# HALO: Enhancing Time Series Generation via Hyperspherical Latents and Masked AutoregRessive Modeling

arXiv: https://arxiv.org/abs/2609.34511 · HTML: https://mlsanity.com/paper/2609.34511/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 48 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 30 of 35)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Sequence Level Training with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06732/) (2015)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [MAGE: MAsked Generative Encoder to Unify Representation Learning and Image Synthesis](https://mlsanity.com/paper/2211.09117/) (2022)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [A Survey of Controllable Text Generation using Transformer-based Pre-trained Language Models](https://mlsanity.com/paper/2201.05337/) (2022)
- [DUET: Dual Clustering Enhanced Multivariate Time Series Forecasting](https://mlsanity.com/paper/2412.10859/) (2024)
- [VisionTS: Visual Masked Autoencoders Are Free-Lunch Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2408.17253/) (2024)
- [Deep Learning for Time Series Classification and Extrinsic Regression: A Current Survey](https://mlsanity.com/paper/2302.02515/) (2023)
- [TAB: Unified Benchmarking of Time Series Anomaly Detection Methods](https://mlsanity.com/paper/2506.18046/) (2025)
- [On the Constrained Time-Series Generation Problem](https://mlsanity.com/paper/2307.01717/) (2023)
- [Vector Quantized Time Series Generation with a Bidirectional Prior Model](https://mlsanity.com/paper/2303.04743/) (2023)
- [Multimodal Latent Language Modeling with Next-Token Diffusion](https://mlsanity.com/paper/2412.08635/) (2024)
- [DBLoss: Decomposition-based Loss Function for Time Series Forecasting](https://mlsanity.com/paper/2510.23672/) (2025)
- [GT-GAN: General Purpose Time Series Synthesis with Generative Adversarial Networks](https://mlsanity.com/paper/2210.02040/) (2022)
- [DAG: A Dual Correlation Network for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2509.14933/) (2025)
- [Kronos: A Foundation Model for the Language of Financial Markets](https://mlsanity.com/paper/2508.02739/) (2025)
- [TimeDP: Learning to Generate Multi-Domain Time Series with Domain Prompts](https://mlsanity.com/paper/2501.05403/) (2025)
- [HMAR: Efficient Hierarchical Masked Auto-Regressive Image Generation](https://mlsanity.com/paper/2506.04421/) (2025)
- [Market-GAN: Adding Control to Financial Market Data Generation with Semantic Context](https://mlsanity.com/paper/2309.07708/) (2023)
- [TimeMosaic: Temporal Heterogeneity Guided Time Series Forecasting via Adaptive Granularity Patch and Segment-wise Decoding](https://mlsanity.com/paper/2509.19406/) (2025)
- [TarDiff: Target-Oriented Diffusion Guidance for Synthetic Electronic Health Record Time Series Generation](https://mlsanity.com/paper/2504.17613/) (2025)

## Abstract (arXiv)

Most existing time series generators rely on a two-stage modeling paradigm: the first stage learns discrete latent representations of time series; the second stage performs autoregressive modeling on these discrete latents through next token prediction. However, this paradigm suffers from two stage-specific limitations: the first stage can lead to information loss when discretizing continuous time series, while the second stage is prone to error accumulation during autoregressive generation. To address these limitations, our core idea is to perform generative modeling in a continuous latent space with a more efficient autoregressive framework. We propose HALO, which enhances time series generation via Hyperspherical Latents and Masked Autoregressive modeling to achieve this goal by tackling two key bottlenecks: (1) variance and scale heterogeneity of continuous latent representations; (2) the difficulty of balancing generation efficiency with temporal correlation modeling. HALO first introduces a hyperspherical VAE that constrains continuous latents to a fixed-radius hyperspherical shell, effectively stabilizing the numerical fluctuations of continuous latent representations. Secondly, we develop a masked autoregressive model that balances parallel decoding and temporal correlation learning, substantially reducing the number of inference steps required for generation and improving generation stability. Our extensive experiments demonstrate that HALO achieves state-of-the-art generation performance while offering significantly improved inference efficiency over existing advanced baselines.