# Binary Spiking Neural Networks as Causal Models

arXiv: https://arxiv.org/abs/2604.27007 · HTML: https://mlsanity.com/paper/2604.27007/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 44 references that are in the map.
- First posted on arXiv 29 Apr 2026.

## Builds on (most cited first, 26 of 26)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Binary Neural Networks: A Survey](https://mlsanity.com/paper/2004.03333/) (2020)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [A Symbolic Approach to Explaining Bayesian Network Classifiers](https://mlsanity.com/paper/1805.03364/) (2018)
- [On The Reasons Behind Decisions](https://mlsanity.com/paper/2002.09284/) (2020)
- [Contrastive Explanation: A Structural-Model Approach](https://mlsanity.com/paper/1811.03163/) (2018)
- [Explaining Naive Bayes and Other Linear Classifiers with Polynomial Time and Delay](https://mlsanity.com/paper/2008.05803/) (2020)
- [On Explaining Random Forests with SAT](https://mlsanity.com/paper/2105.10278/) (2021)
- [SpikingBERT: Distilling BERT to Train Spiking Language Models Using Implicit Differentiation](https://mlsanity.com/paper/2308.10873/) (2023)
- [Interpreting Neural Networks as Gradual Argumentation Frameworks (Including Proof Appendix)](https://mlsanity.com/paper/2012.05738/) (2020)
- [Exploring the Connection Between Binary and Spiking Neural Networks](https://mlsanity.com/paper/2002.10064/) (2020)
- [On Tractable Representations of Binary Neural Networks](https://mlsanity.com/paper/2004.02082/) (2020)
- [BS4NN: Binarized Spiking Neural Networks with Temporal Coding and Learning](https://mlsanity.com/paper/2007.04039/) (2020)
- [SpArX: Sparse Argumentative Explanations for Neural Networks [Technical Report]](https://mlsanity.com/paper/2301.09559/) (2023)
- [A unified logical framework for explanations in classifier systems](https://mlsanity.com/paper/2105.14452/) (2021)
- [The Computational Complexity of Structure-Based Causality](https://mlsanity.com/paper/1412.3076/) (2014)
- [ReStoCNet: Residual Stochastic Binary Convolutional Spiking Neural Network for Memory-Efficient Neuromorphic Computing](https://mlsanity.com/paper/1902.04161/) (2019)
- [The Counterfactual NESS Definition of Causation](https://mlsanity.com/paper/2012.05123/) (2020)
- [BiSNN: Training Spiking Neural Networks with Binary Weights via Bayesian Learning](https://mlsanity.com/paper/2012.08300/) (2020)
- [From SHAP Scores to Feature Importance Scores](https://mlsanity.com/paper/2405.11766/) (2024)
- [A Refutation of Shapley Values for Explainability](https://mlsanity.com/paper/2309.03041/) (2023)
- [Refutation of Shapley Values for XAI -- Additional Evidence](https://mlsanity.com/paper/2310.00416/) (2023)
- [Relevant Irrelevance: Generating Alterfactual Explanations for Image Classifiers](https://mlsanity.com/paper/2405.05295/) (2024)

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

- [The Neural Division of Labor: Biologically-Inspired Modular Architectures for Robust Neuromorphic Computing](https://mlsanity.com/paper/2608.08317/) (2026)

## Abstract (arXiv)

We provide a causal analysis of Binary Spiking Neural Networks (BSNNs) to explain their behavior. We formally define a BSNN and represent its spiking activity as a binary causal model. Thanks to this causal representation, we are able to explain the output of the network by leveraging logic-based methods. In particular, we show that we can successfully use a SAT as well as a SMT solver to compute abductive explanations from this binary causal model. To illustrate our approach, we trained the BSNN on the standard MNIST dataset and applied our SAT-based and SMT-based methods to finding abductive explanations of the network's classifications based on pixel-level features. We also compared the found explanations against SHAP, a popular method used in the area of explainable AI. We show that, unlike SHAP, our approach guarantees that a found explanation does not contain completely irrelevant features.