# Layer-Aware Influence for Online Data Valuation Estimation

arXiv: https://arxiv.org/abs/2510.16007 · HTML: https://mlsanity.com/paper/2510.16007/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 60 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [How Does Batch Normalization Help Optimization?](https://mlsanity.com/paper/1805.11604/) (2018)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [On The Power of Curriculum Learning in Training Deep Networks](https://mlsanity.com/paper/1904.03626/) (2019)
- [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)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [Curriculum Learning: A Survey](https://mlsanity.com/paper/2101.10382/) (2021)
- [Learning with Noisy Labels Revisited: A Study Using Real-World Human Annotations](https://mlsanity.com/paper/2110.12088/) (2021)
- [Prioritized Training on Points that are Learnable, Worth Learning, and Not Yet Learnt](https://mlsanity.com/paper/2206.07137/) (2022)
- [Competence-based Curriculum Learning for Neural Machine Translation](https://mlsanity.com/paper/1903.09848/) (2019)
- [Reverse Curriculum Generation for Reinforcement Learning](https://mlsanity.com/paper/1707.05300/) (2017)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms](https://mlsanity.com/paper/1908.08619/) (2019)
- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [Scaling Up Influence Functions](https://mlsanity.com/paper/2112.03052/) (2021)
- [CurriculumNet: Weakly Supervised Learning from Large-Scale Web Images](https://mlsanity.com/paper/1808.01097/) (2018)
- [DataInf: Efficiently Estimating Data Influence in LoRA-tuned LLMs and Diffusion Models](https://mlsanity.com/paper/2310.00902/) (2023)
- [Learning to Execute](https://mlsanity.com/paper/1410.4615/) (2014)
- [InfoBatch: Lossless Training Speed Up by Unbiased Dynamic Data Pruning](https://mlsanity.com/paper/2303.04947/) (2023)
- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [Input Similarity from the Neural Network Perspective](https://mlsanity.com/paper/2102.05262/) (2021)

## Built on by (most cited first, 2 of 2)

- [From Detrimental to Beneficial: Dynamic Influence-based Valuation and Editing](https://mlsanity.com/paper/2608.22522/) (2026)
- [Not All Rollouts Are Worth Learning: On Trajectory Valuation for Post-Training Reinforcement Learning](https://mlsanity.com/paper/2609.35072/) (2026)

## Abstract (arXiv)

Data-centric learning emphasizes curating high-quality training samples to boost performance rather than designing new architectures. A central problem is to estimate the influence of training sample efficiently. Prior studies largely focus on static influence measured on a converged model, overlooking how data valuation dynamically changes during optimization. This omission neglects the dynamic nature of sample influence during optimization, especially in deep models. To address the computational burden of frequent influence estimation, we develop a layer-aware online estimator that requires only loss-to-output gradients. This design avoids parameter-level and full-network gradients while preserving ranking fidelity. Extensive experiments across LLM pretraining, fine-tuning, and image classification show our method improves accuracy with substantially lower time and memory cost, making dynamic data curation efficient and scalable in practice.