Toto 2.0: Time series forecasting enters the scaling era

Emaad Khwaja

Gerald Woo

Chris Lettieri

Ameet Talwalkar

David Asker

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Today we’re releasing Toto 2, a family of open-weights time series forecasting models, on Hugging Face. Spanning 4m to 2.5B parameters, Toto 2.0 is designed to answer a simple and open question: Can time series foundation models (TSFMs) improve as they scale? Our results show they can. The highlights:

Scaling that works. Every size improves on the one below it, with no sign of saturation at 2.5B.

Best in class on every benchmark we tested. Toto 2.0 takes the top spots on BOOM (Datadog's observability forecasting benchmark), GIFT-Eval (the standard general-purpose benchmark), and TIME (a new contamination-resistant zero-shot benchmark).

A generational jump from Toto 1.0. Toto 2.0 is 7× more parameter-efficient at matching quality and dramatically faster at inference time.

Trained on observability and synthetic data, generalizes broadly. Toto 2.0 does not see any public forecasting data during pretraining, yet leads the field on general-purpose benchmarks.

CRPS Rank vs. parameter count on BOOM (left) and GIFT-Eval (right) for top foundation models; lower is better. The Pareto frontier traces the best CRPS rank achievable at each parameter budget—points on or near it represent the best quality-for-size tradeoff available. Every Toto 2.0 size sits on or near the frontier on both benchmarks, and CRPS rank improves monotonically with model size across the family.  *:first-child]:bg-white block tablet:p-9 desktop-sm:p-12 rounded-3xl bg-white max-h-[calc(100vh-6rem)] overflow-y-auto" data-astro-cid-d4yttbaw> CRPS Rank vs. parameter count on BOOM (left) and GIFT-Eval (right) for top foundation models; lower is better. The Pareto frontier traces the best CRPS rank achievable at each parameter budget—points on or near it represent the best quality-for-size tradeoff available. Every Toto 2.0 size sits on or near the frontier on both benchmarks, and CRPS rank improves monotonically with model size across the family.

This post first walks through the results and scaling behavior, including inference latency improvements and long-horizon stability. It then details where we think the next set of bottlenecks and opportunities for TSFMs are: closing the long-horizon gap with classical baselines, data curation, evaluation that tracks downstream value, and multimodality. We will soon release a technical report providing more details on our training data, our architectural and training recipes, and our u-μP hyperparameter transfer pipeline that tunes hyperparameters once on a small proxy model.

Both the Toto 2.0 model weights and our infrastructure library for distributed u-μP training (dd_unit_scaling) are available under the Apache 2.0 license.

Results

Toto 2.0 sets a new state of the art on BOOM, GIFT-Eval, and TIME. On BOOM, every size sits on the Pareto frontier. Among foundation models on GIFT-Eval, the three largest Toto 2.0 sizes lead the field. On the broader leaderboard that includes finetuned, ensemble, and agentic systems, our finetuned 2.5B (FT) and "Toto 2.0 Family and Friends" (FnF) ensemble take the top two slots outright. On TIME, the three largest Toto 2.0 variants hold top ranks.

All benchmarks report results across several metrics. CRPS (Continuous Ranked Probability Score) measures the quality of a probabilistic forecast, scoring how well a predicted distribution over future values aligns with observed outcomes. It is the metric most directly relevant to production forecasting use cases. MASE (Mean Absolute Scaled Error) measures point forecast accuracy, normalized against a naive seasonal baseline. Where metrics are reported as ranks, scores are averaged across all benchmark datasets to enable comparison across heterogeneous data.

BOOM

BOOM evaluates forecasting on observability metrics like CPU, memory, request latency, and error rates. These are the signals production monitoring systems care about.

BOOM results across CRPS rank, CRPS, and MASE; lower is better. All five Toto 2.0 sizes outrank every other foundation model on every metric. Toto 2.0 22m matches or beats Toto 1.0 across all three with roughly 7× fewer parameters. Toto models are shaded in purple. *:first-child]:bg-white block tablet:p-9 desktop-sm:p-12 rounded-3xl bg-white max-h-[calc(100vh-6rem)] overflow-y-auto" data-astro-cid-d4yttbaw> BOOM results across CRPS rank, CRPS, and MASE; lower is better. All five Toto 2.0 sizes outrank every other foundation model on every metric. Toto 2.0 22m matches or beats Toto 1.0 across all three with roughly 7× fewer parameters. Toto models are shaded in purple.

Every Toto 2.0 size sits on the Pareto frontier of BOOM: at any given parameter count, no other foundation model produces better forecasts. The three largest sizes lead the chart, with CRPS ranks of 3.88 (2.5B), 3.96 (1B), and 4.25 (313m). Behind them, the 22m at 5.52 already clears Toto 1.0 (6.94), establishing a 7× parameter-efficiency improvement over the previous generation. The 4m, at 7.17, is competitive with Toto 1.0 and Chronos-2 (7.39) despite being 30–40× smaller, making it a strong option for edge deployment.

GIFT-Eval: Foundation models

GIFT-Eval is a general-purpose forecasting benchmark spanning 97 datasets across domains such as energy, retail, weather, and finance. Notably, Toto 2.0 base models are not trained on any public data from these domains.

