# Efficient Rectification of Neuro-Symbolic Reasoning Inconsistencies by Abductive Reflection

arXiv: https://arxiv.org/abs/2412.08457 · HTML: https://mlsanity.com/paper/2412.08457/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 20 of its 48 references that are in the map.
- First posted on arXiv 11 Dec 2024.

## Placed in

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

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

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [GAIA: a benchmark for General AI Assistants](https://mlsanity.com/paper/2311.12983/) (2023)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [Rethinking the Expressive Power of GNNs via Graph Biconnectivity](https://mlsanity.com/paper/2301.09505/) (2023)
- [Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphs](https://mlsanity.com/paper/2006.10643/) (2020)
- [Improving Coherence and Consistency in Neural Sequence Models with Dual-System, Neuro-Symbolic Reasoning](https://mlsanity.com/paper/2107.02794/) (2021)
- [Recurrent Relational Networks](https://mlsanity.com/paper/1711.08028/) (2017)
- [MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks](https://mlsanity.com/paper/2111.01564/) (2021)
- [NLocalSAT: Boosting Local Search with Solution Prediction](https://mlsanity.com/paper/2001.09398/) (2020)
- [Integrating Learning and Reasoning with Deep Logic Models](https://mlsanity.com/paper/1901.04195/) (2019)
- [Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions](https://mlsanity.com/paper/2208.04055/) (2022)
- [Injecting Logical Constraints into Neural Networks via Straight-Through Estimators](https://mlsanity.com/paper/2307.04347/) (2023)

## Built on by (most cited first, 9 of 9)

- [A Smooth Transition Between Induction and Deduction: Fast Abductive Learning Based on Probabilistic Symbol Perception](https://mlsanity.com/paper/2502.12919/) (2025)
- [A Learnability Analysis on Neuro-Symbolic Learning](https://mlsanity.com/paper/2503.16797/) (2025)
- [Verification Learning: Make Unsupervised Neuro-Symbolic System Feasible](https://mlsanity.com/paper/2503.12917/) (2025)
- [Curriculum Abductive Learning](https://mlsanity.com/paper/2505.12275/) (2025)
- [Complexity of Faceted Explanations in Propositional Abduction](https://mlsanity.com/paper/2507.14962/) (2025)
- [Adaptive Data-Knowledge Alignment in Genetic Perturbation Prediction](https://mlsanity.com/paper/2510.00512/) (2025)
- [Inferring Latent Intentions: Attributional Natural Language Inference in LLM Agents](https://mlsanity.com/paper/2601.08742/) (2026)
- [HypoAgent: An Agentic Framework for Interactive Abductive Hypothesis Generation over Knowledge Graphs](https://mlsanity.com/paper/2605.31370/) (2026)
- [EM-NeSy: Expectation Maximization for Neurosymbolic Learning](https://mlsanity.com/paper/2606.14463/) (2026)

## Abstract (arXiv)

Neuro-Symbolic (NeSy) AI could be regarded as an analogy to human dual-process cognition, modeling the intuitive System 1 with neural networks and the algorithmic System 2 with symbolic reasoning. However, for complex learning targets, NeSy systems often generate outputs inconsistent with domain knowledge and it is challenging to rectify them. Inspired by the human Cognitive Reflection, which promptly detects errors in our intuitive response and revises them by invoking the System 2 reasoning, we propose to improve NeSy systems by introducing Abductive Reflection (ABL-Refl) based on the Abductive Learning (ABL) framework. ABL-Refl leverages domain knowledge to abduce a reflection vector during training, which can then flag potential errors in the neural network outputs and invoke abduction to rectify them and generate consistent outputs during inference. ABL-Refl is highly efficient in contrast to previous ABL implementations. Experiments show that ABL-Refl outperforms state-of-the-art NeSy methods, achieving excellent accuracy with fewer training resources and enhanced efficiency.