produce a fusion map that explicitly quantifies the fusion weights for the features in each modality.

Producing a fusion map to quantify feature fusion weights typically involves techniques from both deep learning and knowledge representation. In the context of multi-modal data analysis, where you have information from different sources like images (deep learning) and structured data like knowledge graphs (knowledge graph embeddings), a fusion method might involve:

1. **Deep Learning**[^1]:
\- Apply a deep neural network, such as convolutional or recurrent networks, on one or more modalities to extract high-level representations.

   from keras.models import Model
   image_model = create_image_model()
   text_model = create_text_model()
   
   # Obtain modal-specific feature maps
   image_features = image_model(image_data)
   text_features = text_model(text_data)

2. **Set Functions and Equivariance**:
- Use set functions like mean pooling or attention mechanisms to aggregate the features across modalities while considering their relative importance. This step ensures that the fusion process is equivariant to transformations in individual modalities.

   fused_features = combine_features(image_features, text_features, set_function)

3. **Knowledge Graph Embeddings**:
- For knowledge graph embeddings, use methods like TransE, DistMult, or ComplEx to represent entities and relations as vectors, which can be concatenated with the learned modality-specific features.

   kg_embedding_layer = KnowledgeGraphEmbeddingLayer(knowledge_graph)
   kg_features = kg_embedding_layer(entity_ids)

4. **Fusion Weights Quantification**:
- Finally, apply an additional layer, often a fully connected layer or a self-attention mechanism, to learn the fusion weights between the modalities.

   fusion_weights = Dense(1, activation='softmax')(concatenated_features)
   fused_output = dot([fused_features, fusion_weights])

The output `fused_output` would then contain the fused representation, where the values in the fusion weights array indicate the contribution of each modality to the final decision.