Abstract
Multifractal analysis has revealed regularities in many self-seeding phenomena, yet its use in modern deep learning remains limited. Existing end-to-end multifractal methods rely on heavy pooling or strong feature-space decimation, which constrain tasks such as semantic segmentation. Motivated by these limitations, we introduce two inductive priors: Monofractal and Multifractal Recalibration. These methods leverage relationships between the probability mass of the exponents and the multifractal spectrum to form statistical descriptions of encoder embeddings, implemented as channel-attention functions in convolutional networks. Using a U-Net-based framework, we show that multifractal recalibration yields substantial gains over a baseline equipped with other channel-attention mechanisms that also use higher-order statistics. Given the proven ability of multifractal analysis to capture pathological regularities, we validate our approach on three public medical-imaging datasets: ISIC18 (dermoscopy), Kvasir-SEG (endoscopy), and BUSI (ultrasound). Our empirical analysis also provides insights into the behavior of these attention layers. We find that excitation responses do not become increasingly specialized with encoder depth in U-Net architectures due to skip connections, and that their effectiveness may relate to global statistics of instance variability.
Abstract (translated)
多分形分析揭示了许多自激发现象中的规律性，但在现代深度学习中的应用仍然有限。现有的端到端多分形方法依赖于重采样池化或强特征空间降解，这限制了诸如语义分割等任务的灵活性。鉴于这些局限性，我们引入了两种归纳先验：单分形和多分形再校准。这两种方法利用指数的概率质量和多分形频谱之间的关系来形成编码器嵌入的统计描述，并将其实现为卷积网络中的通道注意力函数。使用基于U-Net的框架，我们展示了多分形再校准相对于其他采用高阶统计信息的通道注意机制的基础模型产生了显著的优势。 鉴于多分形分析捕捉病理规律的能力已得到证明，我们在三个公开的医学成像数据集上验证了我们的方法：ISIC18（皮肤镜检查），Kvasir-SEG（内窥镜检查）和BUSI（超声）。我们实证分析还提供了关于这些注意层行为的见解。我们发现，在U-Net架构中，由于跳过连接的存在，兴奋响应不会随着编码器深度的增加而越来越专业化，并且它们的有效性可能与实例变异性的一般统计有关。
URL
https://arxiv.org/abs/2512.02198
