ImProNCDE: Impulse-Corrected Neural Controlled Differential Equations with Prototype Learning for Longitudinal Prognosis Prediction

2026-06-17

AI Summary

This work addresses the challenges of capturing abrupt pathological changes and ensuring stable long-term predictive trajectories in ophthalmic longitudinal follow-up data, which are often sparse, irregularly sampled, and incomplete. To this end, the authors propose a neural controlled differential equation (NCDE) framework integrating Residual Impulse Calibration (RIC) and a Prototype-guided Trajectory Stabilizer (PTS). The RIC module injects impulse corrections at observation times to respond to non-smooth pathological shifts, while the PTS leverages learnable prognostic prototypes to regularize latent trajectory evolution, thereby mitigating error accumulation during numerical integration and enhancing class discriminability. Extensive experiments on multiple public and private ophthalmic datasets (comprising over 1,206 cases) demonstrate that the proposed model significantly outperforms existing sequence modeling approaches, achieving state-of-the-art performance in both prognostic prediction accuracy and trajectory stability.

Abstract

Longitudinal ophthalmic imaging analysis is an essential step for prognosis prediction in ophthalmic diseases. However, AI-assisted prognosis models are challenged by follow-up sequences, which tend to be sparse, irregularly sampled, and incomplete. Although advanced prognosis modeling methods, especially for the methods based on neural controlled differential equations (NCDEs), provide a principled continuous-time framework for sparse and irregular longitudinal data. Unfortunately, two major concerns remain unsolved in clinical follow-up modeling. First, the smooth latent dynamics of standard NCDEs is poorly matched to abrupt pathological changes induced by therapeutic intervention, lesion recurrence, or long follow-up gaps. Second, numerical integration over long horizons can accumulate errors, which will produce unstable latent trajectories and weakened class discrimination. To address these challenges, we propose ImProNCDE, an impulse-corrected NCDE framework with prototype learning for longitudinal ophthalmic prognosis prediction. To capture abrupt pathological changes beyond smooth latent dynamics, ImProNCDE introduces Residual Impulse Calibration (RIC), which injects residual-based impulse corrections at visit times and then recalibrates the latent state when observations deviate from continuous predictions. To further mitigate error accumulation over long horizons, we introduce a Prototype-guided Trajectory Stabilizer (PTS), which aims to attract latent trajectories toward learnable prognosis prototypes to reduce class overlap and which ultimately improves long-horizon stability. Experiments on multiple private and public longitudinal ophthalmic datasets (totalling over 1206 samples) show that ImProNCDE outperforms existing SOTA methods focusing on sequence modeling.

Problem

• longitudinal prognosis prediction
• sparse and irregular data
• abrupt pathological changes
• error accumulation
• ophthalmic imaging

Innovation

• Neural Controlled Differential Equations
• Impulse Correction
• Prototype Learning
• Longitudinal Prognosis
• Ophthalmic Imaging