💻 computer science

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

The paper proposes ImProNCDE, an impulse-corrected Neural Controlled Differential Equation framework enhanced with prototype learning and residual impulse calibration to address the challenges of sparse, irregular, and incomplete longitudinal ophthalmic data by better capturing abrupt pathological changes and stabilizing long-horizon prognosis predictions.

Original authors: Hao Wang, Yupeng Xu, Jinghao Lin, Shuchang Ye, Yige Peng, Jinman Kim, Kun Liu, Lei Bi

Published 2026-06-19

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CC BY 4.0

Original authors: Hao Wang, Yupeng Xu, Jinghao Lin, Shuchang Ye, Yige Peng, Jinman Kim, Kun Liu, Lei Bi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Predicting the Future of Eye Disease

Imagine a doctor trying to predict how a patient's eye disease will behave over the next year. They have a series of photos (OCT scans) taken at different times. But there's a problem: these photos aren't taken on a strict schedule. Sometimes a patient comes in every month; other times, they skip for six months. Plus, the disease doesn't always change slowly; sometimes, a treatment works instantly, or the disease flares up suddenly.

Existing computer models struggle with this. They are like a smooth, slow-moving train that assumes the track is always straight. If the track suddenly jumps or the train hits a pothole (a sudden change in the eye), the train keeps going on its old path and misses the reality.

ImProNCDE is a new AI system designed to be a smarter navigator. It doesn't just guess the future based on a smooth curve; it constantly checks the map against reality and makes sudden "jumps" to correct its course when new information arrives.

How It Works: Three Key Tools

The researchers built this system using three main "tools" to handle the messy, irregular nature of real-world medical data.

1. The Smooth Road (NCDE)

The Problem: Most diseases change gradually, like a river flowing. Standard AI models try to draw a smooth line between two eye scans.
The Solution: The system uses something called a Neural Controlled Differential Equation (NCDE). Think of this as a GPS that draws a smooth, continuous line between your eye scans, even if the scans are months apart. It assumes the disease is flowing like a river between visits.

2. The "Reality Check" (Residual Impulse Calibration - RIC)

The Problem: Sometimes, the "smooth river" assumption breaks. A patient might get a shot (anti-VEGF treatment) that instantly shrinks a swelling, or the disease might suddenly get worse. When the patient returns for their next scan, the photo looks totally different from what the smooth GPS predicted.
The Solution: This is where RIC comes in. Imagine you are driving, and your GPS says "turn left in 1 mile," but you look out the window and see a massive roadblock. You don't keep driving blindly; you slam on the brakes and make a sudden turn.

How it works: When a new eye scan arrives, ImProNCDE compares it to what it predicted would happen. If there is a big difference (a "residual"), it injects a sudden "impulse" or correction into its internal model. It essentially says, "My smooth prediction was wrong; I need to jump my internal state to match this new reality immediately."

3. The "Magnet" (Prototype-guided Trajectory Stabilizer - PTS)

The Problem: If you keep making sudden jumps to correct the path, you might get lost or drift too far away from the truth, especially if you have to predict a long time into the future. The path might become unstable.
The Solution: This is the PTS. Imagine you are navigating a foggy forest. You have a map with three specific "magnets" (prototypes) representing the three possible outcomes: Cured, Not Cured, and Relapsed.

How it works: After the system makes a correction (the "jump"), it gently pulls the path toward the nearest "magnet." This keeps the prediction organized and prevents it from drifting into a confusing middle ground. It ensures that even after many corrections, the final prediction stays clearly in the "Cured" or "Relapsed" zone, making the final diagnosis more reliable.

The Results: Why It Matters

The researchers tested this system on three different groups of eye patients (some with diabetes, some with glaucoma). They compared ImProNCDE against other advanced AI models, including those that try to "generate" future images.

The Winner: ImProNCDE consistently beat the other models.
The Proof: In a test with over 1,200 patient samples, it was better at predicting who would get better and who would get worse.
The Visuals: When the researchers looked at how the AI "thought" (its internal data), they saw that ImProNCDE kept the different patient groups (Cured vs. Relapsed) neatly separated, whereas other models let them mix together like a blurry mess.

Summary

Think of ImProNCDE as a smart, adaptive coach for a runner:

It predicts the runner's pace smoothly between water stations (visits).
If the runner suddenly speeds up or trips (a new scan shows a change), the coach immediately shouts a correction to adjust the plan (RIC).
The coach keeps the runner focused on the finish line, ensuring they don't wander off the track (PTS).

This allows the AI to handle the messy, irregular, and sudden changes of real-life eye disease much better than previous methods.

Technical Summary: ImProNCDE for Longitudinal Ophthalmic Prognosis Prediction

1. Problem Statement

Longitudinal ophthalmic imaging analysis is critical for prognosis prediction, yet existing AI-assisted models face significant challenges due to the nature of clinical follow-up data. Clinical sequences are often sparse, irregularly sampled, and incomplete. While Neural Controlled Differential Equations (NCDEs) offer a principled continuous-time framework for such data, standard implementations suffer from two specific limitations in clinical settings:

Mismatch with Abrupt Changes: Standard NCDEs assume smooth latent dynamics. However, disease trajectories often undergo abrupt pathological shifts due to therapeutic interventions (e.g., anti-VEGF injections), lesion recurrence, or long follow-up gaps. Standard models fail to explicitly recalibrate the latent state when new observations deviate from the smooth continuous prediction.
Error Accumulation: Numerical integration over long horizons can accumulate errors, leading to unstable latent trajectories that drift away from the true pathological status, thereby weakening class discrimination and prognosis accuracy.