GIFT-Eval results, filtered to foundation models only (i.e., excluding finetuned, ensemble, and agentic systems), across CRPS rank, MASE rank, CRPS, and MASE; lower is better. Toto 2.0 sizes are highlighted in purple. The three largest Toto 2.0 sizes lead on CRPS rank, while the 2.5B leads on MASE rank. *:first-child]:bg-white block tablet:p-9 desktop-sm:p-12 rounded-3xl bg-white max-h-[calc(100vh-6rem)] overflow-y-auto" data-astro-cid-d4yttbaw> GIFT-Eval results, filtered to foundation models only (i.e., excluding finetuned, ensemble, and agentic systems), across CRPS rank, MASE rank, CRPS, and MASE; lower is better. Toto 2.0 sizes are highlighted in purple. The three largest Toto 2.0 sizes lead on CRPS rank, while the 2.5B leads on MASE rank.

Toto 2.0 ranks first among foundation models. The three largest sizes score 19.5 (2.5B), 20.3 (1B), and 20.5 (313m) on CRPS rank, with a 1.6-point gap separating the 313m from the next best foundation model, PatchTST-FM r1 [^8] at 22.1. Chronos-2, a strong competitor, sits at 22.4. The 22m at 25.7 beats Toto 1.0 (33.9) by 8 points. Every size strictly improves on the one below it on rank metrics.

GIFT-Eval: Finetuned models

In addition to pretrained foundation models, the GIFT-Eval leaderboard also includes entries for finetuned foundation models (those that have been tuned on the official training split of the benchmark), as well as agentic and ensembling methods that combine multiple foundation models. The five Toto 2.0 base models serve as the starting point for our finetuned models. To see how easily Toto base models can be finetuned for downstream tasks, we explored two approaches that use in-distribution data: finetuning a single model on a mix that includes the GIFT-Eval train split, and ensembling multiple models with a learned per-window weighting scheme. Both place at the top of the leaderboard, with ensembling and finetuning taking first and second on both CRPS and MASE rank.

GIFT-Eval leaderboard, showing all submission types: foundation models, finetuned models, ensembles, and agentic systems together. On this leaderboard, "finetuned" is used as an umbrella term for any model that uses the GIFT-Eval training split, including ensemble and agentic systems. Toto 2.0 sizes are highlighted in purple, with finetuned models outlined in pink. Toto 2.0 FnF takes #1 across CRPS rank, MASE rank, CRPS, and MASE; Toto 2.0 2.5B-FT alone places second, ahead of all prior leaderboard entries. *:first-child]:bg-white block tablet:p-9 desktop-sm:p-12 rounded-3xl bg-white max-h-[calc(100vh-6rem)] overflow-y-auto" data-astro-cid-d4yttbaw> GIFT-Eval leaderboard, showing all submission types: foundation models, finetuned models, ensembles, and agentic systems together. On this leaderboard, "finetuned" is used as an umbrella term for any model that uses the GIFT-Eval training split, including ensemble and agentic systems. Toto 2.0 sizes are highlighted in purple, with finetuned models outlined in pink. Toto 2.0 FnF takes #1 across CRPS rank, MASE rank, CRPS, and MASE; Toto 2.0 2.5B-FT alone places second, ahead of all prior leaderboard entries.

The ensemble takes first on the GIFT-Eval leaderboard, ahead of the finetuned 2.5B. But the more interesting finding is what’s inside the ensemble. The meta-learner’s softmax weights reveal what each candidate actually contributes to that prediction. The Toto 2.0 family is the largest contributor to the ensemble, accounting for 39% of predictions on average—more than any other model in the pool, including Chronos 2 (32%), and more than the four remaining open models combined. The fact that nearly 40% of that combination is consistently routed through Toto demonstrates Toto's distinctive role in capturing patterns that the rest of the pool cannot. In other words: when the meta-learner is free to weight everything it has, it spends more on the Toto family than on any other source.

TIME

TIME is a recent, task-centric zero-shot forecasting benchmark constructed from “fresh” datasets specifically chosen to mitigate the test-set contamination that affects established benchmarks. Toto 2.0 sweeps the top of the leaderboard: the 2.5B, 313m, and 1B take the top three positions on every TIME metric, with the next best external foundation model trailing the 1B by a clear margin. The 22m comes in fifth on rank metrics, ahead of every prior-generation foundation model we tested, and every size from the 22m up outperforms Toto 1.0.

Results on TIME across CRPS rank, MASE rank, CRPS, and MASE; lower is better. Toto 2.0 sizes are highlighted in purple. The 2.5B is the best Toto 2.0 size on every metric; the only deviation from strict monotonicity is the 313m, which slightly outperforms the 1B. *:first-child]:bg-white block tablet:p-9 desktop-sm:p-12 rounded-3xl bg-white max-h-[calc(100vh-6rem)] overflow-y-auto" data-astro-cid-d4yttbaw> Results on TIME across CRPS rank, MASE rank, CRPS, and MASE; lower is better. Toto 2.0 sizes are highlighted in purple. The 2.5B is the best Toto 2.0 size on every metric; the only deviation from strict monotonicity is the 313m, which slightly outperforms the 1B.

Inference latency

Toto 2.0 includes a series of refinements to the Toto 1.0 backbone, including contiguous patch masking (CPM), which lets the model predict an entire forecast in one parallel pass instead of step by step. CPM doesn't just improve forecast quality, it makes Toto 2.0 dramatically faster. A 1024-step forecast with Toto 1.0 requires up to 16 sequential autoregressive steps; with Toto 2.0 in single-pass mode, it's one forward pass.

We evaluate forward pass latency against Toto 1.0 and Chronos-2, the previous SOTA model on GIFT-Eval. Every Toto 2.0 size is

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