# Enabling Verification of Deep Neural Networks in Perception Tasks Using Fuzzy Logic and Concept Embeddings

arXiv: https://arxiv.org/abs/2201.00572 · HTML: https://mlsanity.com/paper/2201.00572/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 49 references that are in the map.
- First posted on arXiv 3 Jan 2022.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [EfficientDet: Scalable and Efficient Object Detection](https://mlsanity.com/paper/1911.09070/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Deep Learning for Generic Object Detection: A Survey](https://mlsanity.com/paper/1809.02165/) (2018)
- [Unmasking Clever Hans Predictors and Assessing What Machines Really Learn](https://mlsanity.com/paper/1902.10178/) (2019)
- [Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks](https://mlsanity.com/paper/2002.10118/) (2020)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Net2Vec: Quantifying and Explaining how Concepts are Encoded by Filters in Deep Neural Networks](https://mlsanity.com/paper/1801.03454/) (2018)
- [Improving model calibration with accuracy versus uncertainty optimization](https://mlsanity.com/paper/2012.07923/) (2020)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [Prediction Error Meta Classification in Semantic Segmentation: Detection via Aggregated Dispersion Measures of Softmax Probabilities](https://mlsanity.com/paper/1811.00648/) (2018)
- [Is Disentanglement all you need? Comparing Concept-based & Disentanglement Approaches](https://mlsanity.com/paper/2104.06917/) (2021)
- [Towards Dependability Metrics for Neural Networks](https://mlsanity.com/paper/1806.02338/) (2018)
- [Expressive Explanations of DNNs by Combining Concept Analysis with ILP](https://mlsanity.com/paper/2105.07371/) (2021)
- [Verification of Size Invariance in DNN Activations using Concept Embeddings](https://mlsanity.com/paper/2105.06727/) (2021)
- [CHAIN: Concept-harmonized Hierarchical Inference Interpretation of Deep Convolutional Neural Networks](https://mlsanity.com/paper/2002.01660/) (2020)

## Built on by (most cited first, 7 of 7)

- [Concept-Based Explanations in Computer Vision: Where Are We and Where Could We Go?](https://mlsanity.com/paper/2409.13456/) (2024)
- [Local Concept Embeddings for Analysis of Concept Distributions in Vision DNN Feature Spaces](https://mlsanity.com/paper/2311.14435/) (2023)
- [Investigating Calibration and Corruption Robustness of Post-hoc Pruned Perception CNNs: An Image Classification Benchmark Study](https://mlsanity.com/paper/2405.20876/) (2024)
- [Revealing Similar Semantics Inside CNNs: An Interpretable Concept-based Comparison of Feature Spaces](https://mlsanity.com/paper/2305.07663/) (2023)
- [Unveiling Ontological Commitment in Multi-Modal Foundation Models](https://mlsanity.com/paper/2409.17109/) (2024)
- [On Background Bias of Post-Hoc Concept Embeddings in Computer Vision DNNs](https://mlsanity.com/paper/2504.08602/) (2025)
- [Attack logics, not outputs: Towards efficient robustification of deep neural networks by falsifying concept-based properties](https://mlsanity.com/paper/2510.03320/) (2025)

## Abstract (arXiv)

One major drawback of deep convolutional neural networks (CNNs) for use in safety critical applications is their black-box nature. This makes it hard to verify or monitor complex, symbolic requirements on already trained computer vision CNNs. In this work, we present a simple, yet effective, approach to verify that a CNN complies with symbolic predicate logic rules which relate visual concepts. It is the first that (1) does not modify the CNN, (2) may use visual concepts that are no CNN in- or output feature, and (3) can leverage continuous CNN confidence outputs. To achieve this, we newly combine methods from explainable artificial intelligence and logic: First, using supervised concept embedding analysis, the output of a CNN is post-hoc enriched by concept outputs. Second, rules from prior knowledge are modelled as truth functions that accept the CNN outputs, and can be evaluated with little computational overhead. We here investigate the use of fuzzy logic, i.e., continuous truth values, and of proper output calibration, which both theoretically and practically show slight benefits. Applicability is demonstrated on state-of-the-art object detectors for three verification use-cases, where monitoring of rule breaches can reveal detection errors.