A constrained recursion algorithm for batch normalization of tree-sturctured LSTM

Tree-structured LSTM is promising way to consider long-distance interaction over hierarchies. However, there have been few research efforts on the hyperparameter tuning of the construction and traversal of tree-structured LSTM. To name a few, hyperparamters such as the interval of state initialization, the number of batches for normalization have been left unexplored specifically in applying batch normalization for reducing training cost and parallelization. In this paper, we propose a novel recursive algorithm for traversing batch normalized tree-structured LSTM. In proposal method, we impose the constraint on the recursion algorithm for the depth-first search of binary tree representation of LSTM for which batch normalization is applied. With our constrained recursion, we can control the hyperparameter in the traversal of several tree-structured LSTMs which is generated in the process of batch normalization. The tree traversal is divided into two steps. At first stage, the width-first search over models is applied for discover the start point of the latest tree-structured LSTM block. Then, the depth-first search is run to traverse tree-structured LSTM. Proposed method enables us to explore the optimized selection of hyperparameters of recursive neural network implementation by changing the constraints of our recursion algorithm. In experiment, we measure and plot the validation loss and computing time with changing the length of internal of state initialization of tree-structured LSTM. It has been turned out that proposal method is effective for hyperparameter tuning such as the number of batches and length of interval of state initialization of tree-structured LSTM.