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

arXiv: https://arxiv.org/abs/2605.00871 · HTML: https://mlsanity.com/paper/2605.00871/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 33 references that are in the map.
- First posted on arXiv 24 Apr 2026.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Temporal Convolutional Networks for Action Segmentation and Detection](https://mlsanity.com/paper/1611.05267/) (2016)
- [Dynamic Convolution: Attention over Convolution Kernels](https://mlsanity.com/paper/1912.03458/) (2019)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [Large Brain Model for Learning Generic Representations with Tremendous EEG Data in BCI](https://mlsanity.com/paper/2405.18765/) (2024)
- [CondConv: Conditionally Parameterized Convolutions for Efficient Inference](https://mlsanity.com/paper/1904.04971/) (2019)
- [Global Filter Networks for Image Classification](https://mlsanity.com/paper/2107.00645/) (2021)
- [Learning Spatio-Temporal Features with 3D Residual Networks for Action Recognition](https://mlsanity.com/paper/1708.07632/) (2017)
- [SiMBA: Simplified Mamba-Based Architecture for Vision and Multivariate Time series](https://mlsanity.com/paper/2403.15360/) (2024)
- [Self-Supervised Graph Neural Networks for Improved Electroencephalographic Seizure Analysis](https://mlsanity.com/paper/2104.08336/) (2021)
- [EEG-TCNet: An Accurate Temporal Convolutional Network for Embedded Motor-Imagery Brain-Machine Interfaces](https://mlsanity.com/paper/2006.00622/) (2020)
- [TSception: Capturing Temporal Dynamics and Spatial Asymmetry from EEG for Emotion Recognition](https://mlsanity.com/paper/2104.02935/) (2021)
- [SpectFormer: Frequency and Attention is what you need in a Vision Transformer](https://mlsanity.com/paper/2304.06446/) (2023)
- [LGGNet: Learning from Local-Global-Graph Representations for Brain-Computer Interface](https://mlsanity.com/paper/2105.02786/) (2021)
- [LUNA: Efficient and Topology-Agnostic Foundation Model for EEG Signal Analysis](https://mlsanity.com/paper/2510.22257/) (2025)
- [Scattering Vision Transformer: Spectral Mixing Matters](https://mlsanity.com/paper/2311.01310/) (2023)
- [MSGM: A Multi-Scale Spatiotemporal Graph Mamba for EEG Emotion Recognition](https://mlsanity.com/paper/2507.15914/) (2025)

## Built on by (most cited first, 1 of 1)

- [QiT: Quantum-Inspired Transformer for Visual Recognition Task](https://mlsanity.com/paper/2609.17789/) (2026)

## Abstract (arXiv)

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.