# Parallel Neurosymbolic Integration with Concordia

arXiv: https://arxiv.org/abs/2306.00480 · HTML: https://mlsanity.com/paper/2306.00480/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 54 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 25 of 25)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Self-Distillation Amplifies Regularization in Hilbert Space](https://mlsanity.com/paper/2002.05715/) (2020)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Cross-Sentence N-ary Relation Extraction with Graph LSTMs](https://mlsanity.com/paper/1708.03743/) (2017)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [Learning Actor Relation Graphs for Group Activity Recognition](https://mlsanity.com/paper/1904.10117/) (2019)
- [Probabilistic Logic Neural Networks for Reasoning](https://mlsanity.com/paper/1906.08495/) (2019)
- [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)
- [Embedding Symbolic Knowledge into Deep Networks](https://mlsanity.com/paper/1909.01161/) (2019)
- [Neural-Symbolic Integration: A Compositional Perspective](https://mlsanity.com/paper/2010.11926/) (2020)
- [Knowledge Distillation as Semiparametric Inference](https://mlsanity.com/paper/2104.09732/) (2021)
- [Neural Network Matrix Factorization](https://mlsanity.com/paper/1511.06443/) (2015)
- [Relational Neural Machines](https://mlsanity.com/paper/2002.02193/) (2020)
- [Analyzing Differentiable Fuzzy Implications](https://mlsanity.com/paper/2006.03472/) (2020)
- [Integrating Knowledge and Reasoning in Image Understanding](https://mlsanity.com/paper/1906.09954/) (2019)
- [Towards Neural Theorem Proving at Scale](https://mlsanity.com/paper/1807.08204/) (2018)
- [Deep Probabilistic Logic: A Unifying Framework for Indirect Supervision](https://mlsanity.com/paper/1808.08485/) (2018)
- [Principled and Efficient Motif Finding for Structure Learning of Lifted Graphical Models](https://mlsanity.com/paper/2302.04599/) (2023)
- [Deep Adaptive Semantic Logic (DASL): Compiling Declarative Knowledge into Deep Neural Networks](https://mlsanity.com/paper/2003.07344/) (2020)

## Built on by (most cited first, 2 of 2)

- [Semantic Objective Functions: A distribution-aware method for adding logical constraints in deep learning](https://mlsanity.com/paper/2405.15789/) (2024)
- [Efficiently Learning Probabilistic Logical Models by Cheaply Ranking Mined Rules](https://mlsanity.com/paper/2409.16238/) (2024)

## Abstract (arXiv)

Parallel neurosymbolic architectures have been applied effectively in NLP by distilling knowledge from a logic theory into a deep model.However, prior art faces several limitations including supporting restricted forms of logic theories and relying on the assumption of independence between the logic and the deep network. We present Concordia, a framework overcoming the limitations of prior art. Concordia is agnostic both to the deep network and the logic theory offering support for a wide range of probabilistic theories. Our framework can support supervised training of both components and unsupervised training of the neural component. Concordia has been successfully applied to tasks beyond NLP and data classification, improving the accuracy of state-of-the-art on collective activity detection, entity linking and recommendation tasks.