# Toto 2.0: Time Series Forecasting Enters the Scaling Era

arXiv: https://arxiv.org/abs/2605.20119 · HTML: https://mlsanity.com/paper/2605.20119/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 47 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 30 of 32)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Muon is Scalable for LLM Training](https://mlsanity.com/paper/2502.16982/) (2025)
- [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [Query-Key Normalization for Transformers](https://mlsanity.com/paper/2010.04245/) (2020)
- [GIFT-Eval: A Benchmark For General Time Series Forecasting Model Evaluation](https://mlsanity.com/paper/2410.10393/) (2024)
- [Chronos-2: From Univariate to Universal Forecasting](https://mlsanity.com/paper/2510.15821/) (2025)
- [Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performance](https://mlsanity.com/paper/2304.11127/) (2023)
- [Dissecting Adam: The Sign, Magnitude and Variance of Stochastic Gradients](https://mlsanity.com/paper/1705.07774/) (2017)
- [TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learning](https://mlsanity.com/paper/2505.23719/) (2025)
- [The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm](https://mlsanity.com/paper/2505.16932/) (2025)
- [NorMuon: Making Muon more efficient and scalable](https://mlsanity.com/paper/2510.05491/) (2025)
- [Time-MMD: Multi-Domain Multimodal Dataset for Time Series Analysis](https://mlsanity.com/paper/2406.08627/) (2024)
- [Moirai 2.0: When Less Is More for Time Series Forecasting](https://mlsanity.com/paper/2511.11698/) (2025)
- [This Time is Different: An Observability Perspective on Time Series Foundation Models](https://mlsanity.com/paper/2505.14766/) (2025)
- [Toto: Time Series Optimized Transformer for Observability](https://mlsanity.com/paper/2407.07874/) (2024)
- [It's TIME: Towards the Next Generation of Time Series Forecasting Benchmarks](https://mlsanity.com/paper/2602.12147/) (2026)
- [u-μP: The Unit-Scaled Maximal Update Parametrization](https://mlsanity.com/paper/2407.17465/) (2024)
- [Time-IMM: A Dataset and Benchmark for Irregular Multimodal Multivariate Time Series](https://mlsanity.com/paper/2506.10412/) (2025)
- [Unit Scaling: Out-of-the-Box Low-Precision Training](https://mlsanity.com/paper/2303.11257/) (2023)
- [TempoPFN: Synthetic Pre-training of Linear RNNs for Zero-shot Time Series Forecasting](https://mlsanity.com/paper/2510.25502/) (2025)
- [Cautious Weight Decay](https://mlsanity.com/paper/2510.12402/) (2025)
- [Decoder-Hybrid-Decoder Architecture for Efficient Reasoning with Long Generation](https://mlsanity.com/paper/2507.06607/) (2025)

