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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.
We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent representatio
We demonstrate a library for the integration of domain knowledge in deep learning architectures. Using this library, the structure of the data is expressed symbolically via graph declarations and the logical constraints over outputs or latent variabl
Symbolic regression is a powerful technique that can discover analytical equations that describe data, which can lead to explainable models and generalizability outside of the training data set. In contrast, neural networks have achieved amazing leve
Continuous integration is an indispensable step of modern software engineering practices to systematically manage the life cycles of system development. Developing a machine learning model is no difference - it is an engineering process with a life c
Learning effective policies for sparse objectives is a key challenge in Deep Reinforcement Learning (RL). A common approach is to design task-related dense rewards to improve task learnability. While such rewards are easily interpreted, they rely on