# A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification

arXiv: https://arxiv.org/abs/2605.16383 · HTML: https://mlsanity.com/paper/2605.16383/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 67 of its 138 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 30 of 67)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [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)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [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)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [Functional Variational Bayesian Neural Networks](https://mlsanity.com/paper/1903.05779/) (2019)
- [Learning to Reason: End-to-End Module Networks for Visual Question Answering](https://mlsanity.com/paper/1704.05526/) (2017)
- [Epistemic Neural Networks](https://mlsanity.com/paper/2107.08924/) (2021)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- ['In-Between' Uncertainty in Bayesian Neural Networks](https://mlsanity.com/paper/1906.11537/) (2019)
- [All You Need is a Good Functional Prior for Bayesian Deep Learning](https://mlsanity.com/paper/2011.12829/) (2020)
- [Credal Bayesian Deep Learning](https://mlsanity.com/paper/2302.09656/) (2023)
- [MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks](https://mlsanity.com/paper/2111.01564/) (2021)
- [Tractable Function-Space Variational Inference in Bayesian Neural Networks](https://mlsanity.com/paper/2312.17199/) (2023)
- [Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?](https://mlsanity.com/paper/2306.09586/) (2023)
- [Neuro-Symbolic AI in 2024: A Systematic Review](https://mlsanity.com/paper/2501.05435/) (2025)
- [Multi-Label Classification Neural Networks with Hard Logical Constraints](https://mlsanity.com/paper/2103.13427/) (2021)
- [ROAD-R: The Autonomous Driving Dataset with Logical Requirements](https://mlsanity.com/paper/2210.01597/) (2022)
- [Fast Predictive Uncertainty for Classification with Bayesian Deep Networks](https://mlsanity.com/paper/2003.01227/) (2020)
- [Credal Learning Theory](https://mlsanity.com/paper/2402.00957/) (2024)
- [Disentangling Epistemic and Aleatoric Uncertainty in Reinforcement Learning](https://mlsanity.com/paper/2206.01558/) (2022)

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

- [Credal Large Language Models for Semantic Commitment under Uncertainty](https://mlsanity.com/paper/2608.23244/) (2026)

## Abstract (arXiv)

Deep neural networks achieve high accuracy on image classification tasks. Yet, they often produce overconfident predictions as which fail to express epistemic uncertainty, and frequently violate logical or structural constraints present in the data. These limitations are particularly pronounced in hierarchical classification, where predictions across fine and coarse levels must remain coherent. We propose, for the first time, a unified neurosymbolic and epistemic modelling framework that augments Swin Transformers with focal set reasoning and differentiable fuzzy logic. Rather than treating labels as isolated categories, our method induces data-driven focal sets within the learnt embedding space, which helps capture epistemic uncertainty over multiple plausible fine-grained classes. These focal sets form the basis of a belief-theoretic layer that uses fuzzy membership functions and t-norm conjunctions to encourage consistency between fine- and coarse-grained predictions. A learnable loss further balances calibration, mass regularisation, and logical consistency, allowing the model to adaptively trade off symbolic structure with data-driven evidence. In experiments on hierarchical image classification, our framework maintains accuracy on par with transformer baselines while providing more calibrated and interpretable predictions, reducing overconfidence and enforcing high logical consistency across hierarchical outputs. Our experimental results show that combining focal set reasoning with fuzzy logic provides a practical step toward deep learning models that are both accurate and epistemically aware.