# Independence Is Not an Issue in Neurosymbolic AI

arXiv: https://arxiv.org/abs/2504.07851 · HTML: https://mlsanity.com/paper/2504.07851/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 10 Apr 2025.

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

- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [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)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Generative Neurosymbolic Machines](https://mlsanity.com/paper/2010.12152/) (2020)
- [Neuro-Symbolic Continual Learning: Knowledge, Reasoning Shortcuts and Concept Rehearsal](https://mlsanity.com/paper/2302.01242/) (2023)
- [VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming](https://mlsanity.com/paper/2202.04178/) (2022)
- [Efficient Generation of Structured Objects with Constrained Adversarial Networks](https://mlsanity.com/paper/2007.13197/) (2020)
- [Neural Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2303.04660/) (2023)
- [On the Independence Assumption in Neurosymbolic Learning](https://mlsanity.com/paper/2404.08458/) (2024)
- [On the Relative Expressiveness of Bayesian and Neural Networks](https://mlsanity.com/paper/1812.08957/) (2018)
- [Probabilistic Neural Circuits](https://mlsanity.com/paper/2403.06235/) (2024)
- [Declarative Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2302.10674/) (2023)
- [Towards Unbiased Exploration in Partial Label Learning](https://mlsanity.com/paper/2307.00465/) (2023)

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

- [Neurosymbolic Reasoning Shortcuts under the Independence Assumption](https://mlsanity.com/paper/2507.11357/) (2025)

## Abstract (arXiv)

A popular approach to neurosymbolic AI is to take the output of the last layer of a neural network, e.g. a softmax activation, and pass it through a sparse computation graph encoding certain logical constraints one wishes to enforce. This induces a probability distribution over a set of random variables, which happen to be conditionally independent of each other in many commonly used neurosymbolic AI models. Such conditionally independent random variables have been deemed harmful as their presence has been observed to co-occur with a phenomenon dubbed deterministic bias, where systems learn to deterministically prefer one of the valid solutions from the solution space over the others. We provide evidence contesting this conclusion and show that the phenomenon of deterministic bias is an artifact of improperly applying neurosymbolic AI.