Deep & Cross Network (DCN) is a neural network architecture developed by Google that combines a cross network with a deep network to efficiently learn explicit and implicit feature interactions. The original DCN was introduced in 2017, with an improved version, DCN v2, released in 2020.
Architecture
- Cross Network: takes the input embedding vector and computes cross-products with itself, each layer increases the polynomial degree by one. The input dimension is maintained throughout the network.
- Deep Network: MLP with ReLU activation function
- Combination: the outputs are concatenated and passed through a final dense layer to produce predictions (usually probability)

DCN v2 Improvements
- Replaces the vector-based cross operation with the matrix-based using low rank decomposition
- Uses Mixture of Experts to decompose the learned matrix into sub-spaces, which are then aggregated with gates

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Advantages
- Automatically learns feature interactions without manual feature engineering
- Lower computational complexity than comparable models
Disadvantages
- Original cross network limited in the types of interactions it can learn
- Hyperparameter tuning can be challenging