# Stochastic Amortization: A Unified Approach to Accelerate Feature and Data Attribution

arXiv: https://arxiv.org/abs/2401.15866 · HTML: https://mlsanity.com/paper/2401.15866/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 76 of its 112 references that are in the map.
- First posted on arXiv 29 Jan 2024.

## Builds on (most cited first, 30 of 76)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (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)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [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)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [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)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Quantifying Attention Flow in Transformers](https://mlsanity.com/paper/2005.00928/) (2020)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [Top-down Neural Attention by Excitation Backprop](https://mlsanity.com/paper/1608.00507/) (2016)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Understanding Deep Networks via Extremal Perturbations and Smooth Masks](https://mlsanity.com/paper/1910.08485/) (2019)
- [Learning to Explain: An Information-Theoretic Perspective on Model Interpretation](https://mlsanity.com/paper/1802.07814/) (2018)

## Built on by (most cited first, 21 of 21)

- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [Capturing the Temporal Dependence of Training Data Influence](https://mlsanity.com/paper/2412.09538/) (2024)
- [Learning to Attribute with Attention](https://mlsanity.com/paper/2504.13752/) (2025)
- [Enhancing Training Data Attribution with Representational Optimization](https://mlsanity.com/paper/2505.18513/) (2025)
- [SHAP zero Explains Biological Sequence Models with Near-zero Marginal Cost for Future Queries](https://mlsanity.com/paper/2410.19236/) (2024)
- [Birds look like cars: Adversarial analysis of intrinsically interpretable deep learning](https://mlsanity.com/paper/2503.08636/) (2025)
- [In-Run Data Shapley for Adam Optimizer](https://mlsanity.com/paper/2602.00329/) (2026)
- [Selective Explanations](https://mlsanity.com/paper/2405.19562/) (2024)
- [On-device Content-based Recommendation with Single-shot Embedding Pruning: A Cooperative Game Perspective](https://mlsanity.com/paper/2411.13052/) (2024)
- [MAnchors: Memorization-Based Acceleration of Anchors via Rule Reuse and Transformation](https://mlsanity.com/paper/2502.11068/) (2025)
- [Revitalizing Black-Box Interpretability: Actionable Interpretability for LLMs via Proxy Models](https://mlsanity.com/paper/2505.12509/) (2025)
- [Unifying and Optimizing Data Values for Selection via Sequential Decision-Making](https://mlsanity.com/paper/2502.04554/) (2025)
- [KAIROS: Scalable Model-Agnostic Data Valuation](https://mlsanity.com/paper/2506.23799/) (2025)
- [Approximating Shapley Explanations in Reinforcement Learning](https://mlsanity.com/paper/2511.06094/) (2025)
- [Optimizing Product Provenance Verification using Data Valuation Methods](https://mlsanity.com/paper/2502.15177/) (2025)
- [Learn to Rank: Visual Attribution by Learning Importance Ranking](https://mlsanity.com/paper/2604.05819/) (2026)
- [Real-Time Visual Attribution Streaming in Thinking Model](https://mlsanity.com/paper/2604.16587/) (2026)
- [Rethinking XAI Evaluation: A Human-Centered Audit of Shapley Benchmarks in High-Stakes Settings](https://mlsanity.com/paper/2604.22662/) (2026)
- [On the Fragility of Data Attribution When Learning Is Distributed](https://mlsanity.com/paper/2605.15520/) (2026)
- [Dynamic Shapley Computation](https://mlsanity.com/paper/2605.20620/) (2026)
- [Marginal Log-Likelihood Increments under Dirichlet-Smoothed Markov Estimation](https://mlsanity.com/paper/2609.25675/) (2026)

## Abstract (arXiv)

Many tasks in explainable machine learning, such as data valuation and feature attribution, perform expensive computation for each data point and are intractable for large datasets. These methods require efficient approximations, and although amortizing the process by learning a network to directly predict the desired output is a promising solution, training such models with exact labels is often infeasible. We therefore explore training amortized models with noisy labels, and we find that this is inexpensive and surprisingly effective. Through theoretical analysis of the label noise and experiments with various models and datasets, we show that this approach tolerates high noise levels and significantly accelerates several feature attribution and data valuation methods, often yielding an order of magnitude speedup over existing approaches.