MuonSSM: Orthogonalizing State Space Models for Sequence Modeling
State space models (SSMs) have emerged as efficient linear-time alternatives to attention for long-sequence modeling. However, existing SSMs often suffer from instability and memory degradation over extended horizons due to poorly conditioned first-order updates and unbalanced update geometry. We introduce MuonSSM, a general framework that stabilizes SSM training by explicitly conditioning the geometry of memory updates rather than the recurrent transition matrix. MuonSSM augments SSMs with a momentum-based pathway and a lightweight Newton Schulz transformation on low-rank input injections, yielding bounded and spectrally conditioned updates while preserving parallel scan complexity. Theo...
| Authors | Thai-Khanh Nguyen, Ngoc-Bich-Uyen Vo, Thieu N. Vo et al. |
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| Primary category | cs.LG |
| Published | 29 June 2026 |
| Last updated at source | 29 June 2026 |
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