# CTSketch: Compositional Tensor Sketching for Scalable Neurosymbolic Learning

arXiv: https://arxiv.org/abs/2503.24123 · HTML: https://mlsanity.com/paper/2503.24123/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 37 references that are in the map.
- First posted on arXiv 31 Mar 2025.

## Builds on (most cited first, 19 of 19)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
- [A Differential Approach to Inference in Bayesian Networks](https://mlsanity.com/paper/1301.3847/) (2013)
- [Scallop: A Language for Neurosymbolic Programming](https://mlsanity.com/paper/2304.04812/) (2023)
- [Closed Loop Neural-Symbolic Learning via Integrating Neural Perception, Grammar Parsing, and Symbolic Reasoning](https://mlsanity.com/paper/2006.06649/) (2020)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference](https://mlsanity.com/paper/2212.12393/) (2022)
- [Neural Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2303.04660/) (2023)
- [Scaling Tractable Probabilistic Circuits: A Systems Perspective](https://mlsanity.com/paper/2406.00766/) (2024)
- [KLay: Accelerating Arithmetic Circuits for Neurosymbolic AI](https://mlsanity.com/paper/2410.11415/) (2024)
- [Differentiable Sampling of Categorical Distributions Using the CatLog-Derivative Trick](https://mlsanity.com/paper/2311.12569/) (2023)
- [TerpreT: A Probabilistic Programming Language for Program Induction](https://mlsanity.com/paper/1608.04428/) (2016)
- [Data-Efficient Learning with Neural Programs](https://mlsanity.com/paper/2406.06246/) (2024)
- [A Fast Convoluted Story: Scaling Probabilistic Inference for Integer Arithmetic](https://mlsanity.com/paper/2410.12389/) (2024)

## Built on by (most cited first, 1 of 1)

- [Panther: Faster and Cheaper Computations with Randomized Numerical Linear Algebra](https://mlsanity.com/paper/2601.15473/) (2026)

## Abstract (arXiv)

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 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 the sketches. We provide theoretical insight into the maximum approximation error. Furthermore, we evaluate CTSketch on benchmarks from the neurosymbolic learning literature, including some designed for evaluating scalability. Our results show that CTSketch pushes neurosymbolic learning to new scales that were previously unattainable, with neural predictors obtaining high accuracy on tasks with one thousand inputs, despite supervision only on the final output.