# Order-Based Schedule of Dynamic Topology for Recurrent Neural Network
## 4 Results  
To validate the proposed system, a comparison was made between Classic LSTM models (often called Vanilla LSTMs) and LSTM networks implemented with the proposed methodology, which will be named DyLSTM models to identify them. The test process and the results obtained are described below. **Dataset**: The process makes use of some time series obtained from the M4 forecasting contest daily training dataset. The time series used by M4 were selected from the database ForeDeCk [24], which contains time series built from multiple and diverse sources. These series came from domains such as industries, services, tourism, imports & exports, demographics, education, labor & wage, government, households, bonds, stocks, insurance, loans, transportation, and natural resources & environment. This dataset has several time series that have different numbers of observations, due to this, were selected randomly 10 series with 1000 observations and 4 series with 4400 observations. Each series was partitioned into 10 divisions of equal sizes. In each stage, there will be 2 subsets, the first for training and the second for the prediction process (test). Starting the model with the first division to consequently feed the system with the following divisions. Creating the training subset of the current phase, by joining the two subsets of the previous phase. In this way, the scenario of the acquisition of new data is simulated. Figure 4 shows the distribution that the data will present for each test. **Training:** In all the phases, the calculation of the order is carried out, as well as one of the three possible training processes is applied: \"growing\", adding new units and/or reactivating connections; \"pruning\", disabling connections; or \"normal\", training and maintaining the current network architecture. For the selection of the training process, is used the decision-making tree, described in the previous section, except for the first two phases. The first phase is the initialization of the models, in which they are trained with the first subset without any modification, keeping their respective current architectures. The second stage will only take into account the difference in the result that [PERSON]'s methodology delivers in the current stage compared to the previous one, applying growing if the order change is greater, pruning if the order is decreased, or maintaining the architecture if the order did not change. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Phase** & **0** & **1** & **2** & **3** & **4** \\ \hline
**Previous Decision** & - & - & G & P & P, N \\
**Error** & \(E_{0}\) & \(E_{1}\) & \(E_{2}\) & \(E_{3}\) & \(E_{4}\) \\ \(\Delta\)**Error** & - & - & \(E_{0}>E_{1}\) & \(E_{1}>E_{2}\) & \(E_{2}<E_{3}\) \\
**Cao** & 4 & 5 & 3 & 4 & 5 \\
**[PERSON]’s Suggest** & - & G & P & G & G \\
**Decision** & - & G & P & N & G \\ \hline \hline \end{tabular}  
* **Note:** On each phase, the error is calculated, from phase 2, \(\Delta\) Error is obtained by comparing the last two results, so can be determined if the error is being reduced or not.  
\end{table} 
Table 1: Decision-Making example by phases. **Cao:** Originally, the calculation of Cao was made to the division that was added to the training subset, this being the test subset in the previous stage \((\mathit{Test}[t-1])\), but looking toward increasing the capacity of the Cao algorithm and giving context to the data was decided to expand its range. Calculating Cao now using windows, being the window of the phase (\(U_{t}\)) the union of the divisions \((t-1)\) and \((t)\), to later make the comparison with the previous window (\(U_{t-1}\)) composed by the divisions \((t-2)\) and \((t-1)\) and thus be able to determine if there is an increase or decrease in the order.