# Candidate Retention for Abductive Learning

arXiv: https://arxiv.org/abs/2609.39561 · HTML: https://mlsanity.com/paper/2609.39561/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 29 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- LLM reasoning

## Builds on (most cited first, 14 of 14)

- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [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)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (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)
- [Abductive Knowledge Induction From Raw Data](https://mlsanity.com/paper/2010.03514/) (2020)
- [A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcuts](https://mlsanity.com/paper/2406.10368/) (2024)
- [Deciphering Raw Data in Neuro-Symbolic Learning with Provable Guarantees](https://mlsanity.com/paper/2308.10487/) (2023)
- [Truncated Variational Expectation Maximization](https://mlsanity.com/paper/1610.03113/) (2016)
- [A Learnability Analysis on Neuro-Symbolic Learning](https://mlsanity.com/paper/2503.16797/) (2025)
- [Reduced Implication-bias Logic Loss for Neuro-Symbolic Learning](https://mlsanity.com/paper/2208.06838/) (2022)
- [Curriculum Abductive Learning](https://mlsanity.com/paper/2505.12275/) (2025)

## Abstract (arXiv)

Abductive learning combines neural perception with symbolic reasoning, using explanations generated by abduction to supervise the perception model. Multiple valid explanations of the same symbolic target can assign conflicting labels to the same inputs. Common policies select a single candidate as a pseudo-label, which may reinforce mistaken assignments, or weight all candidates, which may spread supervision across competing labels. These risks motivate selecting a retained subset to balance supervision sharpness and model-mass coverage. To guide this choice, we bound the coordinate-level supervision error using retained uncertainty, discarded model mass, and model mismatch. For a fixed model and training pair, only the first two terms depend on the retained set. We propose Abductive Candidate Retention (ACR), which uses these terms to guide greedy additions, accepting a candidate when its recovered mass exceeds the increase in retained uncertainty. Experiments show that ACR improves concept accuracy over single-candidate baselines and A3BL in most evaluated aggregated mod-addition settings. Objective ablations support the joint use of uncertainty and posterior mass.