HEC-KAN: Heterogeneous Edge Compression for KolmogorovArnold Networks with Adaptive Focal Loss for Imbalanced ECG Classi cation

KolmogorovArnold Networks (KANs) have become strong classi ers for physiologicalsignals, yet two important e ciency and optimization challenges remain: standard uniformgrid KANs allocate the same spline capacity across edges, which can over-parameterize lessinformative connections, while class weighting during training is often static despite severelabel imbalance.We propose HEC-KAN, a framework with two coupled contributions. First, Heterogeneous Edge Compression (HEC) periodically re-allocates per-edge spline grids using aratedistortion importance criterion and migrates coe cients between grids through an analytic L2 (Galerkin) projection that preserves each edge function, so compression does notrequire re-training from scratch. Second, an adaptive focal loss recomputes per-class weightsevery epoch from validation recall, αc ∝ 1−recallc, steering optimization toward the classesthe model still confuses.On the ve-class MIT-BIH arrhythmia benchmark, HEC-KAN reaches 98.64% accuracy(95% CI 98.4098.82) and 93.18% macro-F1 with approximately 10% fewer trainable parameters than a uniform-grid KAN, and raises sensitivity on the rarest class (F) to 85.0%,compared with 68.8% and 77.5% for the reference KAN and xLSTM baselines. Ablations isolate each contribution, and post-hoc threshold calibration exposes a continuum of screeningversus precision-oriented operating points.The reported results are based on a single-seed study; multi-seed validation and crossdataset evaluation are ongoing.