Related papers: Unifying vectors and matrices of different dimensi…
From condensed matter to quantum chromodynamics, multidimensional spins are a fundamental paradigm, with a pivotal role in combinatorial optimization and machine learning. Machines formed by coupled parametric oscillators can simulate spin…
The understanding of symmetry operations has brought enormous advancements in physics, ranging from elementary particle to condensed matter systems. In quantum mechanics, symmetry operations are described by either unitary or antiunitary…
Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified…
A network embedding is a representation of a large graph in a low-dimensional space, where vertices are modeled as vectors. The objective of a good embedding is to preserve the proximity between vertices in the original graph. This way,…
Numeric tabular datasets are the dominant data format in scientific practice, yet large language models lack native mechanisms for representing numeric datasets in a meaningful way across heterogeneous feature spaces. Existing approaches…
Deep learning techniques have recently demonstrated broad success in predicting complex dynamical systems ranging from turbulence to human speech, motivating broader questions about how neural networks encode and represent dynamical rules.…
Various two-dimensional fabrication methods, such as deposition, etching, milling, laser cutting, and water jetting, suffer from asymmetry between the top and the bottom surface of fabricated parts. Such asymmetry is usually undesirable and…
We present the Complex Envelope Variable Approximation (CEVA) as the very useful and compact method for the analysis of the essentially nonlinear dynamical systems. It allows us to study both the stationary and non-stationary dynamics even…
Based on the matrix expression of general nonlinear numerical analogues presented by the present author, this paper proposes a novel philosophy of nonlinear computation and analysis. The nonlinear problems are considered an ill-posed linear…
Koopman operator theory and Willems' fundamental lemma both can provide (approximated) data-driven linear representation for nonlinear systems. However, choosing lifting functions for the Koopman operator is challenging, and the quality of…
We present a detailed study of the combinatorial interpretation of matrix integrals, including the examples of tessellations of arbitrary genera, and loop models on random surfaces. After reviewing their methods of solution, we apply these…
Combining the predictions of multiple trained models through ensembling is generally a good way to improve accuracy by leveraging the different learned features of the models, however it comes with high computational and storage costs.…
Model merging enables powerful capabilities in neural networks without requiring additional training. In this paper, we introduce a novel perspective on model merging by leveraging the fundamental mechanisms of neural network…
Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA). Prior studies have demonstrated that linear autoencoders (LAEs) can recover the ordered, axis-aligned principal components of PCA by…
A key technique of machine learning and computer vision is to embed discrete weighted graphs into continuous spaces for further downstream processing. Embedding discrete hierarchical structures in hyperbolic geometry has proven very…
We introduce a novel embedding method diverging from conventional approaches by operating within function spaces of finite dimension rather than finite vector space, thus departing significantly from standard knowledge graph embedding…
Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…
For $X \sim X(n; 1, n^{-\alpha_1}, n^{-\alpha_2}, ...)$ in the multiparameter random simplicial complex model we establish necessary and sufficient strict inequalities on the $\alpha_i$'s to linearly embed the complex into…
Model merging has attracted significant attention as a powerful paradigm for model reuse, facilitating the integration of task-specific models into a singular, versatile framework endowed with multifarious capabilities. Previous studies,…
We tackle the challenges of modeling high-dimensional data sets, particularly those with latent low-dimensional structures hidden within complex, non-linear, and noisy relationships. Our approach enables a seamless integration of concepts…