# QUALS: Corpus Equilibrium for Universal Forecasting via Pattern Quantization and Learnability Synchronization

arXiv: https://arxiv.org/abs/2609.20156 · HTML: https://mlsanity.com/paper/2609.20156/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 61 references that are in the map.
- First posted on arXiv 17 Sep 2026.

## Builds on (most cited first, 29 of 29)

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [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)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Vector-quantized Image Modeling with Improved VQGAN](https://mlsanity.com/paper/2110.04627/) (2021)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [Jukebox: A Generative Model for Music](https://mlsanity.com/paper/2005.00341/) (2020)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [GIFT-Eval: A Benchmark For General Time Series Forecasting Model Evaluation](https://mlsanity.com/paper/2410.10393/) (2024)
- [Sundial: A Family of Highly Capable Time Series Foundation Models](https://mlsanity.com/paper/2502.00816/) (2025)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [catch22: CAnonical Time-series CHaracteristics](https://mlsanity.com/paper/1901.10200/) (2019)
- [ForecastPFN: Synthetically-Trained Zero-Shot Forecasting](https://mlsanity.com/paper/2311.01933/) (2023)
- [ChatTS: Aligning Time Series with LLMs via Synthetic Data for Enhanced Understanding and Reasoning](https://mlsanity.com/paper/2412.03104/) (2024)
- [VisionTS: Visual Masked Autoencoders Are Free-Lunch Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2408.17253/) (2024)
- [Reward Shaping to Mitigate Reward Hacking in RLHF](https://mlsanity.com/paper/2502.18770/) (2025)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [Moirai 2.0: When Less Is More for Time Series Forecasting](https://mlsanity.com/paper/2511.11698/) (2025)
- [Restructuring Vector Quantization with the Rotation Trick](https://mlsanity.com/paper/2410.06424/) (2024)
- [Towards a General Time Series Forecasting Model with Unified Representation and Adaptive Transfer](https://mlsanity.com/paper/2405.17478/) (2024)
- [EasyTime: Time Series Forecasting Made Easy](https://mlsanity.com/paper/2412.17603/) (2024)
- [LightGTS: A Lightweight General Time Series Forecasting Model](https://mlsanity.com/paper/2506.06005/) (2025)
- [BLAST: Balanced Sampling Time Series Corpus for Universal Forecasting Models](https://mlsanity.com/paper/2505.17871/) (2025)
- [Seagull: An Infrastructure for Load Prediction and Optimized Resource Allocation](https://mlsanity.com/paper/2009.12922/) (2020)

## Abstract (arXiv)

Ubiquitous time series data across diverse domains enables critical applications in areas such as transportation systems and power grids. Recently, training foundation models on massive datasets to achieve accurate zero-shot forecasting has emerged as a major research focus. However, current studies predominantly prioritize architectural innovations while insufficiently addressing data diversity, often relying on simple data sampling strategies that fail to manage complex data distributions effectively, leading to inefficient use of training data and suboptimal performance. To address this, we propose QUALS, a large-scale time series corpus equilibrium framework. QUALS significantly enhances data efficiency, i.e., enabling existing models to achieve superior performance using only a small fraction of the original training data. Specifically, QUALS operates through two core mechanisms. First, a pattern quantization framework systematically decodes heterogeneous patterns from mixed corpora via vector quantization and uniform binning. Second, a learnability synchronization framework calibrates sampling weights for heterogeneous patterns, bridging the optimization gap between simple and complex motifs to maximize overall training efficiency. Extensive benchmarks demonstrate that pre-training on QUALS consistently achieves superior zero-shot performance, even under substantially reduced training budgets.