## Built on by (most cited first, 30 of 30)

- [Falcon-X: A Time Series Foundation Model for Heterogeneous Multivariate Modeling](https://mlsanity.com/paper/2605.27286/) (2026)
- [Into the ORBIT for Time Series: Training Regimes for Foundation Models](https://mlsanity.com/paper/2608.13262/) (2026)
- [EXAONE Finance 1.0: An Attention-free Time Series Foundation Model for Financial Time Series](https://mlsanity.com/paper/2609.04239/) (2026)
- [Dr-CiK: A Benchmark testing Deep Research for Context-Aided Forecasting](https://mlsanity.com/paper/2605.27904/) (2026)
- [Beyond Numerical Time Series: A Unified Benchmark for Multimodal Forecasting with Heterogeneous Context](https://mlsanity.com/paper/2609.15087/) (2026)
- [t0: A Time-Series Foundation Model for Forecasting with Context](https://mlsanity.com/paper/2609.24559/) (2026)
- [TinyCast: Probabilistic Zero-Shot Forecasting with Computed Periodicity](https://mlsanity.com/paper/2608.15767/) (2026)
- [LLM-based Agents for Forecasting and Prediction: Methods, Training, Evaluation, and Applications](https://mlsanity.com/paper/2608.23058/) (2026)
- [Tabby: An Open Pretraining Recipe for Time Series Foundation Models](https://mlsanity.com/paper/2609.13956/) (2026)
- [Sharp Stability Threshold and Certification for Designing Stable Residual Architectures](https://mlsanity.com/paper/2607.14576/) (2026)
- [Network-Aware Forecasting on Wireless Access Points](https://mlsanity.com/paper/2609.01957/) (2026)
- [Distillation of Synthetic Data for Time Series Foundation Models](https://mlsanity.com/paper/2609.09586/) (2026)
- [When Tomorrow Becomes Today: Self-Evolving Policies for Agentic Time-Series Forecasting](https://mlsanity.com/paper/2609.24862/) (2026)
- [Aurora-X: Built for Extreme Time Series Forecasting](https://mlsanity.com/paper/2609.31038/) (2026)
- [Self-Evolving Time-Series Forecasting Agents with Episodic Memory and Online Policy Learning](https://mlsanity.com/paper/2609.32689/) (2026)
- [Instance-Adaptive Prompts as Context for Time-Series Foundation Models](https://mlsanity.com/paper/2609.34786/) (2026)
- [JudgeCast: Time Series Forecasting with Experience-Informed Covariate Judgements](https://mlsanity.com/paper/2609.36966/) (2026)
- [The Row Normalization Puzzle in Muon](https://mlsanity.com/paper/2609.39114/) (2026)
- [When, Not How Much: Evaluating Time-Series Foundation Models on Sparse Events](https://mlsanity.com/paper/2609.39386/) (2026)
- [OpenTSLM TeeMoE: A Unified Time-Series Language Model for Forecasting, Contextual Prediction, and Reasoning](https://mlsanity.com/paper/2609.40265/) (2026)
- [RACE: Residual-Aware Test-Time Adaptation for Neighbor-Rich Time-Series Foundation Model Forecasting](https://mlsanity.com/paper/2610.00405/) (2026)
- [EvoCast: Reliable Autonomous Research Agents for Iterative Forecasting Architecture Evolution](https://mlsanity.com/paper/2610.04517/) (2026)
- [Pythia: Toward Foundation World Models for Multimodal Time Series](https://mlsanity.com/paper/2610.05240/) (2026)
- [A Unified Scaling Law for Time Series Foundation Models](https://mlsanity.com/paper/2610.05269/) (2026)
- [QiYao-I: A Manifold Based Foundation Model for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2610.06936/) (2026)
- [Timer-M1: A Multivariate Time Series Foundation Model via Learning Primitives](https://mlsanity.com/paper/2610.11734/) (2026)
- [AdaCast: Conditional Parameter Generation for Adaptive Time Series Forecasting](https://mlsanity.com/paper/2610.12240/) (2026)
- [HART: Hybrid Attention-RWKV Time series Foundation Model](https://mlsanity.com/paper/2610.12883/) (2026)
- [GIFT-Eval-CTX: A Benchmark For Contextual Forecasting Model Evaluation](https://mlsanity.com/paper/2610.17794/) (2026)
- [TimeRSI: Towards Self-Improved Agentic Deployment for Time-Series Foundation Models](https://mlsanity.com/paper/2610.19725/) (2026)

## Abstract (arXiv)

We show that time series foundation models scale: a single training recipe produces reliable forecast-quality improvements from 4M to 2.5B parameters. We release Toto 2.0, a family of five open-weights forecasting models trained under this recipe. The Toto 2.0 family sets a new state of the art on three forecasting benchmarks: BOOM, our observability benchmark; GIFT-Eval, the standard general-purpose benchmark; and the recent contamination-resistant TIME benchmark. This report describes our experimental results and details the design decisions behind Toto 2.0: its architecture and training recipe, training data, and the u-muP hyperparameter transfer pipeline. All five base checkpoints are released under Apache 2.0.