Symbolic integration by integrating learning models with different strengths and weaknesses

Integration is indispensable, not only in mathematics, but also in a wide range of other fields. A deep learning method has recently been developed and shown to be capable of integrating mathematical functions that could not previously be integrated on a computer. However, that method treats integration as equivalent to natural language translation and does not reflect mathematical information. In this study, we adjusted the learning model to take mathematical information into account and developed a wide range of learning models that learn the order of numerical operations more robustly. In this way, we achieved a 98.80% correct answer rate with symbolic integration, a higher rate than that of any existing method. We judged the correctness of the integration based on whether the derivative of the primitive function was consistent with the integrand. By building an integrated model based on this strategy, we achieved a 99.79% rate of correct answers with symbolic integration.

An Inductive Transfer Learning Approach using Cycle-consistent Adversarial Domain Adaptation with Application to Brain Tumor Segmentation

With recent advances in supervised machine learning for medical image analysis applications, the annotated medical image datasets of various domains are being shared extensively. Given that the annotation labelling requires medical expertise, such labels should be applied to as many learning tasks as possible. However, the multi-modal nature of each annotated image renders it difficult to share the annotation label among diverse tasks. In this work, we provide an inductive transfer learning (ITL) approach to adopt the annotation label of the source domain datasets to tasks of the target domain datasets using Cycle-GAN based unsupervised domain adaptation (UDA). To evaluate the applicability of the ITL approach, we adopted the brain tissue annotation label on the source domain dataset of Magnetic Resonance Imaging (MRI) images to the task of brain tumor segmentation on the target domain dataset of MRI. The results confirm that the segmentation accuracy of brain tumor segmentation improved significantly. The proposed ITL approach can make significant contribution to the field of medical image analysis, as we develop a fundamental tool to improve and promote various tasks using medical images.