How does the training data affect a model's behavior? This is the question we seek to answer with data attribution. The leading practical approaches to data attribution are based on influence functions (IF). IFs utilize a first-order Taylor approximation to efficiently predict the effect of removing a set of samples from the training set without retraining the model, and are used in a wide variety of machine learning applications. However, especially in the high-dimensional regime (# params Ω(# samples)), they are often imprecise and tend to underestimate the effect of sample removals, even for simple models such as logistic regression. We present rescaled influence functions (RIF), a tool for data attribution which can be used as a dropin replacement for influence functions, with little computational overhead but significant improvement in accuracy. We compare IF and RIF on a range of realworld datasets, showing that RIFs offer significantly better predictions in practice, and present a theoretical analysis explaining this improvement. Finally, we present a simple class of data poisoning attacks that would fool IF-based detections but would be detected by RIF.

Pretrained Large Language Models (LLMs) achieve strong performance across a wide range of tasks, yet exhibit substantial variability in the various layers' training quality with respect to specific downstream applications, limiting their downstream performance. It is therefore critical to estimate layer-wise training quality in a manner that accounts for both model architecture and training data. However, existing approaches predominantly rely on model-centric heuristics (such as spectral statistics, outlier detection, or uniform allocation) while overlooking the influence of data. To address these limitations, we propose LAYERIF, a datadriven framework that leverages Influence Functions to quantify the training quality of individual layers in a principled and task-sensitive manner. By isolating each layer's gradients and measuring the sensitivity of the validation loss to training examples by computing layer-wise influences, we derive data-driven estimates of layer importance. Notably, our method produces task-specific layer importance estimates for the same LLM, revealing how layers specialize for different test-time evaluation tasks. We demonstrate the utility of our scores by leveraging them for two downstream applications: (a) expert allocation in LoRA-MoE architectures and (b) layer-wise sparsity distribution for LLM pruning. Experiments across multiple LLM architectures demonstrate that our model-agnostic, influence-guided allocation leads to consistent gains in task performance.

Causal mediation analysis is crucial for deconstructing complex mechanisms of action. However, in current mediation analysis, complex structures derived from causal discovery lack direct interpretation of mediation pathways, while traditional mediation analysis and effect estimation are limited by the reliance on pre-specified pathways, leading to a disconnection between structure discovery and causal mechanism understanding. Therefore, a unified framework integrating structure discovery, pathway identification, and effect estimation systematically quantifies mediation pathways under structural uncertainty, enabling automated identification and inference of mediation pathways. To this end, we propose Structure-Informed Guided Mediation Analysis (SIGMA), which guides automated mediation pathway identification through probabilistic causal structure discovery and uncertainty quantification, enabling end-to-end propagation of structural uncertainty from structure learning to effect estimation. Specifically, SIGMA employs differentiable Flow-Structural Equation Models to learn structural posteriors, generating diverse Directed Acyclic Graphs (DAGs) to quantify structural uncertainty. Based on these DAGs, we introduce the Path Stability Score to evaluate the marginal probability of pathways, identifying high-confidence mediation paths. For identified mediation pathways, we integrate Efficient Influence Functions with Bayesian model averaging to fuse within-structure estimation uncertainty and between-structure effect variation, propagating uncertainty to the final effect estimates. In synthetic data experiments, SIGMA achieves state-of-the-art performance in pathway identification accuracy and effect quantification precision under structural uncertainty, concurrent multiple pathways, and nonlinear scenarios. In real-world applications using Human Phenotype Project data, SIGMA identifies mediation effects of sleep quality on cardiovascular health through inflammatory and metabolic pathways, uncovering previously unspecified multiple mediation paths.

Training data attribution (TDA) is concerned with understanding model behavior in terms of the training data. This paper draws attention to the common setting where one has access only to the final trained model, and not the training algorithm or intermediate information from training.

Training data attribution (TDA) methods aim to measure how training data impacts a model's predictions. While gradient-based attribution methods, such as influence functions, offer theoretical grounding, their computational costs make them impractical for large-scale applications. Representation-based approaches are far more scalable, but typically rely on heuristic embeddings that are not optimized for attribution, limiting their fidelity. To address these challenges, we propose AirRep, a scalable, representation-based approach that closes this gap by learning task-specific and model-aligned representations optimized explicitly for TDA. AirRep introduces two key innovations: a trainable encoder tuned for attribution quality, and an attention-based pooling mechanism that enables accurate estimation of group-wise influence. We train AirRep using a ranking objective over automatically constructed training subsets labeled by their empirical effect on target predictions. Experiments on instruction-tuned LLMs demonstrate that AirRep achieves performance on par with state-of-the-art gradient-based approaches while being nearly two orders of magnitude more efficient at inference time. Further analysis highlights its robustness and generalization across tasks and models.

