Early machine learning approaches for MCI-to-AD conversion relied on hand-crafted features from single time-point images, such as cortical thickness or hippocampal volume [5] . With the advent of deep learning, convolutional neural networks (CNNs) were used to extract features from baseline scans [6] . However, these methods ignore the crucial temporal dimension. Subsequent work employed RNNs/LSTMs to model longitudinal data [7] . While effective on regularly sampled data, their performance degrades with real-world irregular sampling, a problem our method explicitly addresses.

To handle irregular sampling, methods like Phased LSTMs [8] and GRU-D [9] use time gates or decay mechanisms. More recently, Neural Ordinary Differential Equations (Neural ODEs) [10] have emerged as a powerful architecture for modeling continuous dynamics from discrete observations. They have shown promise in medical applications [11] but have not been fully explored for aligning multi-modal longitudinal neuroimaging data within a causal prediction architecture, which is our key innovation.

Attention mechanisms are widely used to interpret model decisions [12] . In neuroimaging, they help identify disease-relevant regions [13] . However, attention does not guarantee causality; it can highlight spurious correlations. Causal learning methods, particularly using counterfactual reasoning [14] , aim to mitigate this. Invariant risk minimization [15] and counterfactual augmentation [16] are relevant paradigms. Our counterfactual constraint draws inspiration from this line of work, applying it specifically to spatio-temporal attention in neuroimaging.

Let a patient’s longitudinal data be represented as a set of tuples:

$\mathcal{D}={\left\{\left(t_n,X_n^{MRI},X_n^{PET}\right)\right\}}_{n=1}^N$, where $t_n$ is the time of the n-th visit relative to a baseline (e.g., $t_1=0$), and $X_n$ are the corresponding multi-modal images. The visits are irregularly spaced, i.e., $\text{Δ}{t}_n=t_{n+1}-t_n$ is not constant. The goal is to predict a binary label $Y\in \left\{0,1\right\}$ indicating whether the patient will convert from MCI to AD within a predefined future time window (e.g., 3 years).

This module encodes each snapshot $\left(X_n^{MRI},X_n^{PET}\right)$ into a latent vector $z_n$ using a shared encoder network $E_{\varphi }$: This shared encoder $E_{\varphi }$ is specifically designed to handle multi-modal misalignment. It first processes each modality through separate, modality-specific convolutional branches to extract features at the appropriate spatial scale and contrast for MRI and PET data respectively. The outputs of these branches are then concatenated and passed through subsequent shared convolutional layers. This design allows the network to first learn modality-specific representations before fusing them into a unified latent space, effectively aligning the heterogeneous information from different imaging protocols into a coherent representation for the subsequent Neural ODE processing.

$z_n=E_{\varphi }\left(X_n^{MRI},X_n^{PET}\right)$ (1)

The sequence of latent vectors $\left\{\left(t_1,z_1\right),\left(t_2,z_2\right),\cdots ,\left(t_N,z_N\right)\right\}$ represents the patient’s state at observed time points.

We model the continuous trajectory of the patient’s latent state using a Neural ODE. We define a neural network $f_{\theta }$ that parameterizes the derivative of the latent state with respect to time:

$\frac{\text{d}z\left(t\right)}{\text{d}t}=f_{\theta }\left(z\left(t\right),t\right)$ (2)

Given an initial condition $z\left(t_0\right)=z_0$, the latent state at any time $t$ can be found by solving the ODE:

$z\left(t\right)=z_0+{\displaystyle {\int }_{t_0}^t{f}_{\theta }\left(z\left(\tau \right),\tau \right)\text{d}\tau }$ (3)

In practice, we use an ODE solver (e.g., Runge-Kutta) to perform this integration. This allows us to interpolate the latent state at any desired time.

We define a regularized time grid $\mathcal{T}=\left\{{\tau }_1,{\tau }_2,\cdots ,{\tau }_T\right\}$ common to all patients (e.g., ${\tau }_i=i\times 6$ months). For each patient, we solve the Neural ODE to generate a aligned latent sequence:

$Z_{\text{aligned}}=\left[z\left({\tau }_1\right),z\left({\tau }_2\right),\cdots ,z\left({\tau }_T\right)\right]$ (4)

The parameters $\varphi$ and $\theta$ are learned end-to-end by minimizing a reconstruction loss (e.g., Mean Squared Error) between the observed latents $z_n$ and the ODE solutions at the corresponding times $t_n$, ensuring the learned dynamics faithfully represent the patient’s true trajectory.

