# From Reweighting to Rewriting: Unlocking the Intervention Effects of Influential Samples in Training Data Attribution

arXiv: https://arxiv.org/abs/2609.02771 · HTML: https://mlsanity.com/paper/2609.02771/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 45 references that are in the map.
- First posted on arXiv 2 Sep 2026.

## Builds on (most cited first, 30 of 41)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusal](https://mlsanity.com/paper/2402.04249/) (2024)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [BBQ: A Hand-Built Bias Benchmark for Question Answering](https://mlsanity.com/paper/2110.08193/) (2021)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [The WMDP Benchmark: Measuring and Reducing Malicious Use With Unlearning](https://mlsanity.com/paper/2403.03218/) (2024)
- [XSTest: A Test Suite for Identifying Exaggerated Safety Behaviours in Large Language Models](https://mlsanity.com/paper/2308.01263/) (2023)
- [WildGuard: Open One-Stop Moderation Tools for Safety Risks, Jailbreaks, and Refusals of LLMs](https://mlsanity.com/paper/2406.18495/) (2024)
- ["Do Anything Now": Characterizing and Evaluating In-The-Wild Jailbreak Prompts on Large Language Models](https://mlsanity.com/paper/2308.03825/) (2023)
- [ToxiGen: A Large-Scale Machine-Generated Dataset for Adversarial and Implicit Hate Speech Detection](https://mlsanity.com/paper/2203.09509/) (2022)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Do Large Language Models Know What They Don't Know?](https://mlsanity.com/paper/2305.18153/) (2023)
- [WildTeaming at Scale: From In-the-Wild Jailbreaks to (Adversarially) Safer Language Models](https://mlsanity.com/paper/2406.18510/) (2024)
- [Don't Hallucinate, Abstain: Identifying LLM Knowledge Gaps via Multi-LLM Collaboration](https://mlsanity.com/paper/2402.00367/) (2024)
- [Fast Approximate Natural Gradient Descent in a Kronecker-factored Eigenbasis](https://mlsanity.com/paper/1806.03884/) (2018)
- [AbstentionBench: Reasoning LLMs Fail on Unanswerable Questions](https://mlsanity.com/paper/2506.09038/) (2025)
- [If Influence Functions are the Answer, Then What is the Question?](https://mlsanity.com/paper/2209.05364/) (2022)
- [Know Your Limits: A Survey of Abstention in Large Language Models](https://mlsanity.com/paper/2407.18418/) (2024)
- [FastIF: Scalable Influence Functions for Efficient Model Interpretation and Debugging](https://mlsanity.com/paper/2012.15781/) (2020)
- [R-Tuning: Instructing Large Language Models to Say `I Don't Know'](https://mlsanity.com/paper/2311.09677/) (2023)
- [The Art of Saying No: Contextual Noncompliance in Language Models](https://mlsanity.com/paper/2407.12043/) (2024)
- [Alignment for Honesty](https://mlsanity.com/paper/2312.07000/) (2023)
- [Knowledge of Knowledge: Exploring Known-Unknowns Uncertainty with Large Language Models](https://mlsanity.com/paper/2305.13712/) (2023)
- [Uncertainty-Based Abstention in LLMs Improves Safety and Reduces Hallucinations](https://mlsanity.com/paper/2404.10960/) (2024)

## Abstract (arXiv)

Training data attribution (TDA) aims to identify training examples that shape model behavior, but its intervention value depends on both which examples are selected and how they are modified. Influence functions (IF) estimate behavioral changes under infinitesimal reweighting, yet IF-selected examples often show limited advantages over random selection under conventional weight-based interventions. This raises the question of whether influential examples lack intervention value or whether reweighting fails to realize their behavioral leverage.We introduce influence-guided response rewriting, which uses IF to identify intervention targets and replaces their responses with behavior-aligned or behavior-opposed supervision while keeping instructions fixed. Across four open-weight LLMs, we compare rewriting and reweighting on the same influence-selected examples using epistemic abstention as our primary testbed. Response rewriting produces stronger, more persistent, and bidirectional behavioral shifts, while reweighting the same examples yields weak and inconsistent effects. Further analyses show that influence-selected examples provide greater rewriting leverage than alternative selectors, with changes remaining concentrated on target-relevant behaviors. The same qualitative contrast extends to safety refusal. These results distinguish the local reweighting effects captured by influence estimates from the broader intervention leverage of the examples they identify, motivating intervention-aware evaluation of TDA methods.