CTSketch is a novel, scalable neurosymbolic learning algorithm for training neural networks using end-to-end input-output labels.CTSketch decomposes the symbolic program into sub-programs and summarizes each sub-program with a sketched tensor to improve scalability.The algorithm approximates the output distribution of the program using simple tensor operations over input distributions and summaries.CTSketch achieves high accuracy on tasks involving over one thousand inputs, pushing neurosymbolic learning to new scales.