Neurosymbolic Reasoning Shortcuts under the Independence Assumption

TL;DR

This paper demonstrates that the common independence assumption in neurosymbolic predictors limits their ability to model uncertainty and recognize reasoning shortcuts, affecting their reliability and interpretability.

Contribution

It provides a formal proof that independence assumptions prevent NeSy models from representing uncertainty over concept combinations.

Findings

Independence assumption limits uncertainty modeling.

Models can predict correctly for wrong reasons.

Assumption prevents recognition of reasoning shortcuts.

Abstract

The ubiquitous independence assumption among symbolic concepts in neurosymbolic (NeSy) predictors is a convenient simplification: NeSy predictors use it to speed up probabilistic reasoning. Recent works like van Krieken et al. (2024) and Marconato et al. (2024) argued that the independence assumption can hinder learning of NeSy predictors and, more crucially, prevent them from correctly modelling uncertainty. There is, however, scepticism in the NeSy community around the scenarios in which the independence assumption actually limits NeSy systems (Faronius and Dos Martires, 2025). In this work, we settle this question by formally showing that assuming independence among symbolic concepts entails that a model can never represent uncertainty over certain concept combinations. Thus, the model fails to be aware of reasoning shortcuts, i.e., the pathological behaviour of NeSy predictors that predict correct downstream tasks but for the wrong reasons.