Data attribution methods, which quantify the influence of individual training data points on a machine learning model, have gained increasing popularity in data-centric applications in modern AI. Despite a recent surge of new methods developed in this space, the impact of hyperparameter tuning in these methods remains under-explored. In this work, we present the first large-scale empirical study to understand the hyperparameter sensitivity of common data attribution methods. Our results show that most methods are indeed sensitive to certain key hyperparameters. However, unlike typical machine learning algorithms -- whose hyperparameters can be tuned using computationally-cheap validation metrics -- evaluating data attribution performance often requires retraining models on subsets of training data, making such metrics prohibitively costly for hyperparameter tuning. This poses a critical open challenge for the practical application of data attribution methods. To address this challenge, we advocate for better theoretical understandings of hyperparameter behavior to inform efficient tuning strategies. As a case study, we provide a theoretical analysis of the regularization term that is critical in many variants of influence function methods. Building on this analysis, we propose a lightweight procedure for selecting the regularization value without model retraining, and validate its effectiveness across a range of standard data attribution benchmarks. Overall, our study identifies a fundamental yet overlooked challenge in the practical application of data attribution, and highlights the importance of careful discussion on hyperparameter selection in future method development.

We consider the problem of estimating a regularization parameter, or a shrinkage coefficient $α\in (0,1)$ for Regularized Tyler's M-estimator (RTME). In particular, we propose to estimate an optimal shrinkage coefficient by setting $α$ as the solution to a suitably chosen objective function; namely the leave-one-out cross-validated (LOOCV) log-likelihood loss. Since LOOCV is computationally prohibitive even for moderate sample size $n$, we propose a computationally efficient approximation for the LOOCV log-likelihood loss that eliminates the need for invoking the RTME procedure $n$ times for each sample left out during the LOOCV procedure. This approximation yields an $O(n)$ reduction in the running time complexity for the LOOCV procedure, which results in a significant speedup for computing the LOOCV estimate. We demonstrate the efficiency and accuracy of the proposed approach on synthetic high-dimensional data sampled from heavy-tailed elliptical distributions, as well as on real high-dimensional datasets for object recognition, face recognition, and handwritten digit's recognition. Our experiments show that the proposed approach is efficient and consistently more accurate than other methods in the literature for shrinkage coefficient estimation.

For three decades statistical mechanics has been providing a framework to analyse neural networks. However, the theoretically tractable models, e.g., perceptrons, random features models and kernel machines, or multi-index models and committee machines with few neurons, remained simple compared to those used in applications. In this paper we help reducing the gap between practical networks and their theoretical understanding through a statistical physics analysis of the supervised learning of a two-layer fully connected network with generic weight distribution and activation function, whose hidden layer is large but remains proportional to the inputs dimension. This makes it more realistic than infinitely wide networks where no feature learning occurs, but also more expressive than narrow ones or with fixed inner weights. We focus on the Bayes-optimal learning in the teacher-student scenario, i.e., with a dataset generated by another network with the same architecture. We operate around interpolation, where the number of trainable parameters and of data are comparable and feature learning emerges. Our analysis uncovers a rich phenomenology with various learning transitions as the number of data increases. In particular, the more strongly the features (i.e., hidden neurons of the target) contribute to the observed responses, the less data is needed to learn them. Moreover, when the data is scarce, the model only learns non-linear combinations of the teacher weights, rather than "specialising" by aligning its weights with the teacher's. Specialisation occurs only when enough data becomes available, but it can be hard to find for practical training algorithms, possibly due to statistical-to-computational~gaps.

Adam is the de facto optimization algorithm for several deep learning applications, but an understanding of its implicit bias and how it differs from other algorithms, particularly standard first-order methods such as (stochastic) gradient descent (GD), remains limited. In practice, neural networks trained with SGD are known to exhibit simplicity bias -- a tendency to find simple solutions. In contrast, we show that Adam is more resistant to such simplicity bias. To demystify this phenomenon, in this paper, we investigate the differences in the implicit biases of Adam and GD when training two-layer ReLU neural networks on a binary classification task involving synthetic data with Gaussian clusters. We find that GD exhibits a simplicity bias, resulting in a linear decision boundary with a suboptimal margin, whereas Adam leads to much richer and more diverse features, producing a nonlinear boundary that is closer to the Bayes' optimal predictor. This richer decision boundary also allows Adam to achieve higher test accuracy both in-distribution and under certain distribution shifts. We theoretically prove these results by analyzing the population gradients. To corroborate our theoretical findings, we present empirical results showing that this property of Adam leads to superior generalization across datasets with spurious correlations where neural networks trained with SGD are known to show simplicity bias and don't generalize well under certain distributional shifts.

Cautious predictions -- where a machine learning model abstains when uncertain -- are crucial for limiting harmful errors in safety-critical applications. In this work, we identify a novel threat: a dishonest institution can exploit these mechanisms to discriminate or unjustly deny services under the guise of uncertainty. We demonstrate the practicality of this threat by introducing an uncertainty-inducing attack called Mirage, which deliberately reduces confidence in targeted input regions, thereby covertly disadvantaging specific individuals. At the same time, Mirage maintains high predictive performance across all data points. To counter this threat, we propose Confidential Guardian, a framework that analyzes calibration metrics on a reference dataset to detect artificially suppressed confidence. Additionally, it employs zero-knowledge proofs of verified inference to ensure that reported confidence scores genuinely originate from the deployed model. This prevents the provider from fabricating arbitrary model confidence values while protecting the model's proprietary details. Our results confirm that Confidential Guardian effectively prevents the misuse of cautious predictions, providing verifiable assurances that abstention reflects genuine model uncertainty rather than malicious intent.

