# Verification Learning: Make Unsupervised Neuro-Symbolic System Feasible

arXiv: https://arxiv.org/abs/2503.12917 · HTML: https://mlsanity.com/paper/2503.12917/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 36 references that are in the map.
- First posted on arXiv 17 Mar 2025.

## Builds on (most cited first, 18 of 18)

- [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)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [Zero-shot Recognition via Semantic Embeddings and Knowledge Graphs](https://mlsanity.com/paper/1803.08035/) (2018)
- [Closed Loop Neural-Symbolic Learning via Integrating Neural Perception, Grammar Parsing, and Symbolic Reasoning](https://mlsanity.com/paper/2006.06649/) (2020)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [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 with Algorithmic Supervision via Continuous Relaxations](https://mlsanity.com/paper/2110.05651/) (2021)
- [Learning Deductive Reasoning from Synthetic Corpus based on Formal Logic](https://mlsanity.com/paper/2308.07336/) (2023)
- [On the Independence Assumption in Neurosymbolic Learning](https://mlsanity.com/paper/2404.08458/) (2024)
- [Learning by Self-Explaining](https://mlsanity.com/paper/2309.08395/) (2023)
- [Assessing SATNet's Ability to Solve the Symbol Grounding Problem](https://mlsanity.com/paper/2312.11522/) (2023)
- [Efficient Rectification of Neuro-Symbolic Reasoning Inconsistencies by Abductive Reflection](https://mlsanity.com/paper/2412.08457/) (2024)
- [Hybrid Classification and Reasoning for Image-based Constraint Solving](https://mlsanity.com/paper/2003.11001/) (2020)
- [A Smooth Transition Between Induction and Deduction: Fast Abductive Learning Based on Probabilistic Symbol Perception](https://mlsanity.com/paper/2502.12919/) (2025)
- [Learning for Long-Horizon Planning via Neuro-Symbolic Abductive Imitation](https://mlsanity.com/paper/2411.18201/) (2024)

## Built on by (most cited first, 1 of 1)

- [Quantitative Estimation of Target Task Performance from Unsupervised Pretext Task in Semi/Self-Supervised Learning](https://mlsanity.com/paper/2508.07299/) (2025)

## Abstract (arXiv)

The current Neuro-Symbolic (NeSy) Learning paradigm suffers from an over-reliance on labeled data, so if we completely disregard labels, it leads to less symbol information, a larger solution space, and more shortcuts-issues that current Nesy systems cannot resolve. This paper introduces a novel learning paradigm, Verification Learning (VL), which addresses this challenge by transforming the label-based reasoning process in Nesy into a label-free verification process. VL achieves excellent learning results solely by relying on unlabeled data and a function that verifies whether the current predictions conform to the rules. We formalize this problem as a Constraint Optimization Problem (COP) and propose a Dynamic Combinatorial Sorting (DCS) algorithm that accelerates the solution by reducing verification attempts, effectively lowering computational costs and introduce a prior alignment method to address potential shortcuts. Our theoretical analysis points out which tasks in Nesy systems can be completed without labels and explains why rules can replace infinite labels for some tasks, while for others the rules have no effect. We validate the proposed framework through several fully unsupervised tasks including addition, sort, match, and chess, each showing significant performance and efficiency improvements.