AMD-Mamba: Multimodal Deep Survival Model

• AMD-Mamba is a phenotype-aware, multi-modal deep survival framework that predicts progression to late AMD using fundus images, genetic variants, and socio-demographic data.
• It employs a two-stage strategy where a Vision Mamba-based encoder first learns phenotype-driven image representations followed by a multi-scale attention fusion for survival prediction.
• Empirical evaluations on the AREDS cohort show improved 5-year AUC and C-index over traditional CNN methods, establishing a novel risk-derived biomarker for AMD progression.

AMD-Mamba is a phenotype-aware, multi-modal deep survival framework for prognosing progression to late age-related macular degeneration (AMD) from baseline data. It combines color fundus photographs, genetic variants, and socio-demographic variables, and uses a Vision Mamba-based image encoder together with a phenotype-aware representation-learning stage and a multi-scale fusion survival model. Within the reported AREDS study setting, the framework is explicitly designed for baseline-to-event prediction rather than current-stage classification, and it additionally defines a risk-derived AMD biomarker intended to stratify progression risk (Wu et al., 4 Aug 2025).

1. Clinical task and study setting

AMD-Mamba is formulated for prognosis of progression to late AMD in eyes that do not yet have late AMD at baseline. The clinical motivation is that AMD is a progressive retinal disease and late AMD is associated with irreversible central vision loss; the intended use is earlier identification of patients who are likely to progress, so that monitoring, intervention, and treatment planning can be adjusted accordingly (Wu et al., 4 Aug 2025).

The dataset is the public Age-Related Eye Disease Study (AREDS) cohort. The reported study uses 2,741 subjects, 45,818 color fundus photographs, 52 genetic variants, and 3 socio-demographic variables—age, sex, and smoking status. Participant characteristics are given as mean age 73.9 years with SD 4.9, sex distribution 1,545 female / 1,196 male, and smoking status 1,287 never / 1,284 former / 170 current. Each image carries an AMD severity score from 1 to 12, with scores 10 or higher indicating late AMD (Wu et al., 4 Aug 2025).

The framework separates the full cohort into two functional stages. For representation learning, all 45,818 images are used in phenotype classification pretraining. For survival modeling, the paper uses 4,977 images from the base visit of eyes without late AMD $(\text{score}<10)$. Within these baseline cases, the severity counts are 2,189 no AMD, 1,973 early AMD, and 815 intermediate AMD, and 584 progressed to late AMD during follow-up. The paper reports 5-year AUC, but does not specify the exact maximum follow-up duration in years (Wu et al., 4 Aug 2025).

The evaluation protocol is 5-fold cross-validation split by patient ID, with model selection by validation C-index. Images are resized to $224\times224$, augmented with random rotations of $\pm 10^\circ$, horizontally flipped with probability 0.5, and normalized using ImageNet statistics. The paper does not specify a special missing-data imputation strategy, and it does not describe explicit class-imbalance correction such as reweighting or oversampling. Censoring is handled through the Cox partial likelihood (Wu et al., 4 Aug 2025).

2. Two-stage framework and visual backbone

AMD-Mamba is organized as a two-stage system. Stage 1 performs phenotype-aware image representation learning by metric-driven classification. Stage 2 performs multi-modal survival prediction using frozen image features, tabular-variable fusion, and a Cox survival head. The image backbone is based on V-Mamba / Vision Mamba, rather than a conventional CNN, and is modified to combine long-range and local information (Wu et al., 4 Aug 2025).

An input fundus image $\mathbf{I}\in\mathbb{R}^{H\times W\times 3}$ is first processed by a patch embedding layer and then by a hierarchy of Visual State Space (VSS) blocks with downsampling, yielding four multi-scale feature maps: $$\{\mathbf{f}_1,\mathbf{f}_2,\mathbf{f}_3,\mathbf{f}_4\}.$$ The deepest representation is $\mathbf{f}_4$. This hierarchy supplies the later multi-scale fusion stage with image features at different resolutions (Wu et al., 4 Aug 2025).

