arXiv:2607.11462 2026 Architecture 2 ideas extracted · analyzed Aug 30, 2026
The paper introduces a scale derivative of the fractional p-Laplacian: differentiating with respect to the fractional order produces a logarithmic spatial kernel that is more singular near the diagonal and changes sign at large distances. This gives neural networks an explicit mechanism for representing sensitivity across spatial scales rather than applying only one fixed fractional smoothing strength. The most direct transfers are a log-fractional feature layer and a logarithmic fractional-energy regularizer, both testable in convolutional residual networks.
Add a feature transformation that approximates the derivative of a fractional diffusion operator with respect to its order. Instead of only smoothing features with one fractional order, the layer exposes whether a feature changes rapidly across spatial scales, which can help with textures, edges, and multiscale patterns.
Use the derivative of fractional feature energy with respect to its order as a regularizer for intermediate representations. This penalizes unstable scale behavior rather than simply suppressing all high frequencies, so it can preserve useful detail while discouraging uncontrolled changes across spatial scales.