[
    {
        "id": "osp-21919",
        "type": "article-journal",
        "title": "Fractional State Space Transition for Long Sequence Modeling",
        "author": [
            {
                "family": "Kobyzev",
                "given": "Ivan"
            },
            {
                "family": "Ghaddar",
                "given": "Abbas"
            },
            {
                "family": "Nasiri-Sarvi",
                "given": "Ali"
            },
            {
                "family": "Shang",
                "given": "Lifeng"
            },
            {
                "family": "Cui",
                "given": "Yufei"
            }
        ],
        "URL": "https://omanscience.com/en/articles/fractional-state-space-transition-for-long-sequence-modeling",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "abstract": "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 module with parallel training and prefill, while retaining bounded-state autoregressive decoding. Extensive experiments, including 1.3B-parameter language modeling, demonstrate that FRAC consistently improves long-context performance over state-of-the-art SSM baselines while staying competitive on short-context. These results show that fractional dynamics provide a practical and effective prior for long-context SSMs."
    }
]