varying total parameter budgets using optimal early termination. Overall, the NCF models attain slightly lower test losses than their MF counterparts, generally a decrease in the range of $0.03-0.01$ MSE. Interestingly, the optimally terminated NCF models actually suffered from less overfittitng than the MF models did at higher parameter counts. The critical points corresponding to the optimal total parameter also increased, for each $\alpha$. Yet, $\alpha = 0.6$ still performed the best, albeit at a larger higher budget.

[0.49]{} ![Loss under different parameters budgets[]{data-label="fig:ncf_performance"}](images/ncf_learning_curve_9_19.png "fig:"){width="\textwidth"}

[0.49]{} ![Loss under different parameters budgets[]{data-label="fig:ncf_performance"}](images/ncf_rate_performance_9_19.png "fig:"){width="\textwidth"}

Finally, concerning the comparison between mixed and uniform dimension embeddings, we see similar trends and draw the same conclusions as in the MF setting. *Ultimately, we achieve approximately 0.01 lower MSE while using approximately 8$\times$ fewer parameters by using mixed dimension embeddings.*

Deep Learning Recommendation Model
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CTR prediction tasks can be interpreted as event-probability prediction problem or as context-based CF with binary ratings. From the perspective of this work, using mixed dimension embedding layers on real CTR prediction data with state-of-the-art deep recommendation models is an important experiment that shows how mixed dimension embedding layers might scale to real-world recommendation engines.

In our experiments we use state-of-the-art 