# Towards Learning and Explaining Indirect Causal Effects in Neural Networks

arXiv: https://arxiv.org/abs/2303.13850 · HTML: https://mlsanity.com/paper/2303.13850/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 58 references that are in the map.
- First posted on arXiv 24 Mar 2023.

## Builds on (most cited first, 30 of 45)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [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)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Counterfactual Visual Explanations](https://mlsanity.com/paper/1904.07451/) (2019)
- [Right for the Right Reasons: Training Differentiable Models by Constraining their Explanations](https://mlsanity.com/paper/1703.03717/) (2017)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Explaining NonLinear Classification Decisions with Deep Taylor Decomposition](https://mlsanity.com/paper/1512.02479/) (2015)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Recurrent Independent Mechanisms](https://mlsanity.com/paper/1909.10893/) (2019)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [Grad-CAM: Why did you say that?](https://mlsanity.com/paper/1611.07450/) (2016)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Interpretations are useful: penalizing explanations to align neural networks with prior knowledge](https://mlsanity.com/paper/1909.13584/) (2019)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Explaining Classifiers with Causal Concept Effect (CaCE)](https://mlsanity.com/paper/1907.07165/) (2019)
- [Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models](https://mlsanity.com/paper/2011.01625/) (2020)
- [Learning Independent Causal Mechanisms](https://mlsanity.com/paper/1712.00961/) (2017)
- [CXPlain: Causal Explanations for Model Interpretation under Uncertainty](https://mlsanity.com/paper/1910.12336/) (2019)

## Built on by (most cited first, 2 of 2)

- [Concept-Based Abductive and Contrastive Explanations for Behaviors of Vision Models](https://mlsanity.com/paper/2605.06640/) (2026)
- [On Measuring Intrinsic Causal Attributions in Deep Neural Networks](https://mlsanity.com/paper/2505.09660/) (2025)

## Abstract (arXiv)

Recently, there has been a growing interest in learning and explaining causal effects within Neural Network (NN) models. By virtue of NN architectures, previous approaches consider only direct and total causal effects assuming independence among input variables. We view an NN as a structural causal model (SCM) and extend our focus to include indirect causal effects by introducing feedforward connections among input neurons. We propose an ante-hoc method that captures and maintains direct, indirect, and total causal effects during NN model training. We also propose an algorithm for quantifying learned causal effects in an NN model and efficient approximation strategies for quantifying causal effects in high-dimensional data. Extensive experiments conducted on synthetic and real-world datasets demonstrate that the causal effects learned by our ante-hoc method better approximate the ground truth effects compared to existing methods.