### Model Size

The CRN model includes all the learned parameters mentioned in Section \[Model\] ($U_1$, $U_2$, $U_{out1}$, $U_{out2}$, $b_1$, $b_2$, $b_{out1}$, $b_{out2}$). In total, there are $2*L*H + 8*H^2 + 6*H +1$ learned parameters. In practice, the size of the model, when serialized to disk, is roughly $1.5MB$.

![Convergence of the mean q-error on the validation set.[]{data-label="Convergence of the mean q-error on the validation set"}](validationConverage.PNG){width="\linewidth"}

Containment Evaluation {#Containment Evaluation}
======================

In this section we describe how we compared the CRN model to other (baseline) methods. Since to the best of our knowledge, the problem of determining containment rate has not been addressed till now, we used a transformation as described in Section \[From Cardinality to Containment\] below.

From Cardinality to Containment {#From Cardinality to Containment}
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To our knowledge, this is the first work to address the problem of containment rate estimation. In order to compare our results with different baseline methods, we used existing cardinality estimation methods to predict the containment rates, using the Crd2Cnt transformation, as depicted in the middle part diagram in Figure \[fig:teaser\].

### The Crd2Cnt Transformation {#Crd2Cnt Transformation}

Given a cardinality estimation model[^3] $M$, we can convert it to a containment rate estimation model 