Facebook’s DLRM [@naumov2019deep] and the Criteo Kaggle dataset [@Criteo2014]. We train at learning rate $10^{-3}$ using Amsgrad optimizer for a single epoch. For each $\alpha$ we increase the embedding layer’s parameter budget up to 32GB (GPU memory limit). Notice that because of this limitation we do not see the overfitting behavior from earlier sections. Also, as usual we perform 3 replicates per experiment. However, for this task we report accuracy and not loss as discussed earlier in this section.

In Fig \[fig:dlrm\_train\_loss\_sample\], we plot learning curves for the DLRM model based on three different embedding layers. We show that a mixed dimension embeddings with $\alpha = 0.3$ (orange line) produces a learning curve equivalent to that of a $d=32$ uniform dimension embeddings (blue line) using a total parameter count equivalent to that of $d=4$ uniform dimension (green line).

In Fig. \[fig:dlrm\_test\_loss\_summary\], we present test accuracy for DLRM using mixed dimension embedding layers at various $\alpha$ with varying parameter budgets. It is evident that mixed dimension embedding layers improve the memory-performance frontier. In fact, we see a very similar trend compared to the two classical CF settings. *Ultimately, we achieve approximately 0.01% higher accuracy while using approximately half as many parameters 