# Scalable Attribution and Control of Model Behavior During Training

arXiv: https://arxiv.org/abs/2609.33667 · HTML: https://mlsanity.com/paper/2609.33667/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 24 references that are in the map.
- First posted on arXiv 27 Sep 2026.

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

- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [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)
- [8-bit Optimizers via Block-wise Quantization](https://mlsanity.com/paper/2110.02861/) (2021)
- [Persona Vectors: Monitoring and Controlling Character Traits in Language Models](https://mlsanity.com/paper/2507.21509/) (2025)
- [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)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [Scalable Influence and Fact Tracing for Large Language Model Pretraining](https://mlsanity.com/paper/2410.17413/) (2024)
- [MAGIC: Near-Optimal Data Attribution for Deep Learning](https://mlsanity.com/paper/2504.16430/) (2025)
- [Correcting Large Language Model Behavior via Influence Function](https://mlsanity.com/paper/2412.16451/) (2024)
- [Concept Influence: Leveraging Interpretability to Improve Performance and Efficiency in Training Data Attribution](https://mlsanity.com/paper/2602.14869/) (2026)
- [DATE-LM: Benchmarking Data Attribution Evaluation for Large Language Models](https://mlsanity.com/paper/2507.09424/) (2025)
- [How Faithful Is Trajectory-Based Data Attribution? Error Sources, Remedies, and Practical Guidelines](https://mlsanity.com/paper/2605.18814/) (2026)
- [In-Run Data Shapley for Adam Optimizer](https://mlsanity.com/paper/2602.00329/) (2026)
- [A Bayesian Information-Theoretic Approach to Data Attribution](https://mlsanity.com/paper/2604.03858/) (2026)

## Abstract (arXiv)

Attributing and controlling model behavior during training requires identifying each example's contribution quickly enough to act before the next update. However, examples in the same training batch can produce similar behavioral changes, making their individual contributions difficult to distinguish. We address this ambiguity through mutual information, accounting for interference within the batch by quantifying how much the combined behavioral change reveals about each example's contribution. We show that this mutual information is a logarithmic function of Behavioral Gradient Uniqueness (BGU). BGU gives the information measure its geometric interpretation. Our Batch-Space Ghost (BS-Ghost) algorithm makes these scores practical inside the training loop through shared computation in batch space, without storing model-sized example gradients. On a complete 1,000-example Qwen2.5-7B-Instruct workload, our BS-Ghost implementation adds 27 seconds (8.0%) to 5.5 minutes of ordinary training. Removal and retraining demonstrate that BGU identifies data that causally shapes final behavior. At each training step, signed information identifies which examples strengthen or weaken the target behavior, explaining how behavior develops during training. Signed information also enables cheap intervention during training: it predicts how changing example weights will affect behavior in the next update. We then use these predictions to choose weights that steer behavior toward a desired target. This makes our framework a practical foundation for scalable oversight and verification of training pipelines and processes, helping evaluators assess model alignment, understand how it develops during training, and guide interventions that shape ongoing learning.