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We provide a statistical analysis of regularization-based continual learning on a sequence of linear regression tasks, with emphasis on how different regularization terms affect the model performance. We first derive the convergence rate…
A semi-analytic method to compute the first coefficients of the renormalization group functions on a random lattice is introduced. It is used to show that the two-dimensional $O(N)$ non-linear $\sigma$-model regularized on a random lattice…
When neural networks are confronted with unfamiliar data that deviate from their training set, this signifies a domain shift. While these networks output predictions on their inputs, they typically fail to account for their level of…
In this paper, we study norm-based regularization methods for neural networks. We compare existing penalization approaches and introduce two regularization strategies that extend classical ridge- and lasso-type penalties to neural network…
This paper studies the performance of the spectral method in the estimation and uncertainty quantification of the unobserved preference scores of compared entities in a general and more realistic setup. Specifically, the comparison graph…
In this paper, the regularization approach introduced recently for nonparametric estimation of linear systems is extended to the estimation of nonlinear systems modelled as Volterra series. The kernels of order higher than one, representing…
This paper presents a two-stage online algorithm for recovery of low-rank parameter matrix in non-stationary stochastic systems. The first stage applies the recursive least squares (RLS) estimator combined with its singular value…
Heterogeneity is an unwanted variation when analyzing aggregated datasets from multiple sources. Though different methods have been proposed for heterogeneity adjustment, no systematic theory exists to justify these methods. In this work,…
Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…
Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks.…
This paper investigates correct variable selection in finite samples via $\ell_1$ and $\ell_1+\ell_2$ type penalization schemes. The asymptotic consistency of variable selection immediately follows from this analysis. We focus on logistic…
Renormalization-group equations (RGE) is one of the key tools in studying high-energy behavior of the Standard Model (SM). We begin by reviewing one-loop RGE for the dimensionless couplings of the SM and proceed to the state-of-the-art…
We consider the ill-posed inverse problem of identifying a nonlinearity in a time-dependent PDE model. The nonlinearity is approximated by a neural network, and needs to be determined alongside other unknown physical parameters and the…
Reasoning ability has become a defining capability of Large Language Models (LLMs), with Reinforcement Learning with Verifiable Rewards (RLVR) emerging as a key paradigm to enhance it. However, RLVR training often suffers from policy…
We consider the tuning parameter selection rules for nuclear norm regularized multivariate linear regression (NMLR) in high-dimensional setting. High-dimensional multivariate linear regression is widely used in statistics and machine…
Large Language Models have become integral to software development, yet they frequently generate vulnerable code. Existing code vulnerability detection benchmarks employ binary classification, lacking the CWE-level specificity required for…
This paper focuses on recovering an unknown vector $\beta$ from the noisy data $Y=X\beta +\sigma\xi$, where $X$ is a known $n\times p$-matrix, $\xi $ is a standard white Gaussian noise, and $\sigma$ is an unknown noise level. In order to…
Robust adaptation of LLMs and VLMs is often evaluated by average accuracy or average consistency under perturbations. However, these averages can hide a structured failure mode: a prediction may remain correct while probability mass already…
A technique for characterizing and correcting the linearity of radiometric instruments is known by the names the "flux-addition method" and the "combinatorial technique". In this paper, we develop a rigorous uncertainty quantification…
Brittle optimization has been observed to adversely impact model likelihoods for regression and VAEs when simultaneously fitting neural network mappings from a (random) variable onto the mean and variance of a dependent Gaussian variable.…