## 2 Related Work  
Stacked multi-layer LSTMs can achieve better modeling capabilities [15]. However, LSTM recurrent neural networks with too many LSTM layers are not only difficult to train, but also have problems of vanishing gradient when the number of layers reaches a certain depth. Methods that have been proposed to alleviate the above problems include Highway LSTM (HLSTM), Residual LSTM (RLSTM), and GridLSTM. The HLSTM was first proposed in [16], in which memory cells in adjacent layers are directly connected by gated units in the depth direction. The RLSTM [17; 18] introduces \"shortcut connections\" between the LSTM layers, which can also alleviate the problem of vanishing gradient. The design of RLSTM connection that is proposed in [19] is more straightforward. It can be seen from [20] that the accuracy of HLSTM decreases when the number of layers increases to eight layers, and the relative gain of RLSTM is not particularly significant when RLSTM is increased to eight layers. But it is worth noting that whether it is HLSTM or RLSTM, they only mitigate the gradient problem in a single dimension. As we all know, Time-Frequency LSTM (TF-LSTM) is a valid model for improving the acoustic model. The TF-LSTM jointly scans the input over the time and frequency axes to model spectro-temporal warping, and then uses the output activations as the input to a Time-LSTM. The joint time-frequency modeling better normalizes the features for the upper layer Time-LSTMs [3]. However, the TF-LSTM optimizes recognition effect from the feature extraction of the acoustic model. When the number of network layers increases, there is still a problem of vanishing gradient. The Time-Delay Neural Network (TDNN) combines the current output of the hidden layer with the output of several moments before and after as the input to the next hidden layer [21]. This is similar to a bidirectional RNN, except that the context window of the bidirectional RNN can be dynamically adjusted through parameter learning, and TDNN can only achieve a fixed context window size. In addition, since there is a loop when the speech feature propagates in the network, the hidden layer in the bidirectional RNN not only receives the output of the previous hidden layer, but it also obtains the output of itself before and after. This structure allows the bidirectional RNN to theoretically learn infinitely long context information, but in the training process, it also faces the problem of the vanishing gradient. However, we can introduce GridLSTM to effectively solve this problem in the paper. GridLSTM combines the LSTM unit into a unified framework of both time and depth to train deeper networks. Ref. [9] shows that GridLSTM can effectively improve the gradient problem in the training process in speech recognition tasks. Unfortunately, GridLSTM is just a unidirectional recurrent neural network structure. For timing tasks, context information is critical, and this structure can only get the content before the current moment, but the information behind it cannot be used. The biggest difference between the bidirectional grid LSTM model and several alternative models in this paper is that the BiGridLSTM model cleverly utilizes the advantages of combining GridLSTM with bidirectional recurrent neural network structure, improving the effect of the model from various aspects. The GridLSTM contains Time-LSTM blocks calculated along the time dimension and Depth-LSTM blocks calculated along the depth dimension, which use the linear dependence between adjacent gating units in two dimensions to keep the error at a more constant level and allow for the recurrent neural network to learn multiple time steps. It not only can solve the gradient problem that occurs in the time dimension of the common stack LSTM, but can also effectively resolve the gradient from the depth dimension.