Fractional State Space Transition for Long Sequence Modeling
State Space Models (SSMs) compress sequence history into a bounded recurrent state, making the resulting memory law a central architectural choice for long-context performance. Most modern SSMs rely on ODE-based dynamics that lead to exponential forgetting, limiting their ability to retain information over broad temporal ranges. We introduce FRAC, a selective SSM architecture derived from fractional dynamics that replaces this exponential decay with power-law long memory. To make fractional dynamics practical, FRAC approximates the heavy-tailed target kernel with a finite-state, log-spaced sum of exponential modes. This construction turns fractional memory into an efficient recurrent modu...
| Authors | Ivan Kobyzev, Abbas Ghaddar, Ali Nasiri-Sarvi et al. |
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| Primary category | cs.LG |
| Published | 28 September 2026 |
| Last updated at source | 28 September 2026 |
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