  In this work, we report the results of applying deep learning based on hybrid
convolutional-recurrent and purely recurrent neural network architectures to
the dataset of almost one million complete intersection Calabi-Yau four-folds
(CICY4) to machine-learn their four Hodge numbers $h^{1,1}, h^{2,1}, h^{3,1},
h^{2,2}$. In particular, we explored and experimented with twelve different
neural network models, nine of which are convolutional-recurrent (CNN-RNN)
hybrids with the RNN unit being either GRU (Gated Recurrent Unit) or Long Short
Term Memory (LSTM). The remaining four models are purely recurrent neural
networks based on LSTM. In terms of the $h^{1,1}, h^{2,1}, h^{3,1}, h^{2,2}$
prediction accuracies, at 72% training ratio, our best performing individual
model is CNN-LSTM-400, a hybrid CNN-LSTM with the LSTM hidden size of 400,
which obtained 99.74%, 98.07%, 95.19%, 81.01%, our second best performing
individual model is LSTM-448, an LSTM-based model with the hidden size of 448,
which obtained 99.74%, 97.51%, 94.24%, and 78.63%. These results were improved
by forming ensembles of the top two, three or even four models. Our best
ensemble, consisting of the top four models, achieved the accuracies of 99.84%,
98.71%, 96.26%, 85.03%. At 80% training ratio, the top two performing models
LSTM-448 and LSTM-424 are both LSTM-based with the hidden sizes of 448 and 424.
Compared with the 72% training ratio, there is a significant improvement of
accuracies, which reached 99.85%, 98.66%, 96.26%, 84.77% for the best
individual model and 99.90%, 99.03%, 97.97%, 87.34% for the best ensemble.
