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Breast cancer is a significant factor in female mortality. An early cancer diagnosis leads to a reduction in the breast cancer death rate. With the help of a computer-aided diagnosis system, the efficiency increased, and the cost was reduced for the cancer diagnosis. Traditional breast cancer classification techniques are based on handcrafted features techniques, and their performance relies upon the chosen features. They also are very sensitive to different sizes and complex shapes. However, histopathological breast cancer images are very complex in shape. Currently, deep learning models have become an alternative solution for diagnosis, and have overcome the drawbacks of classical classification techniques. Although deep learning has performed well in various tasks of computer vision and pattern recognition, it still has some challenges. One of the main challenges is the lack of training data. To address this challenge and optimize the performance, we have utilized a transfer learning technique which is where the deep learning models train on a task, and then fine-tune the models for another task. We have employed transfer learning in two ways: Training our proposed model first on the same domain dataset, then on the target dataset, and training our model on a different domain dataset, then on the target dataset. We have empirically proven that the same domain transfer learning optimized the performance. Our hybrid model of parallel convolutional layers and residual links is utilized to classify hematoxylin–eosin-stained breast biopsy images into four classes: invasive carcinoma, in-situ carcinoma, benign tumor and normal tissue. To …