Enhancing Sequence Model with Mathematical Reasoning in Symbolic Integration

Sequence model has shown its efficiency in tackling integration problems, outperforming traditional mathematical software on specific datasets. However, it also encounters some challenges: robustness against minor perturbations, compositionality for decomposable operations, and out-of-distribution generalization when dealing with larger values, longer problems, and functions not covered in the training set. These issues arise from the fact that integration problems can only be partially regarded as a language translation task because integration follows its own mathematical rules. To address the above issues, this paper proposes a novel approach that enhances sequence model with mathematical reasoning. We introduce the abstraction of coefficients, perform expression decomposition, and substitute known functions for unknown counterparts. Our model achieves 83.6 accuracy in integration testing, 100 accuracy in robustness testing and 100 accuracy in additive composite expressions. By the mathematical rewriting, it also exhibits notable performance in extrapolation beyond the distribution. Moreover, our model passes the SAGGA test. In general, we obtain a robust symbolic integrator.