# Scallop: A Language for Neurosymbolic Programming

arXiv: https://arxiv.org/abs/2304.04812 · HTML: https://mlsanity.com/paper/2304.04812/

## Key facts

- Cited by 63 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 41 of its 84 references that are in the map.
- First posted on arXiv 10 Apr 2023.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 41)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [LXMERT: Learning Cross-Modality Encoder Representations from Transformers](https://mlsanity.com/paper/1908.07490/) (2019)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Rethinking Spatiotemporal Feature Learning: Speed-Accuracy Trade-offs in Video Classification](https://mlsanity.com/paper/1712.04851/) (2017)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Neural Module Networks](https://mlsanity.com/paper/1511.02799/) (2015)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [Quantifying Generalization in Reinforcement Learning](https://mlsanity.com/paper/1812.02341/) (2018)
- [Neural-Symbolic VQA: Disentangling Reasoning from Vision and Language Understanding](https://mlsanity.com/paper/1810.02338/) (2018)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Binding Language Models in Symbolic Languages](https://mlsanity.com/paper/2210.02875/) (2022)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [CLUTRR: A Diagnostic Benchmark for Inductive Reasoning from Text](https://mlsanity.com/paper/1908.06177/) (2019)
- [How to Train Your HiPPO: State Space Models with Generalized Orthogonal Basis Projections](https://mlsanity.com/paper/2206.12037/) (2022)
- [What Makes Convolutional Models Great on Long Sequence Modeling?](https://mlsanity.com/paper/2210.09298/) (2022)

## Built on by (most cited first, 30 of 63)

- [Proof of Thought : Neurosymbolic Program Synthesis allows Robust and Interpretable Reasoning](https://mlsanity.com/paper/2409.17270/) (2024)
- [KLay: Accelerating Arithmetic Circuits for Neurosymbolic AI](https://mlsanity.com/paper/2410.11415/) (2024)
- [Natural Language Embedded Programs for Hybrid Language Symbolic Reasoning](https://mlsanity.com/paper/2309.10814/) (2023)
- [LASER: A Neuro-Symbolic Framework for Learning Spatial-Temporal Scene Graphs with Weak Supervision](https://mlsanity.com/paper/2304.07647/) (2023)
- [Neurosymbolic Diffusion Models](https://mlsanity.com/paper/2505.13138/) (2025)
- [Exploiting Code Symmetries for Learning Program Semantics](https://mlsanity.com/paper/2308.03312/) (2023)
- [Defining neurosymbolic AI](https://mlsanity.com/paper/2507.11127/) (2025)
- [Teaching Probabilistic Logical Reasoning to Transformers](https://mlsanity.com/paper/2305.13179/) (2023)
- [Data-Efficient Learning with Neural Programs](https://mlsanity.com/paper/2406.06246/) (2024)
- [Relational Programming with Foundation Models](https://mlsanity.com/paper/2412.14515/) (2024)
- [Formal Explanations for Neuro-Symbolic AI](https://mlsanity.com/paper/2410.14219/) (2024)
- [Neural Probabilistic Circuits: Enabling Compositional and Interpretable Predictions through Logical Reasoning](https://mlsanity.com/paper/2501.07021/) (2025)
- [ESCA: Contextualizing Embodied Agents via Scene-Graph Generation](https://mlsanity.com/paper/2510.15963/) (2025)
- [FaccAID: A Transformer Model for Neuro-Symbolic Facade Reconstruction](https://mlsanity.com/paper/2406.01829/) (2024)
- [Dolphin: A Programmable Framework for Scalable Neurosymbolic Learning](https://mlsanity.com/paper/2410.03348/) (2024)
- [Understanding the Logic of Direct Preference Alignment through Logic](https://mlsanity.com/paper/2412.17696/) (2024)
- [NeuroStrata: Harnessing Neurosymbolic Paradigms for Improved Design, Testability, and Verifiability of Autonomous CPS](https://mlsanity.com/paper/2502.12267/) (2025)
- [LogicCBMs: Logic-Enhanced Concept-Based Learning](https://mlsanity.com/paper/2512.07383/) (2025)
- [Lobster: A GPU-Accelerated Framework for Neurosymbolic Programming](https://mlsanity.com/paper/2503.21937/) (2025)
- [Theory-Scale Auto-Formalization of Logics for Computer Science](https://mlsanity.com/paper/2606.26525/) (2026)
- [MTP: A Meaning-Typed Language Abstraction for AI-Integrated Programming](https://mlsanity.com/paper/2405.08965/) (2024)
- [A Learnability Analysis on Neuro-Symbolic Learning](https://mlsanity.com/paper/2503.16797/) (2025)
- [Modal Logic Neural Networks](https://mlsanity.com/paper/2512.03491/) (2025)
- [To Neuro-Symbolic Classification and Beyond by Compiling Description Logic Ontologies to Probabilistic Circuits](https://mlsanity.com/paper/2601.14894/) (2026)
- [Imbalances in Neurosymbolic Learning: Characterization and Mitigating Strategies](https://mlsanity.com/paper/2407.10000/) (2024)
- [A Neuro-Symbolic Framework for Sequence Classification with Relational and Temporal Knowledge](https://mlsanity.com/paper/2505.05106/) (2025)
- [Neuro-Symbolic Frameworks: Conceptual Characterization and Empirical Comparative Analysis](https://mlsanity.com/paper/2509.07122/) (2025)
- [Compiling to linear neurons](https://mlsanity.com/paper/2511.13769/) (2025)
- [The Neural Compiler: Program-to-Network Translation for Hybrid Scientific Machine Learning](https://mlsanity.com/paper/2605.22498/) (2026)
- [Efficient and Sound Probabilistic Verification for AI Agents](https://mlsanity.com/paper/2606.20510/) (2026)

## Abstract (arXiv)

We present Scallop, a language which combines the benefits of deep learning and logical reasoning. Scallop enables users to write a wide range of neurosymbolic applications and train them in a data- and compute-efficient manner. It achieves these goals through three key features: 1) a flexible symbolic representation that is based on the relational data model; 2) a declarative logic programming language that is based on Datalog and supports recursion, aggregation, and negation; and 3) a framework for automatic and efficient differentiable reasoning that is based on the theory of provenance semirings. We evaluate Scallop on a suite of eight neurosymbolic applications from the literature. Our evaluation demonstrates that Scallop is capable of expressing algorithmic reasoning in diverse and challenging AI tasks, provides a succinct interface for machine learning programmers to integrate logical domain knowledge, and yields solutions that are comparable or superior to state-of-the-art models in terms of accuracy. Furthermore, Scallop's solutions outperform these models in aspects such as runtime and data efficiency, interpretability, and generalizability.