Symbolic rule learners generate interpretable solutions, however they require
the input to be encoded symbolically. Neuro-symbolic approaches overcome this
issue by mapping raw data to latent symbolic concepts using a neural network.
Training the neural and symbolic components jointly is difficult, due to slow
and unstable learning, hence many existing systems rely on hand-engineered
rules to train the network. We introduce NeuralFastLAS, a scalable and fast
end-to-end approach that trains a neural network jointly with a symbolic
learner. For a given task, NeuralFastLAS computes a relevant set of rules,
proved to contain an optimal symbolic solution, trains a neural network using
these rules, and finally finds an optimal symbolic solution to the task while
taking network predictions into account. A key novelty of our approach is
learning a posterior distribution on rules while training the neural network to
improve stability during training. We provide theoretical results for a
sufficient condition on network training to guarantee correctness of the final
solution. Experimental results demonstrate that NeuralFastLAS is able to
achieve state-of-the-art accuracy in arithmetic and logical tasks, with a
training time that is up to two orders of magnitude faster than other jointly
trained neuro-symbolic methods.

NeuralFastLAS 是一种可扩展且快速的端到端方法，能够联合训练神经网络和符号学习器，实现在任务中找到最优符号解的能力，并提供了理论结果和实验验证。