Training data attribution (TDA) provides insights into which training data is responsible for a learned model behavior. Gradient-based TDA methods such as influence functions and unrolled differentiation both involve a computation that resembles an inverse Hessian-vector product (iHVP), which is difficult to approximate efficiently. We introduce an algorithm (ASTRA) which uses the EKFAC-preconditioner on Neumann series iterations to arrive at an accurate iHVP approximation for TDA. ASTRA is easy to tune, requires fewer iterations than Neumann series iterations, and is more accurate than EKFAC-based approximations. Using ASTRA, we show that improving the accuracy of the iHVP approximation can significantly improve TDA performance.

Machine learning models have achieved widespread success but often inherit and amplify historical biases, resulting in unfair outcomes. Traditional fairness methods typically impose constraints at the prediction level, without addressing underlying biases in data representations. In this work, we propose a principled framework that adjusts data representations to balance predictive utility and fairness. Using sufficient dimension reduction, we decompose the feature space into target-relevant, sensitive, and shared components, and control the fairness-utility trade-off by selectively removing sensitive information. We provide a theoretical analysis of how prediction error and fairness gaps evolve as shared subspaces are added, and employ influence functions to quantify their effects on the asymptotic behavior of parameter estimates. Experiments on both synthetic and real-world datasets validate our theoretical insights and show that the proposed method effectively improves fairness while preserving predictive performance.

The weighted controlled direct effect (WCDE) generalizes the standard controlled direct effect (CDE) by averaging over the mediator distribution, providing a robust estimate when treatment effects vary across mediator levels. This makes the WCDE especially relevant in fairness analysis, where it isolates the direct effect of an exposure on an outcome, independent of mediating pathways. This work establishes three fundamental advances for WCDE in observational studies: First, we establish necessary and sufficient conditions for the identifiability of the WCDE, clarifying when it diverges from the CDE. Next, we consider nonparametric estimation of the WCDE and derive its influence function, focusing on the class of regular and asymptotically linear estimators. Lastly, we characterize the optimal covariate adjustment set that minimizes the asymptotic variance, demonstrating how mediator-confounder interactions introduce distinct requirements compared to average treatment effect (ATE) estimation. Using synthetic and real-world data, we validate our theory numerically, showing that the proposed optimal valid adjustment set yields the lowest variance at practical sample sizes. Our results offer a principled framework for efficient estimation of direct effects in complex causal systems, with practical applications in fairness and mediation analysis.

Data valuation techniques quantify each training example's contribution to model performance, providing a principled basis for data cleaning, acquisition, and selection. Existing valuation methods remain inadequate: model-based techniques depend on a single fitted model and inherit its biases, while algorithm-based approaches like Data Shapley scale poorly due to their need to train multiple models. Recent work has proposed model-agnostic alternatives based on Wasserstein distance between the training set and a clean reference set, but exact computation is expensive and approximations often misrank examples. We introduce KAIROS, a model-agnostic framework that values examples by their contribution to the Maximum Mean Discrepancy (MMD) between the training set and a clean reference distribution. Unlike Wasserstein methods, MMD admits a closed-form solution that requires no approximations and is scalable to large datasets. Additionally, KAIROS enables efficient online valuation: adding a new batch of m examples requires only O(mN)computation to update all scores, compared to O(N2)in prior work where N is the training set size. Empirical evaluations on noise, mislabeling, and poisoning benchmarks show that KAIROS consistently outperforms state-of-the-art baselines in both accuracy and runtime. On ImageNet, KAIROS achieves up to 15 speedup over the fastest baseline while maintaining superior data valuation quality. Our results demonstrate that model-agnostic methods can match or exceed model-based approaches in performance while scaling to large datasets.

We study how training data contributes to the emergence of toxic behaviors in large language models. Most prior work on reducing model toxicity adopts reactive approaches, such as fine-tuning pre-trained (and potentially toxic) models to align them with human values. In contrast, we propose a proactive approach-- IF-GUIDE--that leverages influence functions to identify and suppress harmful tokens in the training data. To this end, we first show that standard influence functions are ineffective at discovering harmful training records. We then present a novel adaptation that measures token-level attributions from training data to model toxicity, along with techniques for selecting toxic training documents and a learning objective that can be integrated into both pre-training and fine-tuning. Moreover, IF-GUIDE does not rely on human-preference data, which is typically required by existing alignment methods. In our evaluation, we demonstrate that IF-GUIDE substantially reduces both explicit and implicit toxicity--by up to 10 compared to uncensored models, and up to 3 compared to baseline alignment methods such as DPO and RAD--across both pre-training and fine-tuning scenarios. IF-GUIDE is computationally efficient: a billion-parameter model is not necessary for computing influence scores; a million-parameter model--with 7.5 fewer parameters--can effectively serve as a proxy for identifying harmful data.