The core architectural modification is a two-branch VSS block operating on

$\mathbf{X}\in\mathbb{R}^{H\times W\times C}.$

The left branch applies LayerNorm $\rightarrow$ SS2D $\rightarrow$ FFN, where SS2D is the 2D selective scan from V-Mamba and is intended to capture long-range or global dependencies. The right branch applies LayerNorm $\rightarrow$ Spatial Attention (SA) to emphasize important local spatial regions. Their outputs are summed, normalized, processed by Channel Attention (CA), and added back through a residual connection: $224\times224$0

This design is explicitly motivated as a way to capture both local AMD signs such as drusen and broader contextual patterns such as vascular changes. The paper therefore positions AMD-Mamba against prior CNN-based prognosis systems that emphasize local information but may be less suited to long-range image structure (Wu et al., 4 Aug 2025).

At the architectural level, the image encoder is not used in isolation. Its outputs feed a later multi-modal module that combines image information with genetic and socio-demographic variables at multiple scales. A plausible implication is that the backbone is intended not merely as a visual classifier, but as a structured feature extractor whose scale hierarchy remains useful during survival prediction.

3. Phenotype-aware representation learning

The defining methodological feature of AMD-Mamba is the use of AMD severity-derived phenotypes as prior knowledge during representation learning. For Stage 1, the paper groups the AMD severity scores into four phenotype classes:

• No AMD: score $224\times224$1
• Early AMD: scores $224\times224$2
• Intermediate AMD: scores $224\times224$3
• Late AMD: scores $224\times224$4

Rather than using a conventional linear classifier, the model uses a prototype-based cosine classifier. Let the backbone produce latent vector $224\times224$5, and let $224\times224$6 be a learnable matrix of class prototypes, where row $224\times224$7 is the prototype for phenotype class $224\times224$8. The class score is defined by cosine similarity: $224\times224$9

The Stage 1 objective is cross-entropy on these cosine logits: $\pm 10^\circ$0

This is the basis for the paper’s description of an “innovative metric learning strategy” using AMD severity scale score as prior knowledge. Strictly from the printed equations, the implemented objective is a cosine-prototype cross-entropy classifier rather than a triplet or contrastive loss. The “metric learning” characterization refers to structuring the embedding space around clinically meaningful phenotype prototypes (Wu et al., 4 Aug 2025).

The learned prototype matrix is reused in Stage 2. The predicted phenotype is

$\pm 10^\circ$1

and the selected prototype later modulates the multi-modal survival representation. This creates a direct linkage between phenotype-aware representation learning and prognosis. The paper also reports a t-SNE visualization showing clearer class separation than a prior method, which it uses as qualitative support for the phenotype-aware feature space (Wu et al., 4 Aug 2025).

4. Multi-modal fusion and survival modeling

After Stage 1, the image backbone is frozen and the system shifts to survival prediction. The visual branch supplies four pooled image features, denoted $\pm 10^\circ$2, one for each scale. The non-image modalities are concatenated into a tabular vector

$\pm 10^\circ$3

consisting of the 52 genetic variants and 3 socio-demographic variables (Wu et al., 4 Aug 2025).

The tabular branch initializes the fusion query by linear projection: $\pm 10^\circ$4 with $\pm 10^\circ$5. Each image scale is then projected into key and value vectors,

$\pm 10^\circ$6

and the fusion proceeds iteratively: $\pm 10^\circ$7 The paper also states that a feed-forward block with skip connections follows the attention refinement, though it does not provide the exact formula (Wu et al., 4 Aug 2025).

This multi-scale fusion mechanism is one of the main departures from simple late concatenation. The tabular representation repeatedly attends to image features across resolutions, so the fused state is refined from earlier higher-resolution features through deeper semantic features. The paper interprets this as combining image information with clinical variables at different resolutions, thereby improving predictive performance (Wu et al., 4 Aug 2025).

