we choose a hidden layer of size 512, as a good balance between accuracy and training time. Overall, we found that our model performs similarly well across a wide range of settings when considering different batch sizes and learning rates.

![The mean q-error on the validation set with different hidden layer sizes.[]{data-label="The mean q-error on the validation set with different hidden layer sizes"}](H.PNG){width="\linewidth"}

Model Computational Costs
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We analyze the training, prediction, and space costs of the CRN model with the default hyperparameters (H=512, batch size=128, learning rate=0.001).

### Training Time

Figure \[Convergence of the mean q-error on the validation set\] shows how the mean q-error of the validation set decreases with additional epochs, until convergence to a mean q-error of around 4.5. The CRN model requires almost 120 passes on the training set to converge. On average, measured across six runs, a training run with 120 epochs takes almost 200 minutes.

### Prediction Time

The prediction process is dominated by converting the input queries into the corresponding vectors, and then presenting these vectors as input to the CRN model. On average, the prediction time is 0.5ms per single pair of queries, including the overhead introduced by the Tensor-Flow framework.

