Learning Neural Antiderivatives

In particular, we contrasted direct supervision based on antideriva-tive estimates with several method classes that rely on repeated differentiation, including both automatic and numerical approaches. As part of this framework, we explored integral reduction techniques as a means to mitigate the computational overhead associated with repeated integration or differentiation. Our systematic experimental analysis of all presented methods across a diverse set of modalities reveals that differential supervision via naïve automatic differentiation generally outperforms all competing approaches in terms of result quality. However, this performance comes at the cost of substantial training time, particularly for higher-order integration. A practical alternative in many scenarios is numerical differentiation via finite differences, which often achieves a reasonable trade-off between quality and computational cost. Nevertheless, it is important to incorporate a compensation operator to correct for the signal smoothing inherent in this differentiation scheme. Our findings suggest directions for future research, such as investigating progressive supervision paradigms that leverage different supervisory signals throughout the learning process. Interestingly, our analysis reveals that antiderivative quality correlates only weakly with downstream task performance. Cumulative schemes often excel at efficiently computing highly non-local aggregates, where local inaccuracies tend to cancel out.