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Context: Secondly, this autoencoder provides effective representations of user retention for the transformer part. The transformer encoder part needs to be fed with the retention for compressing long-term interests into user embeddings. However, retention is originally in the form of high-dimensional sparse features. This autoencoder encodes retention into the first hidden layer \bm{x}^{(1)}\in\mathbb{R}^{d_{model}}. As a low-dimensional dense encoding, \bm{x}^{(1)} plays an important role in the transformer encoder part. We carefully design our weight matrices for several parts of the model, which helps to solve the sparsity problem and tightly couple the autoencoder part and the transformer parts. As shown in Figure 5, the app embeddings are built based on both the app ID and its corresponding category ID. Even if the usage of some app is gravely sparse, its category can still provide valid information. This setting helps to overcome the problem of sparsity. As introduced previously, we repeatedly use the M\times d_{model} embedding matrix for apps, i.e., at the input and output of the retention autoencoder, the input of the transformer encoder, the output for the masked app prediction, the output of the transformer decoder, as well as the reconstruction part for retention from the user embeddings (bottleneck). We tie the weight matrices of all these parts together, i.e.,(3)\displaystyle\mathbf{W}^{\Omega}=\mathbf{W}^{\Theta}=\mathbf{W}^{\Phi}=\mathbf{W}^{(4)}={\mathbf{W}^{a}}^{\mathrm{T}}.We reduce the total number of parameters by tying weight matrices of the above layers, which benefits of overcoming the problem of sparsity. Moreover, weight tying benefits the backpropagation of the gradient and speeds the convergence.

Question: Which part of the proposed model helps to solve the sparsity problem?
Both transformers and retention autoencoder parts try to solve the sparsity problem by using tied weight matrices.
The reason of this is that \mathbf{W}^{\Omega}=\mathbf{W}^{\Theta}=\mathbf{W}^{\Phi}=\mathbf{W}^{(4)}={\mathbf{W}^{a}}^{\mathrm{T}}. 
Since \mathbf{W}^{\Omega} is used in transformer part and \mathbf{W}^{(4)} is used in autoencoder part, both of them try to solve the sparsity problem.