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In this paper, we consider the geometric landscape connection of the widely studied manifold and factorization formulations in low-rank positive semidefinite (PSD) and general matrix optimization. We establish a sandwich relation on the…

We study skew-product dynamics for a large class of finitely-generated semi--hyperbolic semigroups of rational maps acting on the Riemann sphere, which generalizes both the theory of iteration of a single rational map of a single complex…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

A widely adopted strategy for model enhancement is to use synthetic data generated by a stronger model for supervised fine-tuning (SFT). However, for emerging reasoning models like Qwen3-8B, this approach often fails to improve reasoning…

Approximation of high-dimensional functions is a problem in many scientific fields that is only feasible if advantageous structural properties, such as sparsity in a given basis, can be exploited. A relevant tool for analysing sparse…

We consider the variable selection problem of generalized linear models (GLMs). Stability selection (SS) is a promising method proposed for solving this problem. Although SS provides practical variable selection criteria, it is…

Topological holography is a conjectured correspondence between the symmetry charges and defects of a $D$-dimensional system with the anyons in a $(D+1)$-dimensional topological order: the symmetry topological field theory (SymTFT).…

Semi-supervised Learning (SSL) has witnessed great success owing to the impressive performances brought by various methods based on pseudo labeling and consistency regularization. However, we argue that existing methods might fail to…

Supervised fine-tuning (SFT) is a pivotal approach to adapting large language models (LLMs) for downstream tasks; however, performance often suffers from the ``seesaw phenomenon'', where indiscriminate parameter updates yield progress on…

Gating is a key technique used for integrating information from multiple sources by long short-term memory (LSTM) models and has recently also been applied to other models such as the highway network. Although gating is powerful, it is…

Semi-supervised symmetric non-negative matrix factorization (SNMF) utilizes the available supervisory information (usually in the form of pairwise constraints) to improve the clustering ability of SNMF. The previous methods introduce the…

Deep learning models such as CNNs have surpassed human performance in computer vision tasks such as image classification. However, despite their sophistication, these models lack interpretability which can lead to biased outcomes reflecting…

Despite the success of deep functional maps in non-rigid 3D shape matching, there exists no learning framework that models both self-symmetry and shape matching simultaneously. This is despite the fact that errors due to symmetry mismatch…

This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly constrained SDPs. The key idea is to formulate an approximate…

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…

When constructing finite frames for a given application, the most important consideration is the spectrum of the frame operator. Indeed, the minimum and maximum eigenvalues of the frame operator are the optimal frame bounds, and the frame…

Semi-supervised learning has made remarkable strides by effectively utilizing a limited amount of labeled data while capitalizing on the abundant information present in unlabeled data. However, current algorithms often prioritize aligning…

Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of…

We take a random matrix theory approach to random sketching and show an asymptotic first-order equivalence of the regularized sketched pseudoinverse of a positive semidefinite matrix to a certain evaluation of the resolvent of the same…

This paper studies Young diagrams of symmetric and pseudo-symmetric numerical semigroups and describes new operations on Young diagrams as well as numerical semigroups. These provide new decompositions of symmetric and pseudo-symmetric…