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Tag: theoretical

  • A Theoretical Framework for LLM Fine-tuning Using Early Stopping for Non-random Initialization

    A Theoretical Framework for LLM Fine-tuning Using Early Stopping for Non-random Initialization arXiv:2602.13942v1 Announce Type: new Abstract: In the era of large language models (LLMs), fine-tuning pretrained models has become ubiquitous. Yet the theoretical underpinning remains an open question. A central question is why only a few epochs of fine-tuning are typically sufficient to achieve…

  • Transcendental Regularization of Finite Mixtures:Theoretical Guarantees and Practical Limitations

    Transcendental Regularization of Finite Mixtures:Theoretical Guarantees and Practical Limitations arXiv:2602.03889v1 Announce Type: new Abstract: Finite mixture models are widely used for unsupervised learning, but maximum likelihood estimation via EM suffers from degeneracy as components collapse. We introduce transcendental regularization, a penalized likelihood framework with analytic barrier functions that prevent degeneracy while maintaining asymptotic efficiency. The…

  • A Theoretical and Empirical Taxonomy of Imbalance in Binary Classification

    A Theoretical and Empirical Taxonomy of Imbalance in Binary Classification arXiv:2601.04149v1 Announce Type: new Abstract: Class imbalance significantly degrades classification performance, yet its effects are rarely analyzed from a unified theoretical perspective. We propose a principled framework based on three fundamental scales: the imbalance coefficient $eta$, the sample–dimension ratio $kappa$, and the intrinsic separability $Delta$.…

  • Sparsity via Hyperpriors: A Theoretical and Algorithmic Study under Empirical Bayes Framework

    Sparsity via Hyperpriors: A Theoretical and Algorithmic Study under Empirical Bayes Framework arXiv:2511.06235v1 Announce Type: new Abstract: This paper presents a comprehensive analysis of hyperparameter estimation within the empirical Bayes framework (EBF) for sparse learning. By studying the influence of hyperpriors on the solution of EBF, we establish a theoretical connection between the choice of…

  • A theoretical guarantee for SyncRank

    A theoretical guarantee for SyncRank arXiv:2509.22766v1 Announce Type: new Abstract: We present a theoretical and empirical analysis of the SyncRank algorithm for recovering a global ranking from noisy pairwise comparisons. By adopting a complex-valued data model where the true ranking is encoded in the phases of a unit-modulus vector, we establish a sharp non-asymptotic recovery…

  • Learning Difference-of-Convex Regularizers for Inverse Problems: A Flexible Framework with Theoretical Guarantees

    Learning Difference-of-Convex Regularizers for Inverse Problems: A Flexible Framework with Theoretical Guarantees arXiv:2502.00240v1 Announce Type: new Abstract: Learning effective regularization is crucial for solving ill-posed inverse problems, which arise in a wide range of scientific and engineering applications. While data-driven methods that parameterize regularizers using deep neural networks have demonstrated strong empirical performance, they often…