Phenotypic prior information is injected after fusion by using the predicted prototype $\pm 10^\circ$8 to modulate the final fused representation: $\pm 10^\circ$9 The paper describes this as phenotype-guided survival representation. In effect, the survival feature vector is amplified along prototype-aligned directions associated with the predicted phenotype. The final output is a log-risk score $\mathbf{I}\in\mathbb{R}^{H\times W\times 3}$0, produced by a shallow MLP whose exact structure is not specified (Wu et al., 4 Aug 2025).

Training uses the Cox negative partial log-likelihood: $\mathbf{I}\in\mathbb{R}^{H\times W\times 3}$1 where $\mathbf{I}\in\mathbb{R}^{H\times W\times 3}$2 is the predicted log-risk, $\mathbf{I}\in\mathbb{R}^{H\times W\times 3}$3 is the event indicator, $\mathbf{I}\in\mathbb{R}^{H\times W\times 3}$4 is the event or censoring time, and $\mathbf{I}\in\mathbb{R}^{H\times W\times 3}$5 is the risk set. The prediction target is therefore time to progression to late AMD, modeled through relative risk ranking rather than direct absolute hazard estimation (Wu et al., 4 Aug 2025).

5. Biomarker, training protocol, and empirical performance

The paper additionally defines a new AMD biomarker derived from the model’s predicted risk. It is used to partition cases into high-risk and low-risk groups, and is evaluated in univariate and multivariate Cox analyses together with AMD severity score, socio-demographic variables, genetic variants, and 10 expert-annotated AMD phenotypes. The exact thresholding rule is not specified in the provided text, so the biomarker can only be described precisely as risk-derived rather than by a formal equation (Wu et al., 4 Aug 2025).

In multivariate Cox analysis, the reported biomarker statistics are: $\mathbf{I}\in\mathbb{R}^{H\times W\times 3}$6 The same model includes AMD score with HR $\mathbf{I}\in\mathbb{R}^{H\times W\times 3}$7, age with HR $\mathbf{I}\in\mathbb{R}^{H\times W\times 3}$8, and smoking with HR $\mathbf{I}\in\mathbb{R}^{H\times W\times 3}$9. On the reported hazard-ratio scale, the AMD-Mamba biomarker is presented as the strongest biomarker among the included variables. The paper further states that combining this biomarker with other existing variables yields promising improvements in detecting high-risk AMD patients at early stages (Wu et al., 4 Aug 2025).

The implementation details reported for training are concise. The hardware is an NVIDIA RTX A6000 GPU. Stage 1 uses Adam, learning rate $$\{\mathbf{f}_1,\mathbf{f}_2,\mathbf{f}_3,\mathbf{f}_4\}.$$0, batch size 96, and 50 epochs. Stage 2 also uses Adam, learning rate $$\{\mathbf{f}_1,\mathbf{f}_2,\mathbf{f}_3,\mathbf{f}_4\}.$$1, batch size 512, and 100 epochs. The paper does not report weight decay, dropout, learning-rate schedule, parameter count, or exact embedding dimensions (Wu et al., 4 Aug 2025).

The main predictive results are as follows.

Setting	Metric	AMD-Mamba
Image-only	C-index	$$\{\mathbf{f}_1,\mathbf{f}_2,\mathbf{f}_3,\mathbf{f}_4\}.$$2
Image-only	5-year AUC	$$\{\mathbf{f}_1,\mathbf{f}_2,\mathbf{f}_3,\mathbf{f}_4\}.$$3
Multi-modal	C-index	$$\{\mathbf{f}_1,\mathbf{f}_2,\mathbf{f}_3,\mathbf{f}_4\}.$$4
Multi-modal	5-year AUC	$$\{\mathbf{f}_1,\mathbf{f}_2,\mathbf{f}_3,\mathbf{f}_4\}.$$5

In the image-only setting, these values exceed the reported BagNet results of C-index $$\{\mathbf{f}_1,\mathbf{f}_2,\mathbf{f}_3,\mathbf{f}_4\}.$$6 and 5-year AUC $$\{\mathbf{f}_1,\mathbf{f}_2,\mathbf{f}_3,\mathbf{f}_4\}.$$7, and also exceed the reported 5-year AUC values from Babenko et al. and Yan et al. In the multi-modal setting, AMD-Mamba exceeds the reported Peng et al. results of C-index $$\{\mathbf{f}_1,\mathbf{f}_2,\mathbf{f}_3,\mathbf{f}_4\}.$$8 and 5-year AUC $$\{\mathbf{f}_1,\mathbf{f}_2,\mathbf{f}_3,\mathbf{f}_4\}.$$9, as well as the reported multimodal result from Yan et al. (Wu et al., 4 Aug 2025).

