# Training Data Attribution via Approximate Unrolled Differentiation

arXiv: https://arxiv.org/abs/2405.12186 · HTML: https://mlsanity.com/paper/2405.12186/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 94 references that are in the map.
- First posted on arXiv 20 May 2024.

## Builds on (most cited first, 30 of 59)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [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)
- [Domain Generalization for Object Recognition with Multi-task Autoencoders](https://mlsanity.com/paper/1508.07680/) (2015)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Datamodels: Predicting Predictions from Training Data](https://mlsanity.com/paper/2202.00622/) (2022)
- [Representer Point Selection for Explaining Deep Neural Networks](https://mlsanity.com/paper/1811.09720/) (2018)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Counterfactual Memorization in Neural Language Models](https://mlsanity.com/paper/2112.12938/) (2021)
- [Fast Approximate Natural Gradient Descent in a Kronecker-factored Eigenbasis](https://mlsanity.com/paper/1806.03884/) (2018)

## Built on by (most cited first, 30 of 34)

- [Procedural Knowledge in Pretraining Drives Reasoning in Large Language Models](https://mlsanity.com/paper/2411.12580/) (2024)
- [Capturing the Temporal Dependence of Training Data Influence](https://mlsanity.com/paper/2412.09538/) (2024)
- [Influence Functions for Scalable Data Attribution in Diffusion Models](https://mlsanity.com/paper/2410.13850/) (2024)
- [Most Influential Subset Selection: Challenges, Promises, and Beyond](https://mlsanity.com/paper/2409.18153/) (2024)
- [Unleashing the Power of Data Tsunami: A Comprehensive Survey on Data Assessment and Selection for Instruction Tuning of Language Models](https://mlsanity.com/paper/2408.02085/) (2024)
- [DataMIL: Selecting Data for Robot Imitation Learning with Datamodels](https://mlsanity.com/paper/2505.09603/) (2025)
- [MAGIC: Near-Optimal Data Attribution for Deep Learning](https://mlsanity.com/paper/2504.16430/) (2025)
- [Attribute-to-Delete: Machine Unlearning via Datamodel Matching](https://mlsanity.com/paper/2410.23232/) (2024)
- [LayerIF: Estimating Layer Quality for Large Language Models using Influence Functions](https://mlsanity.com/paper/2505.23811/) (2025)
- [Better Training Data Attribution via Better Inverse Hessian-Vector Products](https://mlsanity.com/paper/2507.14740/) (2025)
- [JacNet: Learning Functions with Structured Jacobians](https://mlsanity.com/paper/2408.13237/) (2024)
- [Score Distillation Sampling for Audio: Source Separation, Synthesis, and Beyond](https://mlsanity.com/paper/2505.04621/) (2025)
- [Infusion: Shaping Model Behavior by Editing Training Data via Influence Functions](https://mlsanity.com/paper/2602.09987/) (2026)
- [Efficient Multi-Agent System Training with Data Influence-Oriented Tree Search](https://mlsanity.com/paper/2502.00955/) (2025)
- [Towards User-Focused Research in Training Data Attribution for Human-Centered Explainable AI](https://mlsanity.com/paper/2409.16978/) (2024)
- [Unraveling Indirect In-Context Learning Using Influence Functions](https://mlsanity.com/paper/2501.01473/) (2025)
- [Distributional Training Data Attribution: What do Influence Functions Sample?](https://mlsanity.com/paper/2506.12965/) (2025)
- [Better Hessians Matter: Studying the Impact of Curvature Approximations in Influence Functions](https://mlsanity.com/paper/2509.23437/) (2025)
- [Train on Validation (ToV): Fast data selection with applications to fine-tuning](https://mlsanity.com/paper/2510.00386/) (2025)
- [Z0-Inf: Zeroth Order Approximation for Data Influence](https://mlsanity.com/paper/2510.11832/) (2025)
- [In-Run Data Shapley for Adam Optimizer](https://mlsanity.com/paper/2602.00329/) (2026)
- [Bergson: An Open Source Library for Data Attribution](https://mlsanity.com/paper/2606.11660/) (2026)
- [Quanda: An Interpretability Toolkit for Training Data Attribution Evaluation and Beyond](https://mlsanity.com/paper/2410.07158/) (2024)
- [Layer-Aware Influence for Online Data Valuation Estimation](https://mlsanity.com/paper/2510.16007/) (2025)
- [Variance Reduction for Expectations with Diffusion Teachers](https://mlsanity.com/paper/2605.21489/) (2026)
- [Small-to-Large Generalization: Data Influences Models Consistently Across Scale](https://mlsanity.com/paper/2505.16260/) (2025)
- [Daunce: Data Attribution through Uncertainty Estimation](https://mlsanity.com/paper/2505.23223/) (2025)
- [A Bayesian Information-Theoretic Approach to Data Attribution](https://mlsanity.com/paper/2604.03858/) (2026)
- [What's a Credit Worth? A Market Framework for Attribution-Aware Compensation in Generative Music](https://mlsanity.com/paper/2607.00641/) (2026)
- [Scalable Multi-Stage Influence Function for Large Language Models via Eigenvalue-Corrected Kronecker-Factored Parameterization](https://mlsanity.com/paper/2505.05017/) (2025)

## Abstract (arXiv)

Many training data attribution (TDA) methods aim to estimate how a model's behavior would change if one or more data points were removed from the training set. Methods based on implicit differentiation, such as influence functions, can be made computationally efficient, but fail to account for underspecification, the implicit bias of the optimization algorithm, or multi-stage training pipelines. By contrast, methods based on unrolling address these issues but face scalability challenges. In this work, we connect the implicit-differentiation-based and unrolling-based approaches and combine their benefits by introducing Source, an approximate unrolling-based TDA method that is computed using an influence-function-like formula. While being computationally efficient compared to unrolling-based approaches, Source is suitable in cases where implicit-differentiation-based approaches struggle, such as in non-converged models and multi-stage training pipelines. Empirically, Source outperforms existing TDA techniques in counterfactual prediction, especially in settings where implicit-differentiation-based approaches fall short.