# Fine-Tuning a Time Series Foundation Model with Wasserstein Loss

arXiv: https://arxiv.org/abs/2409.15367 · HTML: https://mlsanity.com/paper/2409.15367/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 13 references that are in the map.
- First posted on arXiv 18 Sep 2024.

## Builds on (most cited first, 6 of 6)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [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)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)

## Built on by (most cited first, 2 of 2)

- [Post-Training in Time Series Foundation Models: A Unifying Framework](https://mlsanity.com/paper/2607.20002/) (2026)
- [Foundation Model Forecasts: Form and Function](https://mlsanity.com/paper/2510.19345/) (2025)

## Abstract (arXiv)

Inspired by recent advancements in large language models (LLMs) for Natural Language Processing (NLP), there has been a surge in research focused on developing foundational models for time series forecasting. One approach involves training LLM architectures on tokenized time series data using cross-entropy loss. Although this method has demonstrated promising results, cross-entropy loss is primarily designed for classification tasks and does not account for the distance between classes. To address this limitation, we propose using the Wasserstein loss for such architectures. To validate our approach, we fine-tuned a foundational time series model on 22 zero-shot datasets, comparing the performance of cross-entropy loss with that of Wasserstein loss. Our results demonstrate that replacing cross-entropy loss with Wasserstein loss significantly improves point estimation.