Deep learning techniques, namely convolutional neural networks (CNN), have previously been adapted to select gamma-ray events in the TAIGA experiment, having achieved a good quality of selection as compared with the conventional Hillas approach. Another important task for the TAIGA data analysis was also solved with CNN: gamma-ray energy estimation showed some improvement in comparison with the conventional method based on the Hillas analysis. Furthermore, our software was completely redeveloped for the graphics processing unit (GPU), which led to significantly faster calculations in both of these tasks. All the results have been obtained with the simulated data of TAIGA Monte Carlo software; their experimental confirmation is envisaged for the near future.