## 5 Discussion  
Within the development of this proposal, there are several things that have been learned. We have seen that, for the specific problem of calorimeter reconstruction in LHCb, segmenting the reconstruction steps can help in simplifying the development of a deep learning solution. Moreover, as seen in Section 3.2, data can be artificially generated as long as they correctly equally represent all cases to be learned. For more complex functions, such as the one seen in Section 3.4, the understanding of the rules also leads to a simplification of the dataset, where we were able to extract thousands of samples from only 2000 full LHCb simulated events. Understanding that there is no need to work with full simulation data to train specific networks can simplify the training dataset generation on further deep learning developments for the calorimeter reconstruction. In other words, we trained neural networks on the rules that solve a general formulation of the problem. It was proven that the network learns the application of the formulated rules in a generalized context. The complexity reduction on the training data was also reflected into a fast training process and the simplification of the networks, in terms of architecture and the number of parameters, compared with previous deep learning approaches. Comparing the results with the state-of-the-art, we improved the relation between the network's complexity and the amount of training data. Furthermore, the proposed model is validated by construction, since the same reconstruction steps as the current method are being reproduced. As a proof of concept, the performance comparison in this paper is done with the current implementation of the reconstruction self-implemented in Python. In terms of computational time, there is a clear gain in the reconstruction complexity with the proposed approach. However, the execution time could possibly be reduced with a vectorized implementation of the proposal. Apart from that, the proposed implementation clearly benefits from parallel execution, reducing the computational time by nearly a factor three. Moreover, its convolutional formulation could benefit even more from a GPU architecture without conditioning the efficiency, as the insight neural networks and convolutional operators are highly parallelizable. Despite the results, there is still room for improvement in terms of performance. Due to the region-independent strategy used in this approach; clusters that fall in the boundary regions of the calorimeter are now reconstructed partially as two separate clusters in each region. There is the idea of using a graph neural network (GNN) with similar training as the MLP, in order to perform the reconstruction in the boundary regions, as GNNs can model irregular neighborhoods. Another aspect that needs to be worked is the identification of \(\pi^{0}\) particles. By nature, the two photons of the decay of energetic \(\pi^{0}\) particles arrive at the calorimeter as two very close similar energy particles, but need to be reconstructed as a single cluster. Hence, the window that surrounds a pair of photons is bigger than the defined \(3\times 3\). With the current training of the MLP in our proposal, the network wrongly reconstructs these specific photons as two very close overlapping clusters. There is the idea of improving this shortcoming, re-training the network of the current implementation to identify the defined photons and make an ad-hoc reconstruction for those cases. In conclusion, we implemented and tested an alternative approach to the LHCb calorimeter reconstruction. It adapts the current reconstruction steps to a formulation that can be learned by simple deep learning structures. With this, we make sure that the reconstruction process is correct as it mimics the implementation of the current algorithm, gaining in computational complexity. Results from the testing show interesting behavior, in terms of computational time, which could be promising for a full calorimeter reconstruction implementation on GPUs.