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

Classification of electroencephalogram (EEG) signals obtained during motor imagery (MI) has substantial application potential, including communication assistance and rehabilitation support for patients with motor impairments. These signals remain inherently susceptible to physiological artifacts (e.g., eye blinking and swallowing), which pose persistent challenges. Although Transformer-based approaches for classifying EEG signals have been widely adopted, they often struggle to capture fine-grained dependencies within them. To overcome these limitations, we propose Cortical-SSM, a novel architecture that extends deep state space models to capture integrated dependencies of EEG signals across temporal, spatial, and frequency domains. We validated our method across two large-scale public MI EEG datasets containing more than 50 subjects. Our method outperformed baseline methods on both benchmarks. Furthermore, visual explanations derived from our model indicate that it effectively captures neurophysiologically relevant regions of EEG signals. These results indicate that Cortical-SSM provides a robust and interpretable alternative to attention-based architectures for MI EEG decoding. By enabling physiologically grounded feature learning, our method advances the reliability of subject-independent EEG classification and supports the development of practical and clinically deployable brain-computer interface systems.

Medical time series are central to healthcare, enabling continuous monitoring and supporting timely clinical decisions. Despite recent progress, existing methods struggle to jointly model local-global dynamics and handle nonstationarities like baseline drift, while often failing to capture latent channel interactions. To address these challenges, we propose MedMamba, an end-to-end architecture that integrates state space models with domain-specific inductive biases. Specifically, MedMamba first employs multi-scale convolutional embeddings to capture discriminative local morphology. Second, to mitigate nonstationarity, we introduce a tri-branch differential state space encoder that processes raw, temporal-difference, and frequency-domain views, fusing them to emphasize informative patterns while suppressing drift. Furthermore, to uncover latent channel correlations, we design a spatial graph Mamba module that learns a directed dependency structure regularized toward sparsity and acyclicity, which obviates the need for predefined graphs. Extensive experiments on five real-world datasets demonstrate that MedMamba achieves state-of-the-art performance while maintaining linear computational complexity, and ablation studies validate each component's contribution.Code is available at https://github.com/zhangda1018/MedMamba.

Medical time series, such as electrocardiograms (ECG) and electroencephalograms (EEG), exhibit complex temporal dynamics and structured cross-channel dependencies, posing fundamental challenges for automated analysis. Conventional convolutional and recurrent models struggle to capture long-range dependencies, while Transformer-based approaches incur quadratic complexity and often introduce redundant interactions that are misaligned with the intrinsic structure of physiological signals. To address these limitations, we propose MedMamba, a principle-driven multi-scale bidirectional state space architecture tailored for medical time series classification. Our design is guided by three key inductive biases of physiological signals: spatial centralization, multi-timescale temporal composition, and non-causal contextual dependency. These principles are instantiated through a lightweight channel-mixing module for cross-channel reparameterization, multi-scale convolutional tokenization for temporal decomposition, and bidirectional Mamba blocks for efficient global context modeling with linear complexity. Extensive experiments on six benchmark datasets spanning EEG, ECG, and human activity signals demonstrate that MedMamba consistently outperforms state-of-the-art methods across diverse modalities. Notably, it achieves 85.97% accuracy on PTB and establishes new state-of-the-art performance on the challenging ADFTD dataset (54.72% accuracy and 52.01% F1-score). Strong results on long-sequence benchmarks, such as SleepEDF, further validate its capability in modeling long-range dependencies. Moreover, MedMamba achieves a speedup of 4.6x in inference, highlighting its practicality for real-time clinical deployment. These results suggest that principle-guided state space modeling offers an effective and scalable alternative to Transformer-based approaches for medical time series analysis.