curve for $d = 32$ uniform dimension embeddings, which has the lowest validation loss (under early termination). We also plot the learning curve for $d = 4$ as a baseline. Third, we plot the learning curve for mixed dimension embedding layers at $\alpha=0.6$, which uses a number of parameters equivalent to uniform dimension embedding layers at $d = 4$.

Similarly to the MF setting, the optimally terminated model using the $d=32$ embeddings has slightly higher loss than the chosen mixed dimension embeddings. However, unlike in MF, here, we do see that all three models overfit as training progresses, and thus early termination is essential for all three models.

Under prolonged training, the uniform $d=32$ based NCF model overfit severely. The mixed dimension based NCF model overfits signficantly, but not as drastically as the optimal $d=32$ NCF model. The NCF model with $d=4$ embeddings overfits only slightly. Given that the two latter embedding layers, when identically architected and initialized, do not cause the model overfit when the embedding vectors as used for MF, we can attribute the overfitting directly to presence of the MLP layers in the NCF model.

In Fig \[fig:ncf\_test\_loss\_summary\], we report the test loss for different $\alpha$ at 