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LERD: Latent Event-Relational Dynamics for Neurodegenerative Classification

Hairong Chen, Yicheng Feng, Ziyu Jia, Samir Bhatt, Hengguan Huang

TL;DR

This work proposes LERD, an end-to-end Bayesian electrophysiological neural dynamical system that infers latent neural events and their relational structure directly from multichannel EEG without event or interaction annotations.

Abstract

Alzheimer's disease (AD) alters brain electrophysiology and disrupts multichannel EEG dynamics, making accurate and clinically useful EEG-based diagnosis increasingly important for screening and disease monitoring. However, many existing approaches rely on black-box classifiers and do not explicitly model the underlying dynamics that generate observed signals. To address these limitations, we propose LERD, an end-to-end Bayesian electrophysiological neural dynamical system that infers latent neural events and their relational structure directly from multichannel EEG without event or interaction annotations. LERD combines a continuous-time event inference module with a stochastic event-generation process to capture flexible temporal patterns, while incorporating an electrophysiology-inspired dynamical prior to guide learning in a principled way. We further provide theoretical analysis that yields a tractable bound for training and stability guarantees for the inferred relational dynamics. Extensive experiments on synthetic benchmarks and two real-world AD EEG cohorts demonstrate that LERD consistently outperforms strong baselines and yields physiology-aligned latent summaries that help characterize group-level dynamical differences.

LERD: Latent Event-Relational Dynamics for Neurodegenerative Classification

TL;DR

This work proposes LERD, an end-to-end Bayesian electrophysiological neural dynamical system that infers latent neural events and their relational structure directly from multichannel EEG without event or interaction annotations.

Abstract

Alzheimer's disease (AD) alters brain electrophysiology and disrupts multichannel EEG dynamics, making accurate and clinically useful EEG-based diagnosis increasingly important for screening and disease monitoring. However, many existing approaches rely on black-box classifiers and do not explicitly model the underlying dynamics that generate observed signals. To address these limitations, we propose LERD, an end-to-end Bayesian electrophysiological neural dynamical system that infers latent neural events and their relational structure directly from multichannel EEG without event or interaction annotations. LERD combines a continuous-time event inference module with a stochastic event-generation process to capture flexible temporal patterns, while incorporating an electrophysiology-inspired dynamical prior to guide learning in a principled way. We further provide theoretical analysis that yields a tractable bound for training and stability guarantees for the inferred relational dynamics. Extensive experiments on synthetic benchmarks and two real-world AD EEG cohorts demonstrate that LERD consistently outperforms strong baselines and yields physiology-aligned latent summaries that help characterize group-level dynamical differences.
Paper Structure (47 sections, 4 theorems, 44 equations, 4 figures, 6 tables, 4 algorithms)

This paper contains 47 sections, 4 theorems, 44 equations, 4 figures, 6 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Major Contributions.
  3. Related Work
  4. EEG-based AD diagnosis with supervised pipelines
  5. EEG dynamics and latent structure modeling
  6. Problem Formulation
  7. Bayesian Neural Dynamical System
  8. Overview
  9. Learning
  10. Prior: Electrophysiology–informed dLIF prior
  11. Posterior: Event Posterior Differential Equation (EPDE)
  12. Sampling: Mean–Evolving Lognormal Process (MELP)
  13. Event–relational graph (ERG)
  14. Experiments
  15. Toy Dataset
  16. ...and 32 more sections

Key Result

Theorem 4.1

Let $q(t)$ be a strictly positive, integrable density on $[0,S]$ ($0<S\le\infty$). Let the electrophysiology–informed prior be where $r:[0,S]\to[a,b]\subset(0,\infty)$ is measurable with $0<a\le b<\infty$. Define the change of variables $m=-e^{-t}\in[-e^{-S},-1)$ and $M=-\log(-m)=t$. Set Then and for any $\varepsilon\in(0,e^{-S})$, with $\mathcal{U}_{\varepsilon}\to \mathrm{KL}(q\|p_r)$ as $\v

Figures (4)

  • Figure 1: Overview of the LERD pipeline
  • Figure 2: Kernel density estimates of the inferred dLIF frequency distributions across Alzheimer's disease (AD), mild cognitive impairment (MCI), and healthy control (HC) groups for EEG channels F3, O2, Pz, and T3. The decreasing central frequency with increasing disease severity is consistent with established AD EEG slowing and serves as a model-derived latent summary.
  • Figure 3: Comparison of EEG connectivity graphs inferred by LERD versus Pearson correlation-based priors across healthy controls (HC), frontotemporal dementia (FTD), and Alzheimer's disease (AD) groups.
  • Figure 4: Predicted vs. ground-truth boundary times across frequency bands ([5–10], [10–15], [15–20] Hz): STRODE vs. LERD.

Theorems & Definitions (7)

  • Theorem 4.1: IVP–based upper bound for the event–prior KL under dLIF rates
  • Theorem 1.1: Entry–wise and matrix stability
  • Corollary 1.2: Deterministic and probabilistic perturbation bounds
  • Lemma 2.1: Shift–stability of IVPs huang2021strode
  • proof
  • proof
  • proof