The aligned latent sequence $Z_{\text{aligned}}\in {ℝ}^{T\times D}$ is fed into the predictor.

We use a 1D temporal convolutional network (TCN) [17] followed by a Transformer encoder [12] to capture complex long-range dependencies across time. This dual architecture of TCN followed by Transformer was chosen for their complementary strengths in capturing temporal dependencies. The TCN serves as an efficient local feature extractor, using its dilated convolutions to capture multi-scale, short-range patterns within the aligned latent sequence with minimal computational overhead. The Transformer encoder then processes these refined features to model global, long-range dependencies across the entire timeline through its self-attention mechanism. This allows every time point (e.g., baseline) to directly influence and be influenced by every other time point (e.g., 24-month), crucial for identifying complex, non-linear interactions between early and late-stage pathological changes that are characteristic of neurodegenerative progression.

$H_{\text{TCN}}=\text{TCN}\left(Z_{\text{aligned}}\right)$ (5)

$H=\text{Transformer}\left(H_{\text{TCN}}\right)$ (6)

The output $H\in {ℝ}^{T\times D^{\prime }}$ is a refined spatio-temporal representation.

An attention network $g_{\psi }$ generates a dynamic attention weight for each feature dimension at each time step, effectively creating a spatio-temporal attention map $A\left(t,d\right)$:

$A=\sigma \left(g_{\psi }\left(H\right)\right)$ (7)

where $\sigma$ is the sigmoid function, and $A\in {\left[0,1\right]}^{T\times D^{\prime }}$. The attended representation is computed as:

$H_{\text{att}}=A\odot H$ (8)

This attended representation is then global-average-pooled over time and passed through a final classifier (a linear layer) to produce the prediction probability $\hat{Y}=P\left(Y=1|\mathcal{D}\right)$.

This is the core of our causal reasoning. We define a confounder distribution $p_c$, which represents non-causal changes. For neuroimaging, this could be a model of healthy aging or scanner drift. For a given patient’s latent vector at time $\tau$, $z\left(\tau \right)$, and its attention $A\left(\tau \right)$, we generate a counterfactual latent vector:

$\tilde{z}\left(\tau \right)=z\left(\tau \right)+ϵ\odot A\left(\tau \right)\text{where}ϵ~p_c$ (9)

The confounder distribution $p_c$ is central to the validity of our counterfactual constraint. In this work, we model $p_c$ as a zero-mean, isotropic Gaussian distribution, $p_c=\mathcal{N}\left(0,{\sigma }^{2}I\right)$, where $I$ is the identity matrix. This simple prior is chosen to represent non-informative, non-causal variations, such as minor scanner noise or benign anatomical differences not linked to AD pathology. The standard deviation $\sigma$ is a key hyperparameter that controls the magnitude of the counterfactual perturbation. Its value was set to $\sigma =0.15$ through a grid search on the validation set to maximize prognostic performance; this value was found to generate meaningful counterfactuals that altered the latent representation without pushing it into implausible regions of the feature space. While effective, the simplicity of this prior is a limitation, and learning a more sophisticated, data-driven confounder model from large-scale control populations is a focus of future work.

This perturbation applies a confounder-based change specifically to the features the model found most salient. The counterfactual latent sequence ${\tilde{Z}}_{\text{aligned}}$ is processed by the same predictor to get a counterfactual prediction $\tilde{Y}$.

The model is trained with a combined loss function:

$ℒ={ℒ}_{\text{task}}\left(\hat{Y},Y\right)+\beta \cdot {ℒ}_{\text{CF}}$ (10)

The task loss ${ℒ}_{\text{task}}$ is standard binary cross-entropy. The counterfactual loss ${ℒ}_{\text{CF}}$ is the Kullback-Leibler (KL) divergence between the original and counterfactual predictions:

${ℒ}_{\text{CF}}=\text{KL}\left(P\left(\hat{Y}|Z\right)\parallel P\left(\tilde{Y}|\tilde{Z}\right)\right)$ (11)

This loss penalizes the model if its prediction changes under this confounder-based perturbation of attended features. It forces the predictor to rely on features whose predictive power is invariant to these confounders, i.e., features that are more likely to be causally linked to AD pathology. The hyperparameter $\beta$ controls the strength of this causal constraint.

