# Order-Based Schedule of Dynamic Topology for Recurrent Neural Network
## 1 Introduction  
Recurrent Neural Networks (RNN) have proved to be a powerful methodology to solve time series forecasting [1, 2], due to their ability to adapt and recognize short-term and long-term correlations between input data sequences [3]. The capacity that these systems have, that is, how much they can learn and store knowledge, is determined among other features by their topology [4, 5, 6], made up of the number of units that they have and how these units are interconnected, which allows the system to acquire, store, and generalize knowledge. In addition to its topology, the capacity of the network is dependent on the training process that is used. Faced with this situation, the question arises about how the network should be designed, a situation that even today has not been resolved, can be provided some theoretical guidelines [7] that suggest what is likely to work or not work on a given problem, but, ultimately, it has been limited to a process of trial and error, based only on the experience of the designer. Depending on these two factors: topology, and training, it is possible that the short-term memory effect occurs, which causes that, as the network processes more future elements of the series, the parameters that represent the knowledge of the behavior of the sequence in the long term can vanish [8]. This makes it necessary to update the network by adding the new observations acquired over time, a process normally addressed by discarding the previous model and retraining the network from scratch using the new data set. One neural model that successfully deals with vanishing gradients of long-term temporal sequences is the Long-Short Term Memory model (LSTM) [9]. LSTM model addsa constant error carrousel unit (CEC) that allows keeping gradients of data sequences for a long time. Since time series sequences could suddenly change their complexity from one sample time to another, more or less neural units of the model can be needed to process dynamic data, and the LSTM efficiency and precision can be improved by adding functionalities inspired by concepts of biological brain neuroplasticity in the design and updating of architectures during the training time [10]. Some algorithms have been designed to simulate how synaptic connections are modified in biological neuronal networks and therefore how the number of neurons involved in a network is affected, developing techniques such as pruning [11] or growing [12], which represent brain plasticity. Brain plasticity describes the ability of brain areas or neuronal groups to respond functionally and neurologically to their environment, changing their activity in response to intrinsic or extrinsic stimuli by reorganizing their structures, giving them the possibility of growing and/or pruning synapses to fill functional deficiencies [13]. This is why, the objective of these techniques, growing and pruning, is to adapt the architecture of the networks that are already designed, increasing, or decreasing the number of neurons respectively, to deliver an efficient model that improves its performance. In this work the growing and pruning paradigm is developed using LSTM architectures to obtain LSTM models with better performance to solve time series forecasting problems. Based on these methodologies, is proposed an algorithm that provides plasticity to an LSTM model. Which gives it the capacity to reduce or increase the number of neurons of its architecture in order to increase its precision and/or efficiency, applied to time series forecasting. This algorithm is a decision-making grow and prune paradigm, based on the calculation of the order of the data, being this, the way to simulate the stimulus presented in the environment, denoting to the network in which situations it should increase or reduce its connections, obtaining, as a result, a dynamic architecture that can facilitate its design and implementation, as well as improve its time series forecasting, obtaining reduced or larger models, but in both cases improving its performance.