# Improving performance of deep learning models with axiomatic attribution priors and expected gradients

arXiv: https://arxiv.org/abs/1906.10670 · HTML: https://mlsanity.com/paper/1906.10670/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2019.

## Built on by (most cited first, 30 of 32)

- [Benchmarking and Survey of Explanation Methods for Black Box Models](https://mlsanity.com/paper/2102.13076/) (2021)
- [Post hoc Explanations may be Ineffective for Detecting Unknown Spurious Correlation](https://mlsanity.com/paper/2212.04629/) (2022)
- [A Comprehensive Study of Image Classification Model Sensitivity to Foregrounds, Backgrounds, and Visual Attributes](https://mlsanity.com/paper/2201.10766/) (2022)
- [Shapley Explanation Networks](https://mlsanity.com/paper/2104.02297/) (2021)
- [Going Beyond XAI: A Systematic Survey for Explanation-Guided Learning](https://mlsanity.com/paper/2212.03954/) (2022)
- [Towards Robust Classification Model by Counterfactual and Invariant Data Generation](https://mlsanity.com/paper/2106.01127/) (2021)
- [Refining Language Models with Compositional Explanations](https://mlsanity.com/paper/2103.10415/) (2021)
- [Temporal Dependencies in Feature Importance for Time Series Predictions](https://mlsanity.com/paper/2107.14317/) (2021)
- [Show or Suppress? Managing Input Uncertainty in Machine Learning Model Explanations](https://mlsanity.com/paper/2101.09498/) (2021)
- [Towards Rigorous Interpretations: a Formalisation of Feature Attribution](https://mlsanity.com/paper/2104.12437/) (2021)
- [Understanding and Unifying Fourteen Attribution Methods with Taylor Interactions](https://mlsanity.com/paper/2303.01506/) (2023)
- [Efficient Explanations from Empirical Explainers](https://mlsanity.com/paper/2103.15429/) (2021)
- [Improving Interpretability via Explicit Word Interaction Graph Layer](https://mlsanity.com/paper/2302.02016/) (2023)
- [On the Robustness of Explanations of Deep Neural Network Models: A Survey](https://mlsanity.com/paper/2211.04780/) (2022)
- [Interpretable Network Visualizations: A Human-in-the-Loop Approach for Post-hoc Explainability of CNN-based Image Classification](https://mlsanity.com/paper/2405.03301/) (2024)
- [SampleLLM: Optimizing Tabular Data Synthesis in Recommendations](https://mlsanity.com/paper/2501.16125/) (2025)
- [Comparing Baseline Shapley and Integrated Gradients for Local Explanation: Some Additional Insights](https://mlsanity.com/paper/2208.06096/) (2022)
- [Explanation Space: A New Perspective into Time Series Interpretability](https://mlsanity.com/paper/2409.01354/) (2024)
- [Right for the Right Latent Factors: Debiasing Generative Models via Disentanglement](https://mlsanity.com/paper/2202.00391/) (2022)
- [Improving Explainability of Disentangled Representations using Multipath-Attribution Mappings](https://mlsanity.com/paper/2306.09035/) (2023)
- [XRL-Bench: A Benchmark for Evaluating and Comparing Explainable Reinforcement Learning Techniques](https://mlsanity.com/paper/2402.12685/) (2024)
- [Attribution Explanations for Deep Neural Networks: A Theoretical Perspective](https://mlsanity.com/paper/2508.07636/) (2025)
- [Interpreting and improving deep-learning models with reality checks](https://mlsanity.com/paper/2108.06847/) (2021)
- [Interpreting Time Series Transformer Models and Sensitivity Analysis of Population Age Groups to COVID-19 Infections](https://mlsanity.com/paper/2401.15119/) (2024)
- [Tell me why: Training preferences-based RL with human preferences and step-level explanations](https://mlsanity.com/paper/2405.14244/) (2024)
- [EXCODER: EXplainable Classification Of DiscretE time series Representations](https://mlsanity.com/paper/2602.13087/) (2026)
- [UniTAC: Universal Task-Aware Compression via Weighted Distortion Measures](https://mlsanity.com/paper/2608.16696/) (2026)
- [A General Taylor Framework for Unifying and Revisiting Attribution Methods](https://mlsanity.com/paper/2105.13841/) (2021)
- [A model-agnostic approach for generating Saliency Maps to explain inferred decisions of Deep Learning Models](https://mlsanity.com/paper/2209.08906/) (2022)
- [WinTSR: A Windowed Temporal Saliency Rescaling Method for Interpreting Time Series Deep Learning Models](https://mlsanity.com/paper/2412.04532/) (2024)

## Abstract (arXiv)

Recent research has demonstrated that feature attribution methods for deep networks can themselves be incorporated into training; these attribution priors optimize for a model whose attributions have certain desirable properties -- most frequently, that particular features are important or unimportant. These attribution priors are often based on attribution methods that are not guaranteed to satisfy desirable interpretability axioms, such as completeness and implementation invariance. Here, we introduce attribution priors to optimize for higher-level properties of explanations, such as smoothness and sparsity, enabled by a fast new attribution method formulation called expected gradients that satisfies many important interpretability axioms. This improves model performance on many real-world tasks where previous attribution priors fail. Our experiments show that the gains from combining higher-level attribution priors with expected gradients attributions are consistent across image, gene expression, and health care data sets. We believe this work motivates and provides the necessary tools to support the widespread adoption of axiomatic attribution priors in many areas of applied machine learning. The implementations and our results have been made freely available to academic communities.