On the Hardness of Probabilistic Neurosymbolic Learning
This addresses a key bottleneck in training neurosymbolic models for AI applications, offering a practical solution with theoretical guarantees, though it is incremental in improving gradient estimation methods.
The paper tackles the intractability of gradient computation in probabilistic neurosymbolic learning by proving it becomes tractable during training and introducing WeightME, an unbiased gradient estimator that approximates gradients with probabilistic guarantees using a logarithmic number of SAT solver calls, with experiments showing biased approximations fail even when exact solving is feasible.
The limitations of purely neural learning have sparked an interest in probabilistic neurosymbolic models, which combine neural networks with probabilistic logical reasoning. As these neurosymbolic models are trained with gradient descent, we study the complexity of differentiating probabilistic reasoning. We prove that although approximating these gradients is intractable in general, it becomes tractable during training. Furthermore, we introduce WeightME, an unbiased gradient estimator based on model sampling. Under mild assumptions, WeightME approximates the gradient with probabilistic guarantees using a logarithmic number of calls to a SAT solver. Lastly, we evaluate the necessity of these guarantees on the gradient. Our experiments indicate that the existing biased approximations indeed struggle to optimize even when exact solving is still feasible.