When switching an artificial neural network (ANN) from Euclidean distance to cosine similarity, the primary adjustments involve data normalization, modifying distance calculations, and ensuring architectural compatibility. Here’s a breakdown of the key changes:
1. Normalize Input Vectors
Cosine similarity measures the angle between vectors, ignoring their magnitudes. To use it effectively, all input vectors must be normalized to unit length (L2 normalization). This ensures the Euclidean distance between normalized vectors directly relates to cosine similarity: for normalized vectors u and v, Euclidean²(u, v) = 2(1 - cosine(u, v)). In practice, this means adding a preprocessing step to scale vectors to unit length before feeding them into the network. For example, in PyTorch, a normalization layer (torch.nn.functional.normalize) can be inserted before computing distances. If the ANN uses embeddings (e.g., in Siamese networks), normalization must occur before similarity computation to align with cosine behavior.
2. Adjust Distance Computation and Loss Functions
The ANN’s similarity metric must shift from raw Euclidean distance to cosine similarity. However, if vectors are normalized, Euclidean distance can still approximate cosine similarity. For instance, in k-nearest neighbors (k-NN) or clustering algorithms, using Euclidean distance on normalized vectors achieves the same ranking as cosine similarity. If the loss function explicitly relies on Euclidean distance (e.g., contrastive loss), ensure inputs are normalized. For custom implementations, replace Euclidean calculations with the dot product of normalized vectors (cosine(u, v) = u ⋅ v). In frameworks like TensorFlow, this might involve using tf.losses.cosine_distance or manually computing the dot product after normalization.
3. Architectural and Training Considerations
- Gradient Propagation: Normalization layers introduce mathematical constraints (e.g., dividing by the L2 norm). During backpropagation, gradients must account for this operation. For example, the derivative of L2 normalization involves chain rule adjustments to prevent magnitude from influencing updates.
- Regularization and Magnitude: Since cosine similarity ignores vector magnitude, weight regularization (e.g., L2 regularization) may need tuning to avoid conflicting with normalization.
- Index Structures: For nearest-neighbor search (e.g., FAISS or Annoy), ensure vectors are normalized before indexing. Many libraries optimize for inner product search when vectors are unit-normalized, which aligns with cosine similarity.
- Domain Suitability: Verify that ignoring magnitude is acceptable for the task. For example, in NLP, cosine similarity works well for TF-IDF embeddings, but in image processing, pixel intensity magnitude might matter.
By addressing these areas, the transition to cosine similarity maintains the ANN’s effectiveness while aligning with the metric’s assumptions. Testing post-adjustment is critical to validate performance, as hyperparameters (e.g., learning rate) may require retuning.