# A Semantic Loss Function for Deep Learning with Symbolic Knowledge

arXiv: https://arxiv.org/abs/1711.11157 · HTML: https://mlsanity.com/paper/1711.11157/

## Key facts

- Cited by 270 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2017.

## Built on by (most cited first, 30 of 270)

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- [Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcuts](https://mlsanity.com/paper/2305.19951/) (2023)
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- [Neuro-Symbolic Artificial Intelligence: Current Trends](https://mlsanity.com/paper/2105.05330/) (2021)
- [On the Constrained Time-Series Generation Problem](https://mlsanity.com/paper/2307.01717/) (2023)
- [A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference](https://mlsanity.com/paper/2212.12393/) (2022)
- [MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks](https://mlsanity.com/paper/2111.01564/) (2021)
- [Deep Learning with Logical Constraints](https://mlsanity.com/paper/2205.00523/) (2022)
- [Constrained Learning with Non-Convex Losses](https://mlsanity.com/paper/2103.05134/) (2021)
- [Safe Reinforcement Learning via Probabilistic Logic Shields](https://mlsanity.com/paper/2303.03226/) (2023)
- [Modular Design Patterns for Hybrid Learning and Reasoning Systems: a taxonomy, patterns and use cases](https://mlsanity.com/paper/2102.11965/) (2021)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcuts](https://mlsanity.com/paper/2402.12240/) (2024)
- [Multi-Label Classification Neural Networks with Hard Logical Constraints](https://mlsanity.com/paper/2103.13427/) (2021)
- [Neural Network Robustness as a Verification Property: A Principled Case Study](https://mlsanity.com/paper/2104.01396/) (2021)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [NeuPSL: Neural Probabilistic Soft Logic](https://mlsanity.com/paper/2205.14268/) (2022)
- [ROAD-R: The Autonomous Driving Dataset with Logical Requirements](https://mlsanity.com/paper/2210.01597/) (2022)
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- [Character-Centric Story Visualization via Visual Planning and Token Alignment](https://mlsanity.com/paper/2210.08465/) (2022)
- [Neuro-Symbolic Continual Learning: Knowledge, Reasoning Shortcuts and Concept Rehearsal](https://mlsanity.com/paper/2302.01242/) (2023)
- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [EXplainable Neural-Symbolic Learning (X-NeSyL) methodology to fuse deep learning representations with expert knowledge graphs: the MonuMAI cultural heritage use case](https://mlsanity.com/paper/2104.11914/) (2021)
- [Logically Consistent Language Models via Neuro-Symbolic Integration](https://mlsanity.com/paper/2409.13724/) (2024)
- [Logic-induced Diagnostic Reasoning for Semi-supervised Semantic Segmentation](https://mlsanity.com/paper/2308.12595/) (2023)
- [How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Data](https://mlsanity.com/paper/2402.04823/) (2024)

## Abstract (arXiv)

This paper develops a novel methodology for using symbolic knowledge in deep learning. From first principles, we derive a semantic loss function that bridges between neural output vectors and logical constraints. This loss function captures how close the neural network is to satisfying the constraints on its output. An experimental evaluation shows that it effectively guides the learner to achieve (near-)state-of-the-art results on semi-supervised multi-class classification. Moreover, it significantly increases the ability of the neural network to predict structured objects, such as rankings and paths. These discrete concepts are tremendously difficult to learn, and benefit from a tight integration of deep learning and symbolic reasoning methods.