are performed on an immutable snapshot of the database.

After the training phase, to predict the containment rate of an input query pair, the queries first need to be transformed into their feature representation, and then they are presented as input to the model, and the model outputs the estimated containment rate (Section \[Model\]).

We train and test our model using the Tensor-Flow framework [@tensorFlow], and make use of the efficient Adam optimizer [@adam] for training the model.

Hyperparameter Search {#Hyperparameter Search}
---------------------

To optimize our model’s performance, we conducted a search over its hyperparameter space. In particular, we focused on tuning the neural networks hidden layer size (H).

Note that the same H value is shared in all the neural networks of the CRN model, as described in section \[Model\]. During the tuning of the size hyperparameter of the neural network hidden layer, we found that increasing the size of our hidden layer generally led to an increase in the model accuracy, till it reached the best mean q-error on the validation test. Afterwards, the results began to decline in quality because of over-fitting (See Figure \[The mean q-error on the validation set with different hidden layer sizes\]). Hence, 