# A Smooth Transition Between Induction and Deduction: Fast Abductive Learning Based on Probabilistic Symbol Perception

arXiv: https://arxiv.org/abs/2502.12919 · HTML: https://mlsanity.com/paper/2502.12919/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 18 Feb 2025.

## Placed in

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

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [Closed Loop Neural-Symbolic Learning via Integrating Neural Perception, Grammar Parsing, and Symbolic Reasoning](https://mlsanity.com/paper/2006.06649/) (2020)
- [Efficient Probabilistic Logic Reasoning with Graph Neural Networks](https://mlsanity.com/paper/2001.11850/) (2020)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [Distributed Constraint Optimization Problems and Applications: A Survey](https://mlsanity.com/paper/1602.06347/) (2016)
- [Learning Deductive Reasoning from Synthetic Corpus based on Formal Logic](https://mlsanity.com/paper/2308.07336/) (2023)
- [Neural Methods for Logical Reasoning Over Knowledge Graphs](https://mlsanity.com/paper/2209.14464/) (2022)
- [ZOOpt: Toolbox for Derivative-Free Optimization](https://mlsanity.com/paper/1801.00329/) (2017)
- [Efficient Rectification of Neuro-Symbolic Reasoning Inconsistencies by Abductive Reflection](https://mlsanity.com/paper/2412.08457/) (2024)

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

- [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)
- [EM-NeSy: Expectation Maximization for Neurosymbolic Learning](https://mlsanity.com/paper/2606.14463/) (2026)

## Abstract (arXiv)

Abductive learning (ABL) that integrates strengths of machine learning and logical reasoning to improve the learning generalization, has been recently shown effective. However, its efficiency is affected by the transition between numerical induction and symbolical deduction, leading to high computational costs in the worst-case scenario. Efforts on this issue remain to be limited. In this paper, we identified three reasons why previous optimization algorithms for ABL were not effective: insufficient utilization of prediction, symbol relationships, and accumulated experience in successful abductive processes, resulting in redundant calculations to the knowledge base. To address these challenges, we introduce an optimization algorithm named as Probabilistic Symbol Perception (PSP), which makes a smooth transition between induction and deduction and keeps the correctness of ABL unchanged. We leverage probability as a bridge and present an efficient data structure, achieving the transfer from a continuous probability sequence to discrete Boolean sequences with low computational complexity. Experiments demonstrate the promising results.