# Knowledge Enhanced Neural Networks for relational domains

arXiv: https://arxiv.org/abs/2205.15762 · HTML: https://mlsanity.com/paper/2205.15762/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 20 of 20)

- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Visual Relationship Detection with Language Priors](https://mlsanity.com/paper/1608.00187/) (2016)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Hinge-Loss Markov Random Fields and Probabilistic Soft Logic](https://mlsanity.com/paper/1505.04406/) (2015)
- [Augmenting Neural Networks with First-order Logic](https://mlsanity.com/paper/1906.06298/) (2019)
- [Adversarially Regularising Neural NLI Models to Integrate Logical Background Knowledge](https://mlsanity.com/paper/1808.08609/) (2018)
- [MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks](https://mlsanity.com/paper/2111.01564/) (2021)
- [TensorLog: A Differentiable Deductive Database](https://mlsanity.com/paper/1605.06523/) (2016)
- [Relational Neural Machines](https://mlsanity.com/paper/2002.02193/) (2020)
- [Teaching the Old Dog New Tricks: Supervised Learning with Constraints](https://mlsanity.com/paper/2002.10766/) (2020)
- [Logical Rule Induction and Theory Learning Using Neural Theorem Proving](https://mlsanity.com/paper/1809.02193/) (2018)
- [Semi-Supervised Learning using Differentiable Reasoning](https://mlsanity.com/paper/1908.04700/) (2019)
- [NeuralLog: a Neural Logic Language](https://mlsanity.com/paper/2105.01442/) (2021)
- [Neural Logic Rule Layers](https://mlsanity.com/paper/1907.00878/) (2019)

## Built on by (most cited first, 3 of 3)

- [Refining neural network predictions using background knowledge](https://mlsanity.com/paper/2206.04976/) (2022)
- [T-ILR: a Neurosymbolic Integration for LTLf](https://mlsanity.com/paper/2508.15943/) (2025)
- [Knowledge Enhanced Graph Neural Networks for Graph Completion](https://mlsanity.com/paper/2303.15487/) (2023)

## Abstract (arXiv)

In the recent past, there has been a growing interest in Neural-Symbolic Integration frameworks, i.e., hybrid systems that integrate connectionist and symbolic approaches to obtain the best of both worlds. In this work we focus on a specific method, KENN (Knowledge Enhanced Neural Networks), a Neural-Symbolic architecture that injects prior logical knowledge into a neural network by adding on its top a residual layer that modifies the initial predictions accordingly to the knowledge. Among the advantages of this strategy, there is the inclusion of clause weights, learnable parameters that represent the strength of the clauses, meaning that the model can learn the impact of each rule on the final predictions. As a special case, if the training data contradicts a constraint, KENN learns to ignore it, making the system robust to the presence of wrong knowledge. In this paper, we propose an extension of KENN for relational data. One of the main advantages of KENN resides in its scalability, thanks to a flexible treatment of dependencies between the rules obtained by stacking multiple logical layers. We show experimentally the efficacy of this strategy. The results show that KENN is capable of increasing the performances of the underlying neural network, obtaining better or comparable accuracies in respect to other two related methods that combine learning with logic, requiring significantly less time for learning.