# Neuro-Symbolic Forward Reasoning arXiv: https://arxiv.org/abs/2110.09383 ยท HTML: https://mlsanity.com/paper/2110.09383/ ## Key facts - Cited by 16 papers in the map (data through 14 Oct 2026). - Builds on 26 of its 53 references that are in the map. - First posted on arXiv 18 Oct 2021. ## Builds on (most cited first, 26 of 26) - [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015) - [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015) - [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015) - [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016) - [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020) - [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019) - [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019) - [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019) - [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017) - [GENESIS: Generative Scene Inference and Sampling with Object-Centric Latent Representations](https://mlsanity.com/paper/1907.13052/) (2019) - [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017) - [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017) - [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019) - [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016) - [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020) - [Right for the Right Concept: Revising Neuro-Symbolic Concepts by Interacting with their Explanations](https://mlsanity.com/paper/2011.12854/) (2020) - [Generalization and Robustness Implications in Object-Centric Learning](https://mlsanity.com/paper/2107.00637/) (2021) - [Grounding Physical Concepts of Objects and Events Through Dynamic Visual Reasoning](https://mlsanity.com/paper/2103.16564/) (2021) - [Neural Logic Reinforcement Learning](https://mlsanity.com/paper/1904.10729/) (2019) - [Visual Concept-Metaconcept Learning](https://mlsanity.com/paper/2002.01464/) (2020) - [Neuro-Symbolic Visual Reasoning: Disentangling "Visual" from "Reasoning"](https://mlsanity.com/paper/2006.11524/) (2020) - [Conversational Neuro-Symbolic Commonsense Reasoning](https://mlsanity.com/paper/2006.10022/) (2020) - [Differentiable Inductive Logic Programming for Structured Examples](https://mlsanity.com/paper/2103.01719/) (2021) - [Synthesizing Datalog Programs Using Numerical Relaxation](https://mlsanity.com/paper/1906.00163/) (2019) - [Kandinsky Patterns](https://mlsanity.com/paper/1906.00657/) (2019) - [KANDINSKYPatterns -- An experimental exploration environment for Pattern Analysis and Machine Intelligence](https://mlsanity.com/paper/2103.00519/) (2021) ## Built on by (most cited first, 16 of 16) - [Interpretable and Explainable Logical Policies via Neurally Guided Symbolic Abstraction](https://mlsanity.com/paper/2306.01439/) (2023) - [Logically Consistent Language Models via Neuro-Symbolic Integration](https://mlsanity.com/paper/2409.13724/) (2024) - [Can LLMs Reason with Rules? Logic Scaffolding for Stress-Testing and Improving LLMs](https://mlsanity.com/paper/2402.11442/) (2024) - [Learning by Self-Explaining](https://mlsanity.com/paper/2309.08395/) (2023) - [BlendRL: A Framework for Merging Symbolic and Neural Policy Learning](https://mlsanity.com/paper/2410.11689/) (2024) - [Mastering Symbolic Operations: Augmenting Language Models with Compiled Neural Networks](https://mlsanity.com/paper/2304.01665/) (2023) - [Neuro-Symbolic AI: Explainability, Challenges, and Future Trends](https://mlsanity.com/paper/2411.04383/) (2024) - [DeiSAM: Segment Anything with Deictic Prompting](https://mlsanity.com/paper/2402.14123/) (2024) - [Neuro-Symbolic Learning: Principles and Applications in Ophthalmology](https://mlsanity.com/paper/2208.00374/) (2022) - [ILLUME: Rationalizing Vision-Language Models through Human Interactions](https://mlsanity.com/paper/2208.08241/) (2022) - [Neural Meta-Symbolic Reasoning and Learning](https://mlsanity.com/paper/2211.11650/) (2022) - [Neuro-Symbolic Execution of Generic Source Code](https://mlsanity.com/paper/2304.00989/) (2023) - [Bridging the Gap: Representation Spaces in Neuro-Symbolic AI](https://mlsanity.com/paper/2411.04393/) (2024) - [CLMN: Concept based Language Models via Neural Symbolic Reasoning](https://mlsanity.com/paper/2510.10063/) (2025) - [Neurosymbolic Imitation Learning with Human Guidance: A Privileged Information Approach](https://mlsanity.com/paper/2605.07166/) (2026) - [Weakly supervised concept Bottleneck Learning for Robust Two stage Object centric visual reasoning](https://mlsanity.com/paper/2608.22584/) (2026) ## Abstract (arXiv) Reasoning is an essential part of human intelligence and thus has been a long-standing goal in artificial intelligence research. With the recent success of deep learning, incorporating reasoning with deep learning systems, i.e., neuro-symbolic AI has become a major field of interest. We propose the Neuro-Symbolic Forward Reasoner (NSFR), a new approach for reasoning tasks taking advantage of differentiable forward-chaining using first-order logic. The key idea is to combine differentiable forward-chaining reasoning with object-centric (deep) learning. Differentiable forward-chaining reasoning computes logical entailments smoothly, i.e., it deduces new facts from given facts and rules in a differentiable manner. The object-centric learning approach factorizes raw inputs into representations in terms of objects. Thus, it allows us to provide a consistent framework to perform the forward-chaining inference from raw inputs. NSFR factorizes the raw inputs into the object-centric representations, converts them into probabilistic ground atoms, and finally performs differentiable forward-chaining inference using weighted rules for inference. Our comprehensive experimental evaluations on object-centric reasoning data sets, 2D Kandinsky patterns and 3D CLEVR-Hans, and a variety of tasks show the effectiveness and advantage of our approach.