NAKUL-Med: Spectral-Graph State Space Models with Dynamics Kernels for Medical Signals
The rapidly evolving field of medical signal analysis has recently seen the introduction of NAKUL, an innovative model designed to address the limitations of traditional state space models (SSMs). The new model, detailed in the preprint arXiv:2605.00871v1, showcases a comprehensive approach to analyzing multi-channel physiological signals, which are often challenging due to their complex temporal dynamics and spatial dependencies.
NAKUL addresses three primary limitations commonly faced by conventional SSMs:
- Fixed Kernels: Traditional models often utilize fixed kernels that fail to effectively capture the multi-scale temporal dynamics inherent in physiological signals. For example, motor preparation can take hundreds of milliseconds, while execution transients occur in mere tens of milliseconds.
- Markovian State Updates: The reliance on Markovian state updates restricts the model’s ability to incorporate global context, particularly for signals characterized by periodic oscillations.
- Channel-Independent Processing: Ignoring the spatial topology of electrodes results in suboptimal processing, as it does not leverage the inherent structure of the data.
To overcome these challenges, NAKUL introduces three key contributions to enhance the effectiveness of SSMs in medical signal analysis:
- Dynamic Kernel Generation: NAKUL employs parallel SSM branches with varying kernel sizes (3, 5, 7, and 11 timesteps), weighted by a meta-network that analyzes input statistics. This allows for adaptive selection of temporal scales, which is crucial for accurately modeling the dynamics of physiological signals.
- Spectral Context Modeling: The model integrates FFT-based operations complemented by learnable Gaussian frequency band filters. This technique captures global periodic patterns with a complexity of $O(N \log N)$, significantly improving efficiency while maintaining accuracy.
- Graph-Guided Spatial Attention: By leveraging fixed electrode topology, NAKUL provides spatial biases to multi-head attention mechanisms, facilitating principled cross-channel interactions. This enhances the model’s ability to interpret complex multi-channel data.
In performance assessments, NAKUL demonstrates its efficacy on the BCI Competition IV-2a motor imagery benchmark, achieving an impressive accuracy of 91.7$\pm$0.6\%. This performance is comparable to the EEG-Conformer, which achieved 92.1$\pm$0.7\% accuracy, while utilizing 28% fewer parameters (2.5M vs 3.5M) and providing 2.0$\times$ faster inference times (4.3ms vs 8.7ms).
Beyond motor imagery, NAKUL exhibits remarkable versatility, generalizing effectively to various tasks such as EEG emotion recognition (83.6%), multimodal EEG-fMRI integration (91.4%), and medical imaging tasks, including a 92.8% accuracy on ultrasound data. These results underscore the model’s capability to handle diverse medical signal processing challenges.
Ablation studies further highlight the contributions of the dynamic kernels, which alone account for an additional +2.6% improvement in accuracy. Notably, these kernels exhibit interpretable scale selection patterns that correlate with established neural dynamics, suggesting that NAKUL not only enhances performance but also provides valuable insights into the underlying physiological processes.
In summary, NAKUL represents a significant advancement in the field of medical signal analysis, combining dynamic kernel approaches, spectral context modeling, and graph-guided spatial attention to create a robust and versatile model capable of addressing the intricate challenges posed by multi-channel physiological signals.
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