# ss-Mamba: Semantic-Spline Selective State-Space Model

arXiv: https://arxiv.org/abs/2506.14802 · HTML: https://mlsanity.com/paper/2506.14802/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Time series forecasting with SSMs, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 11 of its 13 references that are in the map.
- First posted on arXiv 3 Jun 2025.

## Placed in

- State-space sequence models (S4, Mamba) / [Time series forecasting with SSMs](https://mlsanity.com/ssm/time-series-forecasting-with-ssms/)

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [Time2Vec: Learning a Vector Representation of Time](https://mlsanity.com/paper/1907.05321/) (2019)
- [Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability](https://mlsanity.com/paper/2406.02496/) (2024)
- [Empowering Time Series Analysis with Foundation Models: A Comprehensive Survey](https://mlsanity.com/paper/2405.02358/) (2024)
- [Intervention-Aware Forecasting: Breaking Historical Limits from a System Perspective](https://mlsanity.com/paper/2405.13522/) (2024)
- [Exploring Kolmogorov-Arnold Networks for Interpretable Time Series Classification](https://mlsanity.com/paper/2411.14904/) (2024)
- [ms-Mamba: Multi-scale Mamba for Time-Series Forecasting](https://mlsanity.com/paper/2504.07654/) (2025)

## Abstract (arXiv)

We propose ss-Mamba, a novel foundation model that enhances time series forecasting by integrating semantic-aware embeddings and adaptive spline-based temporal encoding within a selective state-space modeling framework. Building upon the recent success of Transformer architectures, ss-Mamba adopts the Mamba selective state space model as an efficient alternative that achieves comparable performance while significantly reducing computational complexity from quadratic to linear time. Semantic index embeddings, initialized from pretrained language models, allow effective generalization to previously unseen series through meaningful semantic priors. Additionally, spline-based Kolmogorov-Arnold Networks (KAN) dynamically and interpretably capture complex seasonalities and non-stationary temporal effects, providing a powerful enhancement over conventional temporal feature encodings. Extensive experimental evaluations confirm that ss-Mamba delivers superior accuracy, robustness, and interpretability, demonstrating its capability as a versatile and computationally efficient alternative to traditional Transformer-based models in time-series forecasting.