Variational inference often struggles with the posterior geometry exhibited by complex hierarchical Bayesian models. Recent advances in flow-based variational families and Variationally Inferred Parameters (VIP) each address aspects of this challenge, but their formal relationship is unexplored. Here, we prove that the combination of VIP and a full-rank Gaussian can be represented exactly as a forward autoregressive flow augmented with a translation term and input from the model's prior. Guided by this theoretical insight, we introduce the Model-Informed Flow (MIF) architecture, which adds the necessary translation mechanism, prior information, and hierarchical ordering. Empirically, MIF delivers tighter posterior approximations and matches or exceeds state-of-the-art performance across a suite of hierarchical and non-hierarchical benchmarks.

This paper introduces a novel Knockoff-guided compressive sensing framework, referred to as \TheName{}, which enhances signal recovery by leveraging precise false discovery rate (FDR) control during the support identification phase. Unlike LASSO, which jointly performs support selection and signal estimation without explicit error control, our method guarantees FDR control in finite samples, enabling more reliable identification of the true signal support. By separating and controlling the support recovery process through statistical Knockoff filters, our framework achieves more accurate signal reconstruction, especially in challenging scenarios where traditional methods fail. We establish theoretical guarantees demonstrating how FDR control directly ensures recovery performance under weaker conditions than traditional $\ell_1$-based compressive sensing methods, while maintaining accurate signal reconstruction. Extensive numerical experiments demonstrate that our proposed Knockoff-based method consistently outperforms LASSO-based and other state-of-the-art compressive sensing techniques. In simulation studies, our method improves F1-score by up to 3.9x over baseline methods, attributed to principled false discovery rate (FDR) control and enhanced support recovery. The method also consistently yields lower reconstruction and relative errors. We further validate the framework on real-world datasets, where it achieves top downstream predictive performance across both regression and classification tasks, often narrowing or even surpassing the performance gap relative to uncompressed signals. These results establish \TheName{} as a robust and practical alternative to existing approaches, offering both theoretical guarantees and strong empirical performance through statistically grounded support selection.

Simone Di Gregorio and Francesco Iafrate Abstract We take into consideration generalization bounds in [3] for the problem of the estimation of the drift component for ergodic stochasti c differential equations, when the estimator is a ReLU neural network and the estimatio n is non-parametric with respect to the statistical model. We show a practical wa y to enforce the theoretical estimation procedure, enabling inference on noisy and roug h functional data. Results are shown for a simulated It ˆ o-Taylor approximation of the sample paths. The problem of statistical modeling for multi-dimensional ergodic diffusions from discrete observations has a long-standing literature that largely focused on parametric approaches to the estimation of the coefficient set [4, 5]. In this work, we pick a different approach stemming from the analysis in [3], focus ing on neural network estimators of the drift coefficient and without parametric as sumptions on the statistical model.

Traditional data analysis often represents data as a weighted graph with pairwise similarities, but many problems do not naturally fit this framework. In line clustering, points in a Euclidean space must be grouped so that each cluster is well approximated by a line segment. Since any two points define a line, pairwise similarities fail to capture the structure of the problem, necessitating the use of higher-order interactions modeled by geometric hypergraphs. We encode geometry into a 3-uniform hypergraph by treating sets of three points as hyperedges whenever they are approximately collinear. The resulting hypergraph contains information about the underlying line segments, which can then be extracted using community recovery algorithms. In contrast to classical hypergraph block models, latent geometric constraints in this construction introduce significant dependencies between hyperedges, which restricts the applicability of many standard theoretical tools. We aim to determine the fundamental limits of line clustering and evaluate hypergraph-based line clustering methods. To this end, we derive information-theoretic thresholds for exact and almost exact recovery for data generated from intersecting lines on a plane with additive Gaussian noise. We develop a polynomial-time spectral algorithm and show that it succeeds under noise conditions that match the information-theoretic bounds up to a polylogarithmic factor.

Mixture-of-experts networks (MoEs) have demonstrated remarkable efficiency in modern deep learning. Despite their empirical success, the theoretical foundations underlying their ability to model complex tasks remain poorly understood. In this work, we conduct a systematic study of the expressive power of MoEs in modeling complex tasks with two common structural priors: low-dimensionality and sparsity. For shallow MoEs, we prove that they can efficiently approximate functions supported on low-dimensional manifolds, overcoming the curse of dimensionality. For deep MoEs, we show that $\cO(L)$-layer MoEs with $E$ experts per layer can approximate piecewise functions comprising $E^L$ pieces with compositional sparsity, i.e., they can exhibit an exponential number of structured tasks. Our analysis reveals the roles of critical architectural components and hyperparameters in MoEs, including the gating mechanism, expert networks, the number of experts, and the number of layers, and offers natural suggestions for MoE variants.