# Data Attribution in Large Language Models via Bidirectional Gradient Optimization

arXiv: https://arxiv.org/abs/2606.04928 · HTML: https://mlsanity.com/paper/2606.04928/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [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)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [WIT: Wikipedia-based Image Text Dataset for Multimodal Multilingual Machine Learning](https://mlsanity.com/paper/2103.01913/) (2021)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Datamodels: Predicting Predictions from Training Data](https://mlsanity.com/paper/2202.00622/) (2022)
- [Simfluence: Modeling the Influence of Individual Training Examples by Simulating Training Runs](https://mlsanity.com/paper/2303.08114/) (2023)
- [Large Language Models for Disease Diagnosis: A Scoping Review](https://mlsanity.com/paper/2409.00097/) (2024)
- [Scalable Influence and Fact Tracing for Large Language Model Pretraining](https://mlsanity.com/paper/2410.17413/) (2024)
- [Theoretical and Practical Perspectives on what Influence Functions Do](https://mlsanity.com/paper/2305.16971/) (2023)
- [Repairing Neural Networks by Leaving the Right Past Behind](https://mlsanity.com/paper/2207.04806/) (2022)
- [Data Attribution for Text-to-Image Models by Unlearning Synthesized Images](https://mlsanity.com/paper/2406.09408/) (2024)
- [Unlearning Traces the Influential Training Data of Language Models](https://mlsanity.com/paper/2401.15241/) (2024)
- [The Mirrored Influence Hypothesis: Efficient Data Influence Estimation by Harnessing Forward Passes](https://mlsanity.com/paper/2402.08922/) (2024)
- [Large-Scale Training Data Attribution for Music Generative Models via Unlearning](https://mlsanity.com/paper/2506.18312/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) are increasingly deployed across diverse applications, raising critical questions for governance, accountability, and data provenance. Understanding which training data most influenced a model's output remains a fundamental open problem. We address this challenge through training data attribution (TDA) for auto-regressive LLMs by expanding upon the inverse formulation: How would training data be affected if the model had seen the generated output during training? Our method perturbs the base model using bidirectional gradient optimization (gradient ascent and descent) on a generated text sample and measures the resulting change in loss across training samples. Our framework supports attribution at arbitrary data granularity, enabling both factual and stylistic attribution. We evaluate our method against baselines on pretrained models with known datasets, and show that it outperforms previous work on influence metrics, thereby enhancing model interpretability, an essential requirement for accountable AI systems.