# Curriculum Abductive Learning

arXiv: https://arxiv.org/abs/2505.12275 · HTML: https://mlsanity.com/paper/2505.12275/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 29 of its 79 references that are in the map.
- First posted on arXiv 18 May 2025.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [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)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [Compositional Generalization via Neural-Symbolic Stack Machines](https://mlsanity.com/paper/2008.06662/) (2020)
- [Generalization on the Unseen, Logic Reasoning and Degree Curriculum](https://mlsanity.com/paper/2301.13105/) (2023)
- [Scallop: A Language for Neurosymbolic Programming](https://mlsanity.com/paper/2304.04812/) (2023)
- [Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcuts](https://mlsanity.com/paper/2305.19951/) (2023)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference](https://mlsanity.com/paper/2212.12393/) (2022)
- [MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks](https://mlsanity.com/paper/2111.01564/) (2021)
- [BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcuts](https://mlsanity.com/paper/2402.12240/) (2024)
- [Neuro-Symbolic Continual Learning: Knowledge, Reasoning Shortcuts and Concept Rehearsal](https://mlsanity.com/paper/2302.01242/) (2023)
- [Neuro-Symbolic Entropy Regularization](https://mlsanity.com/paper/2201.11250/) (2022)
- [Neuro-Symbolic Hierarchical Rule Induction](https://mlsanity.com/paper/2112.13418/) (2021)
- [On the Independence Assumption in Neurosymbolic Learning](https://mlsanity.com/paper/2404.08458/) (2024)
- [Injecting Logical Constraints into Neural Networks via Straight-Through Estimators](https://mlsanity.com/paper/2307.04347/) (2023)
- [Learning with Logical Constraints but without Shortcut Satisfaction](https://mlsanity.com/paper/2403.00329/) (2024)
- [On the Hardness of Probabilistic Neurosymbolic Learning](https://mlsanity.com/paper/2406.04472/) (2024)
- [Efficient Rectification of Neuro-Symbolic Reasoning Inconsistencies by Abductive Reflection](https://mlsanity.com/paper/2412.08457/) (2024)
- [Deciphering Raw Data in Neuro-Symbolic Learning with Provable Guarantees](https://mlsanity.com/paper/2308.10487/) (2023)
- [The KANDY Benchmark: Incremental Neuro-Symbolic Learning and Reasoning with Kandinsky Patterns](https://mlsanity.com/paper/2402.17431/) (2024)
- [Mathematical Logic in Computer Science](https://mlsanity.com/paper/1802.03292/) (2018)
- [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)

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

- [Candidate Retention for Abductive Learning](https://mlsanity.com/paper/2609.39561/) (2026)

## Abstract (arXiv)

Abductive Learning (ABL) integrates machine learning with logical reasoning in a loop: a learning model predicts symbolic concept labels from raw inputs, which are revised through abduction using domain knowledge and then fed back for retraining. However, due to the nondeterminism of abduction, the training process often suffers from instability, especially when the knowledge base is large and complex, resulting in a prohibitively large abduction space. While prior works focus on improving candidate selection within this space, they typically treat the knowledge base as a static black box. In this work, we propose Curriculum Abductive Learning (C-ABL), a method that explicitly leverages the internal structure of the knowledge base to address the ABL training challenges. C-ABL partitions the knowledge base into a sequence of sub-bases, progressively introduced during training. This reduces the abduction space throughout training and enables the model to incorporate logic in a stepwise, smooth way. Experiments across multiple tasks show that C-ABL outperforms previous ABL implementations, significantly improves training stability, convergence speed, and final accuracy, especially under complex knowledge setting.