We used data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) [18] . Our cohort consisted of 500 MCI patients (250 converters (MCI-C), 250 non-converters (MCI-NC)) with at least three longitudinal T1-weighted MRI and FDG-PET scans each. Data was preprocessed: MRIs were segmented and normalized to a common space; PET scans were co-registered to their corresponding MRI and intensity normalized. We used data from baseline, 12-month, and 24-month visits as inputs and defined conversion as a clinical diagnosis of AD within 36 months from baseline.

We implemented CASCADE-Net in PyTorch [19] using the TorchDiffEq package. The model was trained with the Adam optimizer [20] for 100 epochs with an initial learning rate of 1e⁻⁴. We used a 5-fold cross-validation strategy. We compared against several strong baselines:

Performance was evaluated using Area Under the ROC Curve (AUC), Accuracy (ACC), Sensitivity (SEN), and Specificity (SPEC).

CASCADE-Net exhibited significantly faster convergence compared to all baseline models, stabilizing after approximately 25 epochs—2.4× faster than the standard LSTM (60 epochs) and 1.4× faster than the Neural ODE approach (35 epochs). This accelerated convergence can be attributed to several architectural innovations:

Efficient Gradient Propagation: The integration of Neural ODE solvers with causal attention mechanisms enables more stable gradient flow during backpropagation. Unlike traditional recurrent architectures that suffer from vanishing gradient problems in long temporal sequences, our continuous-time formulation maintains gradient integrity across irregular time intervals.

Regularized Learning Dynamics: The causality-aware constraints act as an implicit regularizer, preventing the model from overfitting to spurious correlations in the early training phases. This regularization effect is particularly evident in the smooth, monotonic decrease of both training and validation losses in Figure 2 , contrasting with the occasional fluctuations observed in baseline models.

The loss curves in Figure 2 reveal distinct optimization patterns across different architectures:

CASCADE-Net demonstrated the most stable optimization trajectory, with both training and validation losses decreasing smoothly without significant oscillations. This stability suggests that the spatio-temporal alignment module effectively resolves the distribution mismatches between irregularly sampled inputs and the regularized latent space.

Neural ODE-based approaches showed improved stability over traditional RNN variants but still exhibited minor fluctuations, particularly during the first 20 epochs. This indicates that while continuous-time modeling helps, it requires additional architectural components (as implemented in CASCADE-Net) to achieve optimal stability.

GRU-D and Standard LSTM models displayed pronounced oscillations throughout training, reflecting the challenges of handling irregular sampling patterns and long-term dependencies without explicit temporal alignment mechanisms.

The validation loss curves in Figure 2 provide compelling evidence for CASCADE-Net’s superior generalization capabilities:

Minimal Overfitting Gap: The small divergence between training and validation losses ( $\text{Δ}=0.0085$) indicates excellent generalization, significantly outperforming Neural ODE ( $\text{Δ}=0.012$), GRU-D ( $\text{Δ}=0.015$), and LSTM ( $\text{Δ}=0.018$) models. This reduced generalization gap demonstrates the effectiveness of our causal regularization in preventing overfitting to training-specific patterns.

Early Stopping Robustness: CASCADE-Net reached near-optimal performance much earlier than comparative models, as clearly shown in Figure 3 , suggesting practical advantages for clinical applications where computational resources may be limited. The model maintained stable performance after convergence, without exhibiting the performance degradation observed in some baseline models during extended training.

The Receiver Operating Characteristic analysis in Figure 4 provides critical insights into the discriminatory power of CASCADE-Net. The model achieves an exceptional AUC value of 0.87 as in Figure 5 and Figure 6 , significantly outperforming all comparative models.

Clinical Interpretation of AUC Performance:

The Precision-Recall analysis reveals CASCADE-Net’s strong clinical applicability, maintaining high precision (AP = 0.85) across all recall levels. This consistency is particularly valuable for clinical deployment where different operating points may be required based on specific clinical scenarios.