2. Methodology: ImProNCDE

The authors propose ImProNCDE (Impulse-Corrected Neural Controlled Differential Equations), a framework designed to model irregular longitudinal ophthalmic trajectories while handling abrupt pathological shifts. The pipeline consists of three coupled components:

A. Spatial Semantic Embedding and Continuous Path Construction

Encoder: A pretrained retinal foundation encoder (RETFound) extracts visit-level imaging embeddings ( $x_i$ ) from irregular OCT scans.
Continuous Control Path: To drive the differential equation, these discrete visit embeddings are lifted into a continuous, differentiable control path $x(t)$ using natural cubic Hermite spline interpolation.
Control Signal: The analytical derivative of this spline, $u(t) = \frac{dx(t)}{dt}$ , serves as the continuous control signal for the NCDE solver, allowing the latent system to evolve continuously between visits while being guided by patient-specific temporal context.

B. Residual Impulse Calibration (RIC)

To address the mismatch between smooth NCDE predictions and abrupt observed changes, RIC recalibrates the latent state at each visit time $t_{i+1}$ :

Residual Computation: The model compares the NCDE-predicted latent state ( $h_{pred}$ ) with the newly observed imaging feature ( $x_{gt}$ ). A residual $r$ is computed: $r = x_{gt} - W_{align}h_{pred}$ .
Impulse Generation: The residual is projected into a compact code and used to compute an outer-product interaction with the current latent state. A learnable gain function maps this to a residual-to-state gain matrix.
State Recalibration: An impulse correction $\Delta h$ is applied to the latent state: $h_{new} = h_{pred} + \beta \Delta h$ . This allows the model to "jump" the latent trajectory to align with the new observation when a significant deviation occurs.

C. Prototype-guided Trajectory Stabilizer (PTS)

To mitigate long-horizon drift and improve class separability, PTS imposes a class-aware geometric constraint:

Learnable Prototypes: The model learns a set of prognosis prototypes $\{p_k\}$ , each representing a latent anchor for a specific outcome class.
Mahalanobis Distance: The proximity between the corrected state $h_{new}$ and each prototype is measured using a diagonal Mahalanobis distance, which learns dimension-wise scaling of the latent space.
Stabilization: A prototype-guided force pulls the latent state toward the weighted barycenter of the prototypes: $h_{stabilized} = h_{new} + \alpha \sum w_k (p_k - h_{new})$ . This regularizes the trajectory toward outcome-relevant regions.

D. Aggregation and Optimization

The corrected latent sequence is aggregated using a Transformer encoder with positional embeddings to capture cross-visit dependencies. The final classification token is passed through a linear head for endpoint prognosis prediction. The model is optimized using a standard cross-entropy loss on the sequence-level prognosis label.

3. Key Contributions

ImProNCDE Framework: A novel impulse-corrected NCDE framework specifically designed for sparse and irregular longitudinal ophthalmic data, capable of capturing discontinuous pathological progression through continuous-time dynamics.
Residual Impulse Calibration (RIC): A mechanism that measures the residual mismatch between predicted and observed states to apply adaptive impulse corrections, realigning latent trajectories with actual disease status at visit times.
Prototype-guided Trajectory Stabilizer (PTS): A method using learnable prognosis prototypes and Mahalanobis geometry to constrain corrected trajectories, reducing long-horizon drift and improving endpoint separability.

4. Experimental Results

The method was evaluated on three datasets: OCT4DME (public, short-term treatment response), GRAPE (public, natural glaucoma progression), and OURS (in-house, multi-center diabetic retinopathy with anti-VEGF intervention).

Performance: ImProNCDE outperformed existing State-of-the-Art (SOTA) methods, including traditional sequence models (RNN, LSTM, Transformer), medical time-series backbones (Medformer, ViTST), and adapted diffusion-based models (DiffMIC, TrajDiff).
- On the OURS dataset, ImProNCDE achieved 73.30% accuracy and 89.56% AUC, outperforming the strongest competitor (DiffMIC) by 0.18% in accuracy and 1.91% in AUC.
- On GRAPE, it achieved 89.74% accuracy, significantly outperforming the next best method by over 10 percentage points.
- On OCT4DME, it achieved 77.98% accuracy and 84.92% AUC.
Ablation Studies: Removing the full impulse mechanism (RIC) caused a drastic drop in F1-score (from 71.50% to 35.89% on the OURS dataset), confirming its necessity for handling visit-level deviations. Similarly, removing prototype stabilization (PTS) reduced F1 to 44.61%, validating its role in long-horizon stability.
Representation Analysis: t-SNE visualizations and clustering metrics (Silhouette score, ARI, NMI) demonstrated that ImProNCDE produces more compact and separated latent clusters for different prognosis classes compared to raw RETFound features.

5. Significance and Claims

The paper claims that ImProNCDE provides an effective framework for modeling sparse, irregular, and clinically dynamic ophthalmic follow-up sequences. Its significance lies in:

Handling Clinical Reality: Unlike standard continuous models that assume smooth evolution, ImProNCDE explicitly accounts for the abrupt pathological changes induced by treatment or disease recurrence, which are common in clinical follow-ups but often missed by standard NCDEs.
Stability: By integrating prototype learning, the framework addresses the issue of error accumulation over long horizons, ensuring that the latent trajectory remains anchored to clinically meaningful outcome regions.
Generalizability: The method demonstrates robust performance across diverse clinical scenarios, including intervention-driven cohorts (anti-VEGF), natural progression cohorts, and short-term response settings, without requiring explicit future image generation.

The authors note that while the current evaluation is limited to ophthalmology and anti-VEGF interventions, the framework offers a promising direction for modeling irregular longitudinal data in other medical domains, though further validation is required.