## 4 Results and Discussion
### Comparison of Performances for Two Algorithms  
By comparing the two algorithms, the main aspects of each method can be highlighted as shown in Table 2.  
Thus, it can be observed that Algorithm 2 appears to be superior when evaluated against the fundamental performance criteria provided earlier. Parallelization is based on the multiprocessing library in the Python programming language. As an implementation, an algorithm for splitting the array of events into threads was used. Figure 10 illustrates how the number of threads affects the run-time of the parallel algorithm. The algorithm was tested on a compute node with multiple cores and the following specifications: 32 cores, 64 Gb of memory, an AMD Ryzen processor, and 2 Tb of disk memory (SSD). This system supports up to 64 parallel threads. In our experiment, we tested the computation time results for the sequential code without parallelization, with 2, 4, 8, 16, 32, and 64 parallel threads. Our experiment used a track table consisting of 42,102 tracks. The average execution time of a subroutine to calculate the optimum helix parameters for 1 track from the whole set is approximately 0.5 \(\times\) 10\({}^{-3}\) s.  
The results demonstrate a significant speed-up of up to six-fold. However, there is some decline in the speed-up achieved for higher thread numbers due to the additional memory fill factor. It is worth noting that this algorithm may face limitations in processing large datasets with high memory requirements. Neural Network Algorithm for Track Recognition and Its Performance Results with False Tracks before and after Applying the Track Rejection Criterion  
For the training, we used the TrackNET model as a software application that employs a deep recurrent neural network for local tracking. This network retrieves each track individually, progressing station by station. The model's specifications have been thoroughly explained. The efficacy of track recovery is determined by evaluating recall and precision, \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Number of** & **Computational** & **Memory** \\  & **Iterations** & **Complexity** & **Consumption** \\ \hline Algorithm 1 & Small & High & High \\ Algorithm 2 & Average & Average & Average \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Aspects of two algorithms. Figure 10: Comparative running times of the two proposed parallel algorithms. the two most commonly used metrics. Recall denotes the proportion of true tracks that are recovered entirely, while precision indicates the proportion of actual tracks among all the tracks detected by the model. To train the neural network, 50,000 model SPD events of simplified geometry were used. Each sample event, apart from the tracks (on average 5), contained false (noise) tracks, with an average of 60 false tracks per event. The trained model is able to reconstruct 90% or more tracks. However, the neural network also outputs false tracks along with real tracks, with the number of false tracks being much higher. Therefore, in the total number of tracks from the dataset, reconstructed with TrackNETv3, only 2% are true tracks. In order to increase the share of true tracks in the total number of all reconstructed tracks, we used a value of \(\chi^{2}\) as a criterion for elimination. A false track is far enough away from the reconstructed helix, as opposed to a true track, that if the threshold for \(\chi^{2}\) is chosen correctly, only false tracks will be screened out among all reconstructed tracks. The screening threshold was calculated under ideal conditions, on a sample containing only true tracks, as the average value of \(\chi^{2}\) plus 3 standard deviations, so that its value is 0.023. The distribution of \(\chi^{2}\) for both true and false tracks is shown in Figures 11 and 12. Figure 11: Distribution of \(\chi^{2}\) for true tracks. Figure 12: Distribution of \(\chi^{2}\) for false tracks. Figure 13 illustrates how the recall and precision metrics vary with changes in the false track rejection criterion.