The quantitative results demonstrate CASCADE-Net’s superior performance across all evaluation metrics:

Area Under the Curve (AUC): 0.87 ± 0.01

CASCADE-Net achieves outstanding discriminatory power, representing a 19% relative improvement over Baseline CNN and 13% improvement over Neural ODE ablation. This indicates excellent ability to distinguish between converters and non-converters across all classification thresholds.

Accuracy: 79.4% ± 1.2%

The model correctly classifies approximately 4 out of 5 patients, representing substantial 16% and 11% improvements over Baseline CNN and Standard LSTM respectively, demonstrating effective temporal alignment and causal attention mechanisms.

Balanced Sensitivity (0.80) and Specificity (0.79)

The nearly identical values indicate excellent performance balance without significant class bias. The 80% sensitivity enables early intervention for true converters, while 79% specificity reduces unnecessary interventions for non-converters.

The confusion matrix analysis in Figure 7 reveals several key advantages:

Reduced False Positives: CASCADE-Net demonstrates significantly fewer false positives (21% vs 34% for baseline), reducing unnecessary treatments and patient anxiety in clinical settings.

Enhanced True Positive Detection: The 80% true positive rate provides longer intervention windows for actual converters, enabling more effective treatment planning.

Balanced Classification: Nearly equal sensitivity and specificity values indicate excellent balance between identifying true converters and avoiding false alarms, particularly valuable given typical class imbalances in clinical datasets.

The classification reports reveal CASCADE-Net’s superior characteristics:

Precision: Substantially higher for both classes (0.786 vs 0.652 for MCI-NC; 0.790 vs 0.678 for MCI-C), demonstrating more reliable positive predictions.

Recall: Balanced across both classes (0.792 vs 0.784), unlike the baseline which shows significant imbalance (0.704 vs 0.624).

F1-Score: Markedly higher values (0.789 vs 0.677 for MCI-NC; 0.787 vs 0.650 for MCI-C), representing 16.5% and 21.1% improvements respectively. This statistics are well summarised in Table 1 and Table 2 for CASCADE Net and Baseline CNN respectively.

CASCADE-Net exhibits exceptional balance across performance metrics:

Class Balance: Minimal differences between classes (0.006 across metrics) compared to baseline’s 12.8% recall difference.

Metric Consistency: Close alignment between precision, recall, and F1-score indicates robust and reliable classification behavior.

The performance characteristics have profound clinical implications:

Early Intervention: 80% sensitivity enables identification of most future AD cases, facilitating earlier interventions.

Resource Optimization: 79% specificity reduces unnecessary referrals and testing, optimizing healthcare resource allocation.

Trustworthy Predictions: Balanced performance across metrics ensures clinically reliable predictions without systematic bias.

Computational Efficiency: Rapid convergence and stable optimization make CASCADE-Net feasible for deployment in resource-constrained healthcare settings.

The performance improvements are statistically significant (p < 0.01) across all metrics. Small standard deviations (±0.01 for AUC, ±1.2% for accuracy) indicate consistent performance across validation folds, demonstrating robustness and generalizability.

The ablation study reveals progressive improvements:

The comprehensive performance analysis demonstrates that CASCADE-Net achieves state-of-the-art predictive performance while providing balanced, clinically-reliable predictions. The model’s excellent discriminatory power (AUC: 0.87), balanced sensitivity/specificity (0.80/0.79), and consistent performance across metrics position it as a valuable tool for MCI-to-AD conversion prediction with significant potential impact on patient care and resource allocation in clinical practice.

The convergence behavior aligns with our theoretical framework regarding causality-aware learning:

The rapid stabilization of loss curves in Figure 2 supports our hypothesis that explicit modeling of causal relationships reduces the hypothesis space that the model needs to explore during training. By incorporating domain knowledge about temporal dependencies and causal mechanisms in neurodegenerative progression, CASCADE-Net avoids learning spurious correlations that often plague purely data-driven approaches.

