Ambiguous medical image segmentation aims to provide a series of diverse but plausible segmentation hypotheses. However, existing methods introduce stochasticity in a fixed and pre-defined manner, failing to form a progressive semantic modeling process. To address these challenges, we propose KANResDiff to learn local residual diffusion with Kolmogorov-Arnold Network, thereby assigning distinct roles across stages for ambiguity modeling. Specifically, we propose Independent Time Encoding that offers spline-based time embeddings instead of linear ones from MLPs, which enhances the independence across inference stages and assigns progressive semantic roles to different stages. We propose Residual Schrodinger Bridge that injects deterministic residual prior with learnable weights by constructing local Schrodinger Bridge instead of following manually settings, achieving a flexible deterministic-stochastic interaction and stage-aware ambiguity modeling thanks to local optimal diffusion path. Extensive experimental results on two public datasets demonstrate that KANResDiff achieves SOTA performance on GED and HM-IoU, with maximum improvements of 16.8% and 7.7%, respectively, while maintaining competitive performance on the MDM metric. Source code is available at https://github.com/PerceptionComputingLab/KANResDiff.
Early and scalable detection of mild cognitive impairment (MCI) remains an unresolved clinical challenge. Existing EEG-based screening approaches are constrained by handcrafted feature pipelines that discard neurophysiologically meaningful domain structure and deep learning classifiers that sacrifice interpretability for performance. No existing work unifies physiologically organized concept encoders, cross-concept interaction modeling, and nonlinear tabular classification in a sleep EEG-based MCI detection framework. This study proposes Concept-guided Polynomial-transformed Tabular learning using Kolmogorov-Arnold Network (CPTabKAN), which maps heterogeneous EEG-derived features into domain-informed concept representations, expands them via degree-2 polynomial transformation to expose first- and second-order interactions, and applies a Fourier-parameterized TabKAN classifier to learn nonlinear decision boundaries. CPTabKAN was evaluated on the Study of Osteoporotic Fractures cohort (372 subjects, overnight polysomnography), using 1,379 features organized into ten physiologically motivated concept groups. Under 10-fold cross-validation, CPTabKAN-Second Order achieved a weighted F1-score of 0.9038 (SD 0.034), outperforming GradientBoosting by 5.65 percentage points (t(9)=1.934,p=0.043, one-sided paired test), with advantages persisting under SMOTE-based balancing. Ablation analysis confirmed independent contributions from each component. Concept importance analysis revealed that power spectral density, multi-scale entropy, and Hjorth parameters dominated first-order weights, while cross-concept interactions involving Lempel-Ziv-Welch complexity, statistics, demographics, and slow oscillations exceeded all first-order scores. These results demonstrate that concept-structured, interaction-aware tabular learning surfaces physiologically coherent reasoning, supporting clinical trust.