# BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcuts

arXiv: https://arxiv.org/abs/2402.12240 · HTML: https://mlsanity.com/paper/2402.12240/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 90 references that are in the map.
- First posted on arXiv 19 Feb 2024.

## Builds on (most cited first, 30 of 59)

- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Calibrating Deep Neural Networks using Focal Loss](https://mlsanity.com/paper/2002.09437/) (2020)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Mitigating Neural Network Overconfidence with Logit Normalization](https://mlsanity.com/paper/2205.09310/) (2022)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [Practical Deep Learning with Bayesian Principles](https://mlsanity.com/paper/1906.02506/) (2019)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [Repulsive Deep Ensembles are Bayesian](https://mlsanity.com/paper/2106.11642/) (2021)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Probabilistic Concept Bottleneck Models](https://mlsanity.com/paper/2306.01574/) (2023)
- [Concept-based Explainable Artificial Intelligence: A Survey](https://mlsanity.com/paper/2312.12936/) (2023)
- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [Learning Linear Causal Representations from Interventions under General Nonlinear Mixing](https://mlsanity.com/paper/2306.02235/) (2023)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [Explainable Object-induced Action Decision for Autonomous Vehicles](https://mlsanity.com/paper/2003.09405/) (2020)
- [On Mixup Regularization](https://mlsanity.com/paper/2006.06049/) (2020)
- [Concept Bottleneck Model with Additional Unsupervised Concepts](https://mlsanity.com/paper/2202.01459/) (2022)

## Built on by (most cited first, 30 of 37)

- [Neuro-Symbolic AI in 2024: A Systematic Review](https://mlsanity.com/paper/2501.05435/) (2025)
- [Logically Consistent Language Models via Neuro-Symbolic Integration](https://mlsanity.com/paper/2409.13724/) (2024)
- [What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?](https://mlsanity.com/paper/2409.07953/) (2024)
- [Sum of Squares Circuits](https://mlsanity.com/paper/2408.11778/) (2024)
- [A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcuts](https://mlsanity.com/paper/2406.10368/) (2024)
- [Proof of Thought : Neurosymbolic Program Synthesis allows Robust and Interpretable Reasoning](https://mlsanity.com/paper/2409.17270/) (2024)
- [On the Independence Assumption in Neurosymbolic Learning](https://mlsanity.com/paper/2404.08458/) (2024)
- [Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lens](https://mlsanity.com/paper/2502.11245/) (2025)
- [Neurosymbolic Diffusion Models](https://mlsanity.com/paper/2505.13138/) (2025)
- [A Probabilistic Neuro-symbolic Layer for Algebraic Constraint Satisfaction](https://mlsanity.com/paper/2503.19466/) (2025)
- [Neuro-Symbolic AI: Explainability, Challenges, and Future Trends](https://mlsanity.com/paper/2411.04383/) (2024)
- [AutoMonitor-Bench: Evaluating the Reliability of LLM-Based Misbehavior Monitor](https://mlsanity.com/paper/2601.05752/) (2026)
- [Neural Probabilistic Circuits: Enabling Compositional and Interpretable Predictions through Logical Reasoning](https://mlsanity.com/paper/2501.07021/) (2025)
- [How to Square Tensor Networks and Circuits Without Squaring Them](https://mlsanity.com/paper/2512.17090/) (2025)
- [The Road to Generalizable Neuro-Symbolic Learning Should be Paved with Foundation Models](https://mlsanity.com/paper/2505.24874/) (2025)
- [How Do Artificial Intelligences Think? The Three Mathematico-Cognitive Factors of Categorical Segmentation Operated by Synthetic Neurons](https://mlsanity.com/paper/2501.06196/) (2024)
- [A Learnability Analysis on Neuro-Symbolic Learning](https://mlsanity.com/paper/2503.16797/) (2025)
- [Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AI](https://mlsanity.com/paper/2510.25497/) (2025)
- [Imbalances in Neurosymbolic Learning: Characterization and Mitigating Strategies](https://mlsanity.com/paper/2407.10000/) (2024)
- [MARS: A neurosymbolic approach for interpretable drug discovery](https://mlsanity.com/paper/2410.05289/) (2024)
- [Gradient-Based Optimization on G"odel Logic as Discrete Local Search](https://mlsanity.com/paper/2503.01817/) (2025)
- [Synthetic Categorical Restructuring large Or How AIs Gradually Extract Efficient Regularities from Their Experience of the World](https://mlsanity.com/paper/2503.10643/) (2025)
- [Concepts Worth Having: Refining VLM-Guided Concept Bottleneck Models with Minimal Annotations](https://mlsanity.com/paper/2605.16405/) (2026)
- [A Scalable Approach to Probabilistic Neuro-Symbolic Robustness Verification](https://mlsanity.com/paper/2502.03274/) (2025)
- [Curriculum Abductive Learning](https://mlsanity.com/paper/2505.12275/) (2025)
- [On Improving Neurosymbolic Learning by Exploiting the Representation Space](https://mlsanity.com/paper/2602.07973/) (2026)
- [Constraint-Based Analysis of Reasoning Shortcuts in Neurosymbolic Learning](https://mlsanity.com/paper/2604.23377/) (2026)
- [Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models](https://mlsanity.com/paper/2605.18202/) (2026)
- [Intra-neuronal attention within language models Relationships between activation and semantics](https://mlsanity.com/paper/2503.12992/) (2025)
- [Neuro-symbolic Weak Supervision: Theory and Semantics](https://mlsanity.com/paper/2503.18509/) (2025)

## Abstract (arXiv)

Neuro-Symbolic (NeSy) predictors that conform to symbolic knowledge - encoding, e.g., safety constraints - can be affected by Reasoning Shortcuts (RSs): They learn concepts consistent with the symbolic knowledge by exploiting unintended semantics. RSs compromise reliability and generalization and, as we show in this paper, they are linked to NeSy models being overconfident about the predicted concepts. Unfortunately, the only trustworthy mitigation strategy requires collecting costly dense supervision over the concepts. Rather than attempting to avoid RSs altogether, we propose to ensure NeSy models are aware of the semantic ambiguity of the concepts they learn, thus enabling their users to identify and distrust low-quality concepts. Starting from three simple desiderata, we derive bears (BE Aware of Reasoning Shortcuts), an ensembling technique that calibrates the model's concept-level confidence without compromising prediction accuracy, thus encouraging NeSy architectures to be uncertain about concepts affected by RSs. We show empirically that bears improves RS-awareness of several state-of-the-art NeSy models, and also facilitates acquiring informative dense annotations for mitigation purposes.