Fast and Scalable Caputo Fractional Gradient Descent via Perturbation-Preserving Memory Compression
Fractional gradient descent (FGD) incorporates long-range memory through Caputo-type operators and has been shown to improve stability in ill-conditioned and nonconvex optimization problems. Despite these advantages, its practical use remains limited, mainly due to the high computational cost of evaluating history-dependent convolutions, which scales quadratically with the number of iterations. In this paper, we focus on making Caputo-based optimization computationally viable without sacrificing its intrinsic memory structure. We begin by expressing the fractional descent direction as a discrete convolution over past gradients, which provides a unified view of the method. Based on this fo...
| Authors | Hwanseo Lee, Junseo Lee, Hyunju Kim |
|---|---|
| Primary category | math.OC |
| Published | 16 July 2026 |
| Last updated at source | 16 July 2026 |
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