# Neuron Activation-based Computation of Logical Explanations for Deep Neural Networks

arXiv: https://arxiv.org/abs/2609.14099 · HTML: https://mlsanity.com/paper/2609.14099/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 53 references that are in the map.
- First posted on arXiv 12 Sep 2026.

## Builds on (most cited first, 18 of 18)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Understanding Deep Image Representations by Inverting Them](https://mlsanity.com/paper/1412.0035/) (2014)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [Torchattacks: A PyTorch Repository for Adversarial Attacks](https://mlsanity.com/paper/2010.01950/) (2020)
- [A Symbolic Approach to Explaining Bayesian Network Classifiers](https://mlsanity.com/paper/1805.03364/) (2018)
- [On Guaranteed Optimal Robust Explanations for NLP Models](https://mlsanity.com/paper/2105.03640/) (2021)
- [Logic-Based Explainability in Machine Learning](https://mlsanity.com/paper/2211.00541/) (2022)
- [Towards Verified Artificial Intelligence](https://mlsanity.com/paper/1606.08514/) (2016)
- [VeriX: Towards Verified Explainability of Deep Neural Networks](https://mlsanity.com/paper/2212.01051/) (2022)
- [Delivering Inflated Explanations](https://mlsanity.com/paper/2306.15272/) (2023)
- [Explaining, Fast and Slow: Abstraction and Refinement of Provable Explanations](https://mlsanity.com/paper/2506.08505/) (2025)
- [Space Explanations of Neural Network Classification](https://mlsanity.com/paper/2511.22498/) (2025)
- [Efficiently Computing Compact Formal Explanations](https://mlsanity.com/paper/2409.03060/) (2024)

## Abstract (arXiv)

Formal explainability of classifying neural networks (NNs) is an active area of research, providing explanations with provable guarantees of the classification within continuous regions of the input feature space. However, the existing techniques are either limited to individual input features without guarantees on their relations or the provided solutions fail to scale to deep architectures. This paper addresses these issues by introducing a flexible symbolic framework for an efficient, guided computation of explanations of the NN behavior, parametrized by the activations of internal neurons, and using logical engines such as SMT solvers. Unlike prior methods that rely on specialized NN verifiers, our method yields explanations that are not restricted in shape. Our algorithm is implementable on top of a general-purpose logical solver, isolating the NN-specific encoding from the algorithmic framework. We experimented with a wide range of benchmarks from the domains of image recognition and medicine, illustrating the advantages of the new method, particularly in computational efficiency. Notably, our approach enables logical explanation of deep networks not amenable to prior logic-based methods.