Many computational tasks benefit from being formulated as the composition of neural networks followed by a discrete symbolic program. The goal of neurosymbolic learning is to train the neural networks using only end-to-end input-output labels of the composite. We introduce CTSketch, a novel, scalable neurosymbolic learning algorithm. CTSketch uses two techniques to improve the scalability of neurosymbolic inference: decompose the symbolic program into sub-programs and summarize each sub-program with a sketched tensor. This strategy allows us to approximate the output distribution of the program with simple tensor operations over the input distributions and summaries. We provide theoretical insight into the maximum error of the approximation. Furthermore, we evaluate CTSketch on many benchmarks from the neurosymbolic literature, including some designed for evaluating scalability. Our results show that CTSketch pushes neurosymbolic learning to new scales that have previously been unattainable by obtaining high accuracy on tasks involving over one thousand inputs.

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