## 4 Proposed Model Structure
LSTM is particularly proficient at categorizing processes such as time series and learning from experience. After the encoding is complete, based on the output result of the hidden layer, the output layer is decoded and reconstructed according to Equation (2) to produce an output of the same size as the input layer neuron. The purpose of the autoencoder section is to map input \(x\in[0,1]^{d}\) to a latent representation \(y\in[0,1]^{d}\), where the mapping is performed by the function  
\[yi=s(Wx_{i}+b) \tag{1}\]  
Through  
\[z_{i}=s\big{(}W^{\prime}yi+b^{\prime}\big{)} \tag{2}\]  
This concealed representation is mapped back into a reconstruction of the same shape as input \(x\). Here, \(s\) represents a non-linear function, such as the sigmoid function. The first component is the encoder, while the second is the decoder. This model's parameters minimize the average reconstruction error. The model consists of one input layer, one convolutional layer (Conv1D), two LSTM layers, one max pooling layer, and one dense layer in output. Figure 3 shows the training model with the proposed deep autoencoder scheme. Figure 2: The general structure of the proposed deep autoencoder. In addition, the checkpoint network improves the weights. Checkpointing is a crucial functionality that expedites failure recovery, reducing the total training time and ensuring continuous progress. Checkpoints are periodic captures of the current state of a running process, which are then stored in a durable storage medium. The individual loads the most recent checkpoint to recover from a setback and recommence training. In addition to the imperative of failure recovery, the utilization of checkpoints is necessary for transferring training processes across various nodes or clusters. This transition may be necessary for server maintenance (for instance, urgent security updates that cannot be delayed), hardware malfunctions, network complications, and the optimization or reallocation of resources. Another significant application of checkpoints involves the real-time publication of snaps of trained models to enhance the accuracy of inference, commonly referred to as online training. For example, we can employ an interim model obtained by checkpointing for prediction serving. This method allows the model to continue training on more recent datasets, ensuring the freshness of the inference model. We can also utilize checkpoints for transfer learning, a technique where an intermediate structure state is an initial point for training toward a distinct objective [10]. Figure 4 shows the training loop with a checkpoint network. Figure 4: The training looping with checkpoint network [10]. Figure 3: The training model of the proposed deep autoencoder. The evaluation of the model occurs at the conclusion of each epoch, and the weights corresponding to the highest accuracy and lowest loss during that specific epoch are retained and saved. In the event that the weights in the model during a specific epoch fail to yield the optimal accuracy or loss, as determined by the user-defined criteria, the weights will not be preserved. However, the training process will persist, commencing from the aforementioned condition.