FRACTAL: SSM with Fractional Recurrent Architecture for Computational Temporal Analysis of Long Sequences

• URL: http://arxiv.org/abs/2605.08833v1
• Date: Sat, 09 May 2026 09:38:44 GMT
• Title: FRACTAL: SSM with Fractional Recurrent Architecture for Computational Temporal Analysis of Long Sequences
• Abstract summary: This paper proposes a Fractional Recurrent Architecture for Computational Temporal Analysis of Long sequences (FRACTAL)<n>By deriving projection operators with analytically characterized spectral properties and a tunable index, the proposed method sensitivity to recent signal perturbations while preserving the spectral structure that encodes fractional scale-invariant memory dynamics.<n>FRACTAL achieves an average score of 87.11% on the Long Range Arena benchmark, including 61.85% on the ListOps task, outperforming the S5 model.
• Score: 13.320173396455226
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Effective sequence modeling fundamentally requires balancing the retention of unbounded history with the high-resolution detection of abrupt short-term variations common in real-world phenomena. However, existing state space models (SSMs) relying on high-order polynomial projection operators (HiPPO) face a critical trade-off where uniform measures dilute recent information to maintain timescale invariance, while exponential measures sacrifice global context to capture local dynamics. This paper proposes a Fractional Recurrent Architecture for Computational Temporal Analysis of Long sequences (FRACTAL), a novel architecture integrating fractional measure theory into recursive memory updates to address this limitation. By deriving projection operators with analytically characterized spectral properties and a tunable singularity index, the proposed method amplifies sensitivity to recent signal perturbations while preserving the spectral structure that encodes scale-invariant memory dynamics. This theoretical innovation is instantiated within a simplified diagonalized state space framework by modulating input projection initialization to enable simultaneous capture of multi-scale temporal features. FRACTAL achieves an average score of 87.11\% on the Long Range Arena benchmark, including 61.85\% on the ListOps task, outperforming the S5 model.

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