Due to the complexity and illegibility of medical images, it brings inconvenience and difficulty to the diagnosis of medical personnel. To address these issues, an optimization algorithm called GSL(Gradient sine linear) based on Adam algorithm improvement is proposed in this paper, which introduces gradient pruning strategy, periodic adjustment of learning rate, and linear interpolation strategy. The gradient trimming technique can scale the gradient to prevent gradient explosion, while the periodic adjustment of the learning rate and linear interpolation strategy adjusts the learning rate according to the characteristics of the sinusoidal function, accelerating the convergence while reducing the drastic parameter fluctuations, improving the efficiency and stability of training. The experimental results show that compared to the classic Adam algorithm, this algorithm can demonstrate better classification accuracy, the GSL algorithm achieves an accuracy of 78% and 75.2% on the MobileNetV2 network and ShuffleNetV2 network under the Gastroenterology dataset; and on the MobileNetV2 network and ShuffleNetV2 network under the Glaucoma dataset, an accuracy of 84.72% and 83.12%. The GSL optimizer achieved significant performance improvement on various neural network structures and datasets, proving its effectiveness and practicality in the field of deep learning, and also providing new ideas and methods for solving the difficulties in medical image recognition.

Aiming at a series of limitations of the Adam algorithm, such as hyperparameter sensitivity and unstable convergence, in this paper, an improved optimization algorithm, the Cycle-Norm-Adam (CN-Adam) algorithm, is proposed. The algorithm integrates the ideas of a cyclic exponential decay learning rate (CEDLR) and gradient paradigm constraintsand accelerates the convergence speed of the Adam model and improves its generalization performance by dynamically adjusting the learning rate. In order to verify the effectiveness of the CN-Adam algorithm, we conducted extensive experimental studies. The CN-Adam algorithm achieved significant performance improvementsin both standard datasets. The experimental results show that the CN-Adam algorithm achieved 98.54% accuracy in the MNIST dataset and 72.10% in the CIFAR10 dataset. Due to the complexity and specificity of medical images, the algorithm was tested in a medical dataset and achieved an accuracy of 78.80%, which was better than the other algorithms. The experimental results show that the CN-Adam optimization algorithm provides an effective optimization strategy for improving model performance and promoting medical research.

The Adam algorithm is a widely used optimizer for neural network training due to efficient convergence speed. The algorithm is prone to unstable learning rate and performance degradation on some models. To solve these problems, in this paper, an improved algorithm named Linear Curvature Momentum Adam (LCMAdam) is proposed, which introduces curvature-controlled gradient and linear interpolation strategies. The curvature-controlled gradient can make the gradient update smoother, and the linear interpolation technique can adaptively adjust the size of the learning rate according to the characteristics of the curve during the training process so that it can find the exact value faster, which improves the efficiency and robustness of training. The experimental results show that the LCMAdam algorithm achieves 98.49% accuracy on the MNIST dataset, 75.20% on the CIFAR10 dataset, and 76.80% on the Stomach dataset, which is more difficult to recognize medical images. The LCMAdam optimizer achieves significant performance gains on a variety of neural network structures and tasks, proving its effectiveness and utility in the field of deep learning.

In the field of deep learning, the traditional Vision Transformer (ViT) model has some limitations when dealing with local details and long-range dependencies; especially in the absence of sufficient training data, it is prone to overfitting. Structures such as retinal blood vessels and lesion boundaries have distinct fractal properties in medical images. The Fractional Convolution Vision Transformer (FCViT) model is proposed in this paper, which effectively compensates for the deficiency of ViT in local feature capture by fusing convolutional information. The ability to classify medical images is enhanced by analyzing frequency domain features using fractional-order Fourier transform and capturing global information through a self-attention mechanism. The three-branch architecture enables the model to fully understand the data from multiple perspectives, capturing both local details and global context, which in turn improves classification performance and generalization. The experimental results showed that the FCViT model achieved 93.52% accuracy, 93.32% precision, 92.79% recall, and a 93.04% F1-score on the standardized fundus glaucoma dataset. The accuracy on the Harvard Dataverse-V1 dataset reached 94.21%, with a precision of 93.73%, recall of 93.67%, and F1-score of 93.68%. The FCViT model achieves significant performance gains on a variety of neural network architectures and tasks with different source datasets, demonstrating its effectiveness and utility in the field of deep learning.

In the field of deep learning, the design of optimization algorithms and neural network structures is crucial for improving model performance. Recent advances in medical image analysis have revealed that many pathological features exhibit fractal-like characteristics in their spatial distribution and morphological patterns. This observation has opened new possibilities for developing fractal-inspired deep learning approaches. In this study, we propose the following: (1) a novel Region-Module Adam (RMA) optimizer that incorporates fractal-inspired region-weighting to prioritize areas with higher fractal dimensionality, and (2) an ECA-Enhanced Shuffle MobileNet (ESM) architecture designed to capture multi-scale fractal patterns through its enhanced feature extraction modules. Our experiments demonstrate that this fractal-informed approach significantly improves classification accuracy compared to conventional methods. On gastrointestinal image datasets, the RMA algorithm achieved accuracies of 83.60%, 81.60%, and 87.30% with MobileNetV2, ShuffleNetV2, and ESM networks, respectively. For glaucoma fundus images, the corresponding accuracies reached 84.90%, 83.60%, and 92.73%. These results suggest that explicitly considering fractal properties in medical image analysis can lead to more effective diagnostic tools.