# StoxLSTM: A Stochastic Extended Long Short-Term Memory Network for Time Series Forecasting

arXiv: https://arxiv.org/abs/2509.01187 · HTML: https://mlsanity.com/paper/2509.01187/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 50 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis](https://mlsanity.com/paper/2410.16032/) (2024)
- [Sequential Neural Models with Stochastic Layers](https://mlsanity.com/paper/1605.07571/) (2016)
- [Dilated Recurrent Neural Networks](https://mlsanity.com/paper/1710.02224/) (2017)
- [Probabilistic Forecasting with Temporal Convolutional Neural Network](https://mlsanity.com/paper/1906.04397/) (2019)
- [Learning Stochastic Recurrent Networks](https://mlsanity.com/paper/1411.7610/) (2014)
- [Unlocking the Power of LSTM for Long Term Time Series Forecasting](https://mlsanity.com/paper/2408.10006/) (2024)
- [xLSTM-Mixer: Multivariate Time Series Forecasting by Mixing via Scalar Memories](https://mlsanity.com/paper/2410.16928/) (2024)
- [xLSTMTime : Long-term Time Series Forecasting With xLSTM](https://mlsanity.com/paper/2407.10240/) (2024)
- [MMFNet: Multi-Scale Frequency Masking Neural Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2410.02070/) (2024)

## Abstract (arXiv)

The Extended Long Short-Term Memory (xLSTM) network has demonstrated strong capability in modeling complex long-term dependencies in time series data. Despite its success, the deterministic architecture of xLSTM limits its representational capacity and forecasting performance, especially on challenging real-world time series datasets characterized by inherent uncertainty, stochasticity, and complex hierarchical latent dynamics. In this work, we propose StoxLSTM, a stochastic xLSTM within a designed state space modeling framework, which integrates latent stochastic variables directly into the recurrent units to effectively model deep latent temporal dynamics and uncertainty. The designed state space model follows an efficient non-autoregressive generative approach, achieving strong predictive performance without complex modifications to the original xLSTM architecture. Extensive experiments on publicly available benchmark datasets demonstrate that StoxLSTM consistently outperforms state-of-the-art baselines, achieving superior performance and generalization.