Furthermore, the parallel decrease in both training and validation losses suggests that the causal inductive biases embedded in our architecture align well with the underlying data-generating process of MCI-to-AD conversion, validating our approach to integrating clinical domain knowledge with deep learning methodologies.

In conclusion, the training dynamics and convergence analysis in Figure 2 and Figure 3 not only demonstrate CASCADE-Net’s practical advantages in terms of efficiency and stability but also provide empirical validation of our theoretical framework for causality-aware spatio-temporal modeling in clinical prognostic prediction.

As shown in Table 3 , CASCADE-Net achieves the best performance across all metrics, significantly outperforming all baseline models (paired t-test, p < 0.01). This demonstrates the overall effectiveness of our integrated approach. The improvement over the Standard LSTM highlights the benefit of handling irregular sampling. The gain over GRU-D suggests the Neural ODE offers a more powerful continuous dynamic model. The significant jump over the Neural ODE + Classifier ablation underscores the critical contribution of our novel Causal Spatial Attention mechanism.

Table 4 presents the results of our ablation study. Each component contributes positively to the final performance. Removing the Temporal Alignment module causes the largest performance drop, confirming its necessity. Using a standard attention mechanism without the counterfactual loss ( $\beta =0$) leads to a noticeable drop in AUC, suggesting that without the causal constraint, the model learns slightly less robust features. Replacing the counterfactual loss with a standard $L_1$ sparsity constraint on attention performs worse, indicating that our CF loss does more than just sparsify attention—it guides it toward causal features.

Figure 8 visualizes the dynamic attention maps for example patients. For a converter patient, the attention progressively focuses on regions known to be severely affected in AD, such as the medial temporal lobe (including the hippocampus), entorhinal cortex, and temporoparietal association areas. This evolving pattern aligns with the known Braak staging of neurofibrillary tangle pathology [21] . For a non-converter, the attention is either more diffuse, stable, or focuses on areas less specific to AD progression. This interpretable output provides a clear, data-driven rationale for the model’s prediction, which can be invaluable for clinical experts.

CASCADE-Net provides a comprehensive solution to several key challenges in longitudinal medical image analysis. The Neural ODE-based alignment offers a principled, continuous-time approach to handling irregular sampling, superior to discrete RNN-based approximations. The integration of a counterfactual constraint within the learning objective is a significant step towards building more causally-aware AI models for healthcare. It moves beyond correlation towards learning invariant mechanisms, which should theoretically improve generalization across different hospitals and scanner protocols. The dynamic attention maps provided by CASCADE-Net offer tangible clinical utility beyond a simple prognostic score. For instance, a clinician reviewing a case with high predicted conversion risk ( $\hat{Y}>0.8$) could examine the attention evolution over the 24-month timeline. If the maps show progressively increasing attention in the hippocampus and entorhinal cortex—regions known to be affected early in AD—this objective, data-driven visualization could support a decision to shorten the next monitoring interval from 12 to 6 months. Conversely, if the attention pattern is diffuse or stable, even with a moderate risk score, a clinician might maintain a standard monitoring schedule. This interpretable output transforms the model from a black-box predictor into a decision-support tool that provides a clear rationale for clinical actions. A limitation of our current work is the definition of the confounder distribution $p_c$. In this study, we modeled it as a simple Gaussian based on population statistics for age-related change. Furthermore, our model was developed and validated exclusively on data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) cohort. While ADNI provides high-quality, well-curated data, its specific inclusion criteria and demographic profile may limit the immediate generalizability of our findings to more diverse, real-world clinical populations with different ethnic backgrounds, comorbidities, and imaging protocols. Future work will focus on learning more sophisticated confounder models from large-scale control data and, crucially, validating the CASCADE-Net framework on independent, multi-site datasets to confirm its robustness and clinical utility across diverse healthcare settings.

We presented CASCADE-Net, a novel end-to-end pipeline for predicting MCI-to-AD conversion. By integrating Neural ODEs for dynamic temporal alignment with a counterfactually-regularized attention mechanism, our model achieves state-of-the-art prognostic performance. More importantly, it provides interpretable, spatio-temporal explanations that are grounded in causal reasoning, making its predictions more trustworthy and actionable for clinical practice. This architecture is general and can be adapted to other neurodegenerative diseases and longitudinal analysis tasks.