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这项实证研究探讨了分数阶优化器与分形激活函数在神经网络训练中的相互作用，展示了选择性的配对，并强调控制分数阶记忆是一个有前景的方向。
This paper introduces DFSC, a PyTorch environment built around a Mittag-Leffler Spectral Layer (MLSL) that enables error-controlled, differentiable fractional propagation in hybrid neural models. It separates known fractional dynamics from data-driven corrections, supports batched/dense/sparse operator paths, and provides certified error bounds in certain regimes.