# A Linear Interpolation and Curvature-Controlled Gradient Optimization Strategy Based on [PERSON]
## 3 Experimental Design and Analysis of Results
### Experimental Results and Analysis
The results in Figure 4 show that, on the CIFAR10 dataset, although the accuracy of the LCMAdam algorithm is slightly lower than that of the Adam and NAdam algorithms at the beginning of the training period, the accuracy of the LCMAdam algorithm surpasses that of the remaining six algorithms as the training progresses, and the algorithm improves its accuracy by 6.71% compared to the Adam algorithm. The accuracy of the LCMAdam algorithm is improved by 5.35% and 6.14% compared to the improved Adam algorithm-based NAdam algorithm and StochGradAdam algorithm, respectively. This advantage can be attributed to the curvature-controlled gradient strategy employed by the LCMAdam optimizer. During the training process, the LCMAdam algorithm ensures the smoothness of the gradient update by limiting the curvature of the gradient. By adjusting the change in the size of the curvature, the LCMAdam algorithm can effectively avoid drastic fluctuations in the gradient, thus improving the stability of model training. Figure 4: Accuracy of different algorithms for the CIFAR10 dataset. Figure 3: Performance comparison of various algorithms on the MNIST dataset: (**a**) comparison of accuracy; (**b**) comparison of loss values. Figure 5 shows that the LCMAdam algorithm has a slightly lower loss value than the other algorithms at the beginning of training. As the number of training rounds increases, the Adam algorithm is lower than the algorithm by 0.06 in comparison. The accuracy of several different algorithms was compared on the Stomach dataset. According to the results in Figure 6, the accuracy of the Adadelta and SGD algorithms is significantly lower than the other five algorithms as the number of training rounds increases. The LCMAdam algorithm improves by 2.6%, 2%, and 6.6% compared to the Adam algorithm as well as the NAdam algorithm and StochGradAdam algorithm, which are improved based on the Adam algorithm. This advantage can be attributed to the linear interpolation control change learning rate strategy, which constantly changes the value of the learning rate during training and utilizes linear interpolation to approximate the learning rate for adjustment. By adjusting the learning rate in a timely and precise manner, the LCMAdam algorithm can converge to the optimal solution more efficiently and be more responsive to changes and challenges during training, which in turn improves performance and stability. The loss values for the test set of several different algorithms were compared for the Stomach dataset. The results in Figure 7 show that, as the number of training rounds increases, the Adadelta algorithm has significantly higher loss values than the other optimization algorithms. The LCMAdam algorithm outperforms  
Figure 5: Loss values of different algorithms for the CIFAR10 dataset. Figure 6: Accuracy of different algorithms on the Stomach dataset. with lower loss values. Specifically, when compared to the Adam algorithm, as well as the NAdam algorithm and the StochGradAdam algorithm, which are based on the improvement of the Adam algorithm; the LCMAdam algorithm reduces the loss values by 0.223, 0.157, and 0.2707. Based on Figure 8, on the CIFAR10 dataset, the LCMAdam algorithm has slightly lower GPU power consumption compared to the StochGradAdam algorithm, but still outperforms the Adam algorithm and other compared algorithms. This is due to the LCMAdam algorithm's dynamic learning rate adjustment strategy, which results in a slightly longer training time compared to some other algorithms. The LCMAdam algorithm's dynamic learning rate adjustment strategy offers more precise guidance for model optimization, thereby enhancing the model's convergence speed and performance to some extent. Based on the observations in Figure 9, it can be seen that the GPU power consumption of the seven algorithms is basically equal when facing a more difficult dataset to recognize, such as Stomach, but there is a slight difference in their processing time.