Understanding Data Influence with Differential Approximation

• URL: http://arxiv.org/abs/2508.14648v1
• Date: Wed, 20 Aug 2025 11:59:32 GMT
• Title: Understanding Data Influence with Differential Approximation
• Authors: Haoru Tan, Sitong Wu, Xiuzhe Wu, Wang Wang, Bo Zhao, Zeke Xie, Gui-Song Xia, Xiaojuan Qi,
• Abstract summary: We introduce a new formulation to approximate a sample's influence by accumulating the differences in influence between consecutive learning steps, which we term Diff-In.<n>By employing second-order approximations, we approximate these difference terms with high accuracy while eliminating the need for model convexity required by existing methods.<n>Our theoretical analysis demonstrates that Diff-In achieves significantly lower approximation error compared to existing influence estimators.
• Score: 63.817689230826595
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Data plays a pivotal role in the groundbreaking advancements in artificial intelligence. The quantitative analysis of data significantly contributes to model training, enhancing both the efficiency and quality of data utilization. However, existing data analysis tools often lag in accuracy. For instance, many of these tools even assume that the loss function of neural networks is convex. These limitations make it challenging to implement current methods effectively. In this paper, we introduce a new formulation to approximate a sample's influence by accumulating the differences in influence between consecutive learning steps, which we term Diff-In. Specifically, we formulate the sample-wise influence as the cumulative sum of its changes/differences across successive training iterations. By employing second-order approximations, we approximate these difference terms with high accuracy while eliminating the need for model convexity required by existing methods. Despite being a second-order method, Diff-In maintains computational complexity comparable to that of first-order methods and remains scalable. This efficiency is achieved by computing the product of the Hessian and gradient, which can be efficiently approximated using finite differences of first-order gradients. We assess the approximation accuracy of Diff-In both theoretically and empirically. Our theoretical analysis demonstrates that Diff-In achieves significantly lower approximation error compared to existing influence estimators. Extensive experiments further confirm its superior performance across multiple benchmark datasets in three data-centric tasks: data cleaning, data deletion, and coreset selection. Notably, our experiments on data pruning for large-scale vision-language pre-training show that Diff-In can scale to millions of data points and outperforms strong baselines.

Related papers

• Z0-Inf: Zeroth Order Approximation for Data Influence [47.682602051124235]
  We introduce a highly efficient zeroth-order approximation for estimating the influence of training data.<n>Our approach achieves superior accuracy in estimating self-influence and comparable or improved accuracy in estimating train-test influence for fine-tuned large language models.
  arXiv  Detail & Related papers  (2025-10-13T18:30:37Z)
• Capturing the Temporal Dependence of Training Data Influence [100.91355498124527]
  We formalize the concept of trajectory-specific leave-one-out influence, which quantifies the impact of removing a data point during training.<n>We propose data value embedding, a novel technique enabling efficient approximation of trajectory-specific LOO.<n>As data value embedding captures training data ordering, it offers valuable insights into model training dynamics.
  arXiv  Detail & Related papers  (2024-12-12T18:28:55Z)
• SoftDedup: an Efficient Data Reweighting Method for Speeding Up Language Model Pre-training [12.745160748376794]
  We propose a soft deduplication method that maintains dataset integrity while selectively reducing the sampling weight of data with high commonness. Central to our approach is the concept of "data commonness", a metric we introduce to quantify the degree of duplication. Empirical analysis shows that this method significantly improves training efficiency, achieving comparable perplexity scores with at least a 26% reduction in required training steps.
  arXiv  Detail & Related papers  (2024-07-09T08:26:39Z)
• DiffPuter: Empowering Diffusion Models for Missing Data Imputation [56.48119008663155]
  This paper introduces DiffPuter, a tailored diffusion model combined with the Expectation-Maximization (EM) algorithm for missing data imputation.<n>Our theoretical analysis shows that DiffPuter's training step corresponds to the maximum likelihood estimation of data density.<n>Our experiments show that DiffPuter achieves an average improvement of 6.94% in MAE and 4.78% in RMSE compared to the most competitive existing method.
  arXiv  Detail & Related papers  (2024-05-31T08:35:56Z)
• Stochastic Amortization: A Unified Approach to Accelerate Feature and Data Attribution [62.71425232332837]
  We show that training amortized models with noisy labels is inexpensive and surprisingly effective. This approach significantly accelerates several feature attribution and data valuation methods, often yielding an order of magnitude speedup over existing approaches.
  arXiv  Detail & Related papers  (2024-01-29T03:42:37Z)
• Online Importance Sampling for Stochastic Gradient Optimization [33.42221341526944]
  We propose a practical algorithm that efficiently computes data importance on-the-fly during training.<n>We also introduce a novel metric based on the derivative of the loss w.r.t. the network output, designed for mini-batch importance sampling.
  arXiv  Detail & Related papers  (2023-11-24T13:21:35Z)
• AST: Effective Dataset Distillation through Alignment with Smooth and High-Quality Expert Trajectories [18.266786462036553]
  We propose an effective DD framework named AST, standing for Alignment with Smooth and high-quality expert Trajectories. We conduct extensive experiments on datasets of different scales, sizes, and resolutions.
  arXiv  Detail & Related papers  (2023-10-16T16:13:53Z)
• Robust Learning with Progressive Data Expansion Against Spurious Correlation [65.83104529677234]
  We study the learning process of a two-layer nonlinear convolutional neural network in the presence of spurious features. Our analysis suggests that imbalanced data groups and easily learnable spurious features can lead to the dominance of spurious features during the learning process. We propose a new training algorithm called PDE that efficiently enhances the model's robustness for a better worst-group performance.
  arXiv  Detail & Related papers  (2023-06-08T05:44:06Z)
• LAVA: Data Valuation without Pre-Specified Learning Algorithms [20.578106028270607]
  We introduce a new framework that can value training data in a way that is oblivious to the downstream learning algorithm. We develop a proxy for the validation performance associated with a training set based on a non-conventional class-wise Wasserstein distance between training and validation sets. We show that the distance characterizes the upper bound of the validation performance for any given model under certain Lipschitz conditions.
  arXiv  Detail & Related papers  (2023-04-28T19:05:16Z)
• Minimizing the Accumulated Trajectory Error to Improve Dataset Distillation [151.70234052015948]
  We propose a novel approach that encourages the optimization algorithm to seek a flat trajectory. We show that the weights trained on synthetic data are robust against the accumulated errors perturbations with the regularization towards the flat trajectory. Our method, called Flat Trajectory Distillation (FTD), is shown to boost the performance of gradient-matching methods by up to 4.7%.
  arXiv  Detail & Related papers  (2022-11-20T15:49:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.