NAKUL-Med: Spectral-Graph State Space Models with Dynamics Kernels for Medical Signals

State space models (SSMs) achieve linear-time complexity but struggle with multi-channel physiological signals due to three limitations: fixed kernels cannot capture multi-scale temporal dynamics (motor preparation over hundreds of milliseconds vs. execution transients in tens of milliseconds), Markovian state updates restrict global context for periodic oscillations, and channel-independent processing ignores spatial electrode topology. We introduce NAKUL, extending SSMs for medical signal analysis through three contributions: (1) Dynamic Kernel Generation-parallel SSM branches with varying kernel sizes (3, 5, 7, 11 timesteps) are weighted by a meta-network that analyzes input statistics, enabling adaptive temporal scale selection; (2) Spectral Context Modeling-FFT-based operations with learnable Gaussian frequency band filters capture global periodic patterns in O(N log N) complexity; (3) Graph-Guided Spatial Attention-fixed electrode topology provides spatial biases to multi-head attention for principled cross-channel interaction. On BCI Competition IV-2a motor imagery (our primary benchmark), NAKUL achieves 91.7±0.6% accuracy, matching EEG-Conformer (92.1±0.7%) while using 28% fewer parameters (2.5M vs 3.5M) and 2.0× faster inference (4.3ms vs 8.7ms). The model generalizes to EEG emotion recognition (83.6%), multimodal EEG-fMRI (91.4%), and medical imaging (92.8% on ultrasound), demonstrating architectural versatility. Ablations show dynamic kernels contribute +2.6% and exhibit interpretable scale selection patterns correlated with known neural dynamics.