# A Linear Interpolation and Curvature-Controlled Gradient Optimization Strategy Based on [PERSON]
## 3 Experimental Design and Analysis of Results
### Experimental Results and Analysis  
In order to comprehensively assess the performance advantage of the LCMAdam algorithm over other optimization algorithms, a series of classical optimization algorithms were selected for comparative experiments (the initial conditions were the same for each experiment, and the comparison was only the difference in the accuracy and loss values between the different algorithms), including SGD, Adagrad, Adalelta, Adam, Nadam, and StochGradAdam. Multiple experiments were conducted with different datasets and learning rate conditions to comprehensively evaluate their performance. The comparison of the experimental results of different optimization algorithms is shown in Table 3.  
The experimental setup was as follows:  
1. Algorithm selection: the SGD, Adagrad, Adadelta, Adam, Nadam, StochGradAdam, and LCMAdam algorithms were selected for comparison. 2. Number of training rounds: to ensure a fair comparison, the number of training rounds (Epoch) in the experiment was set to 100. 3. Batch size: to maintain consistency in the experiment, we set the batch size to 128. 4. Learning rate setting: the initial learning rate of all algorithms was set to 0.001. The maximum learning rate of the LCMAdam algorithm was set to 0.005, the minimum learning rate was set to 0.001, and the maximum change of learning rate was set to 0.001. 5. Other hyperparameters: the cycle length (period) in the LCMAdam optimizer was set to 1.1. 6. Multiple experiments: since the LCMAdam algorithm needed to adjust the cycle length and the maximum variation in the learning rate, we conducted multiple experiments on each dataset and selected the best results as the experimental results. \begin{table}
\begin{tabular}{c c} \hline \hline
**Software** & **Version** \\ \hline Python & 3.10 \\ Torch & 2.0.1 \\ Torchvision & 0.15.0 \\ Lightning & 2.1.2 \\ Cuda & Cu118 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main software versions in the experiment. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Number of** **Samples** & **Training Set** & **Test Set** & **Validation Set** & **Category** & **Data** **Characteristics** \\ \hline MNIST & 70,000 & 55,000 & 5000 & 10,000 & 10 & \begin{tabular}{c} Image size unification, data \\ diversity, moderate data volume \\ \end{tabular} \\ \hline CIFAR10 & 60,000 & 45,000 & 5000 & 10,000 & 10 & \
\begin{tabular}{c} RGB image, relatively small scale, \\ small image size \\ \end{tabular} \\ \hline Stomach & 1885 & 900 & 485 & 500 & 8 &
\begin{tabular}{c} RGB image, few categories, \\ recognition difficulty \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental dataset. * Experimental results: 17 comparative experiments were conducted on MNIST, CIFAR10, and Stomach datasets, and the average of the 17 results was taken as the final result to reflect the advantages of the LCMAdam algorithm in solving the Adam algorithm problem and improving the generalization ability. The LCMAdam algorithm aims to improve the generalization ability of the model and solve the oscillation problem caused by the algorithm's non-convergence. To evaluate the performance of the LCMAdam algorithm on various neural networks, different datasets were used for training. The MNIST dataset, consisting of grayscale images with a size of 28 \(\times\) 28 pixels each, was used to train a simple fully connected neural network. On the other hand, the CIFAR10 and Stomach datasets were used to train a MobileNetV2 lightweight neural network. These two datasets contain color RGB images. To compare the algorithms, we selected cross datasets and observed their convergence on all three datasets. The learning rate settings are the same as in Table 3. In order to comprehensively demonstrate the performance of the LCMAdam algorithm under different combinations of hyperparameter settings, three different combinations of maximum variation values of the learning rate and cycle lengths were designed and comparative experiments were conducted.