifacts. A plausible implication is that TiRex-2 is trained less as a benchmark-specialized forecaster and more as a transfer-oriented prior over multivariate temporal structure.

The training configuration is specified as follows. The corpus includes Chronos public training, approximately 30 M univariate series; synthetic GP, approximately 15 M; chaotic dysts, 1 %; and GIFT-Eval hold-out. Separate checkpoints were trained with overlapping datasets removed per benchmark to avoid leakage. Optimization uses AdamW with weight decay 0.01, gradient clipping at 1.0, bf16 mixed precision, and batch size 64 on 2 $V=V_{\rm tgt}+V_{\rm pcov}+V_{\rm fcov}$4 H100. The learning-rate schedule is OneCycleLR with cosine warmup over 5 % of 700 k steps, from $V=V_{\rm tgt}+V_{\rm pcov}+V_{\rm fcov}$5 up to $V=V_{\rm tgt}+V_{\rm pcov}+V_{\rm fcov}$6, then cosine anneal to $V=V_{\rm tgt}+V_{\rm pcov}+V_{\rm fcov}$7. The architecture uses 12 alternating mLSTM/sLSTM xLSTM blocks, $V=V_{\rm tgt}+V_{\rm pcov}+V_{\rm fcov}$8, heads $V=V_{\rm tgt}+V_{\rm pcov}+V_{\rm fcov}$9, $L=\lceil(T+F)/P\rceil$0, and dropout $L=\lceil(T+F)/P\rceil$1. The default sequence layout is input context $L=\lceil(T+F)/P\rceil$2, forecast horizon $L=\lceil(T+F)/P\rceil$3, and patch length $L=\lceil(T+F)/P\rceil$4, corresponding to 64 input tokens and 10 output tokens. A short post-training phase of 100 k steps with $L=\lceil(T+F)/P\rceil$5 extends the configuration to $L=\lceil(T+F)/P\rceil$6 and $L=\lceil(T+F)/P\rceil$7.

5. Reported empirical behavior

Zero-shot forecasting was evaluated on fev-bench and GIFT-Eval. On fev-bench, TiRex-2 attains the best average SQL and MASE, beats Chronos-2, Moirai-2, Toto-1.0, and TimesFM-2.5, achieves pairwise mean win rates above 60 % against all baselines on SQL, and has the highest skill score relative to seasonal naïve. On GIFT-Eval, comprising 28 heterogeneous datasets, it sets a new state of the art in MASE and CRPS and outperforms TiRex-1.0, FlowState, PatchTST-FM, and others (Podest et al., 1 Jul 2026).

Beyond aggregate benchmark scores, the paper emphasizes robustness under deployment-relevant stress tests.

Evaluation setting	Reported outcome
fev-bench	Best average SQL and MASE; pairwise mean win rate exceeds 60 % against all baselines
GIFT-Eval	New state of the art in MASE and CRPS
Streaming up to 32 million time steps	MASE remains flat across the entire range
Chaotic “dysts” up to 1056-step horizons	Outperforms Chronos-2 at all horizons
Covariate-shift tolerance	Quantile loss remains informative over much larger $L=\lceil(T+F)/P\rceil$8 than Chronos-2 or other multivariate models

The streaming stress test uses a noisy AR(1) process streamed to 32 million time steps. TiRex-2’s MASE remains flat across the full range, far beyond both the 2k pre-training and 8k post-training context lengths, and each new patch is processed in constant time. In long-horizon forecasting on chaotic “dysts,” across 135 trajectories at multiple granularities and horizons up to 1056 steps, TiRex-2 outperforms Chronos-2 at all horizons, with larger gains at fine resolution. Under covariate shift, when a target random walk is paired with a lagged covariate $L=\lceil(T+F)/P\rceil$9, its quantile loss remains informative over much larger $N$0 than Chronos-2 or other multivariate models. Taken together, these results suggest that the model’s recurrent memory is not merely a complexity optimization; it also stabilizes extrapolation under contexts far longer than those seen during pretraining.

6. Ecosystem position, limitations, and naming ambiguity

A related software-development result is the integration of TiRex into the Darts FoundationModel API, alongside Chronos-2, TimesFM 2.5, and PatchTST-FM. In that context, TiRex is often referred to as “TiRex-2” to distinguish it from earlier toy implementations. Darts exposes standardized interfaces for zero-shot or fine-tuned forecasting, uncertainty estimation, covariate handling, backtesting, and multi-series batching (Dai et al., 25 Jun 2026).

The limitations described for TiRex-2 are specific rather than generic. Because future-known covariates are processed bidirectionally in the time mixer, streaming updates to those covariates require a fresh pass, although only along the future-covariate streams. In practice, the reported assumption is that calendar or planned-event covariates are static over a forecast window; if they change online, they can be shifted into the past region to recover full streaming speed. Streaming also operates at patch granularity, so sub-patch changes are not incorporated until the next patch boundary. A proposed future direction is dynamic covariate selection, in which an in-context estimate of each covariate’s contribution would prune uninformative streams from group attention and reduce inference FLOPs without retraining (Podest et al., 1 Jul 2026).

The name “TiRex-2” has also been used in other, unrelated literatures. It should not be conflated with “T-Rex2: Towards Generic Object Detection via Text-Visual Prompt Synergy,” an open-set object detector (Jiang et al., 2024); with the “TIREX estimation algorithm (‘TiRex-2’)” in extreme-response sufficient dimension reduction (Aghbalou et al., 2021); or with Tau-REx II, an exoplanet emission-spectrum retrieval framework (Waldmann et al., 2015). In current time-series usage, however, TiRex-2 most specifically denotes the multivariate, streaming extension of the TiRex forecasting foundation model (Podest et al., 1 Jul 2026).