The ablation study is structurally important because it isolates the role of the main components. The baseline Mamba image model M1 attains C-index 0.8634 $\mathbf{f}_4$0 0.0126. Adding clinical-variable fusion by concatenation (M2) raises this to 0.8713 $\mathbf{f}_4$1 0.0110. Replacing concatenation with multi-scale attention fusion (M3) yields 0.8781 $\mathbf{f}_4$2 0.0158. Adding hard phenotype-label guidance (M4) gives the full-model best result of 0.8873 $\mathbf{f}_4$3 0.0093. Soft-label phenotype guidance (M5) yields 0.8810 $\mathbf{f}_4$4 0.0080. Replacing Mamba with DenseNet under the otherwise strong configuration (M6) reduces performance to 0.8729 $\mathbf{f}_4$5 0.0097. Using 12-category phenotype labels (M7) or binary labels (M8) is also worse than the 4-class formulation (Wu et al., 4 Aug 2025).

These results support three narrow conclusions grounded in the paper’s own evidence: the Mamba backbone is stronger than the DenseNet substitute within this framework, multi-scale attention fusion is stronger than simple concatenation, and the 4-class phenotype structure is more effective than either coarser binary labels or the finer 12-category grouping.

6. Position within the Mamba literature, limitations, and terminology

Within the broader Mamba literature, AMD-Mamba is a domain-specific medical-imaging framework rather than a generic state-space-model variant. It should not be conflated with other Mamba-based works that use similar naming patterns but address unrelated problems, such as anomalous-diffusion analysis with Bi-Mamba (Lavaud et al., 2024), PDE surrogate acceleration with LE-PDE++ (Liang et al., 2024), edge deployment with eMamba (Kim et al., 14 Aug 2025), or multimodal diffusion generation with MDM (Lu et al., 15 Oct 2025). Its closest conceptual neighbors are Mamba-based medical or vision systems that adapt state-space models to structured imaging tasks, but the paper’s specific contribution is the combination of AMD prognosis, phenotype-aware supervision, and multi-modal survival modeling (Wu et al., 4 Aug 2025).

Several limitations are explicit or directly visible from the reported setup. The study is evaluated only on AREDS using patient-level 5-fold cross-validation and does not include an external validation cohort. Stage 2 uses only baseline fundus images, even though AREDS is longitudinal. The multimodal design assumes availability of genetic testing and complete socio-demographic variables, but the paper does not report missing-modality handling or performance degradation when some modalities are absent. The biomarker is derived from the model’s own predicted risk, yet the exact thresholding rule is not specified in the provided text. The training description omits model size, number of attention heads, embedding dimensions, and calibration analysis. These omissions constrain exact replication and deployment assessment (Wu et al., 4 Aug 2025).

There is also a narrower methodological nuance. The paper repeatedly describes Stage 1 as metric learning, but the printed equations instantiate a cosine-prototype cross-entropy classifier. This suggests that the contribution lies less in a new metric-loss family than in using severity-derived phenotype prototypes to structure the embedding space and then reusing those prototypes in survival prediction. That interpretation remains consistent with the reported equations and ablations, while avoiding claims not printed in the paper.

In synthesis, AMD-Mamba defines a specific research line within ophthalmic AI: prognosis of progression to late AMD from multimodal baseline data, using a Vision Mamba-derived local-global encoder, phenotype-aware prototype supervision, multi-scale clinical-image fusion, and Cox survival modeling. Its reported performance and biomarker analysis indicate that this combination is effective on AREDS, but the paper remains a single-cohort study whose broader clinical generalization, missing-modality robustness, and external validation remain open questions (Wu et al., 4 Aug 2025).