A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper studies node embeddings of networks, revealing their geometric properties.
Study finds significant instability in node embeddings due to randomness.
Random complexes can be embedded linearly if certain conditions on parameters are met.
Landmark-based node embeddings approximate shortest path distances in random graphs.
MCE reduces embedding instability in nonlinear dimensionality reduction.
Study on linking numbers in random book embeddings of complete graphs.
Heterogeneous information network (HIN) embedding has gained increasing interests recently. However, the current way of random-walk based HIN embedding methods have paid few attention to the higher-order Markov chain nature of meta-path guided random walks, especially to the stationarity issue. In this paper, we system…
In order to model entanglements of polymers in a confined region, we consider the linking numbers and writhes of cycles in random linear embeddings of complete graphs in a cube. Our main results are that for a random linear embedding of in a cube, the mean sum of squared linking numbers and the mean sum of square…
Random walks on metric spaces embed quasi-isometrically into the space.
ARGEW improves node embeddings for weighted homophilous graphs by emphasizing strong edge weights.
The study analyzes convergence of random-walk embeddings in graph theory.
Higher-order proximity preserved network embedding has attracted increasing attention. In particular, due to the superior scalability, random-walk-based network embedding has also been well developed, which could efficiently explore higher-order neighborhoods via multi-hop random walks. However, despite the success of …
Network representation learning in low dimensional vector space has attracted considerable attention in both academic and industrial domains. Most real-world networks are dynamic with addition/deletion of nodes and edges. The existing graph embedding methods are designed for static networks and they cannot capture evol…
The paper examines how well node similarities are preserved by random projections in graph embeddings.
Paper explores embedding methods for detecting pseudo-cliques in random graphs, showing limitations and potential.
The fields of compressed sensing (CS) and matrix completion have shown that high-dimensional signals with sparse or low-rank structure can be effectively projected into a low-dimensional space (for efficient acquisition or processing) when the projection operator achieves a stable embedding of the data by satisfying th…
RESTA defends LLMs against jailbreaking attacks by adding random noise to embeddings.
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function , consistent estimators of the mean embedding of a random variable lead to consistent estimators of the mean embedding of . For Matérn ke…
Improved guarantees for sparse random embeddings with explicit bounds and empirical superiority.
EGORSE optimizes high-dimensional problems using random and supervised embeddings.
Hermite polynomials improve private data generation by reducing feature count.
Graph embedding has recently gained momentum in the research community, in particular after the introduction of random walk and neural network based approaches. However, most of the embedding approaches focus on representing the local neighborhood of nodes and fail to capture the global graph structure, i.e. to retain …
A fast graph embedding method for large graphs.
Let G be an acylindrically hyperbolic group. We consider a random subgroup H in G, generated by a finite collection of independent random walks. We show that, with asymptotic probability one, such a random subgroup H of G is a free group, and the semidirect product of H acting on E(G) is hyperbolically embedded in G, w…
Randomized Geometric Algebra for Convex Neural Networks Optimizes Transfer Learning.
The paper corrects for node degree in spectral clustering using random walk Laplacian.
Enhanced GNN with expanded attention window and partially random embeddings.
This work analyzes PPR-based node embeddings and their topological information.
This work improves tensor decomposition methods, especially for large datasets.
SOLAR improves search efficiency and accuracy with sparse, orthogonal embeddings.
The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional space into the original one, resulting in a more manageable optimization problem. S…
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when representing graphs. Some recent global graph kernels, which utilizes the align…
New algorithm reduces sketching dimension to effective problem size.
NodeSig efficiently computes binary node embeddings for scalable graph analysis.
Expected centre of mass for random embeddings is constant.
Continuous vector representations of words and objects appear to carry surprisingly rich semantic content. In this paper, we advance both the conceptual and theoretical understanding of word embeddings in three ways. First, we ground embeddings in semantic spaces studied in cognitive-psychometric literature and introdu…
In network embedding, random walks play a fundamental role in preserving network structures. However, random walk based embedding methods have two limitations. First, random walk methods are fragile when the sampling frequency or the number of node sequences changes. Second, in disequilibrium networks such as highly bi…
We develop embeddings for nonlinear subspaces preserving vector norms.
This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows mitigating the drawbacks of the high extrinsic dimensionality while avoiding the…
In this paper new general modewise Johnson-Lindenstrauss (JL) subspace embeddings are proposed that are both considerably faster to generate and easier to store than traditional JL embeddings when working with extremely large vectors and/or tensors. Corresponding embedding results are then proven for two different type…
The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning computation-efficient kernel embeddings from specific data. In the framework, the h…
RR-GCN uses random transformations instead of learned weights for node embeddings.
G-Net constructs binary neural networks with high accuracy using randomized binary embeddings.
We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above that, the presented framework covers multivariate randomized functions. As a bypr…
Neumann eigenmaps improve landmark-based diffusion map embeddings.
We propose a differentially private data generation paradigm using random feature representations of kernel mean embeddings when comparing the distribution of true data with that of synthetic data. We exploit the random feature representations for two important benefits. First, we require a minimal privacy cost for tra…
Optimal subspace embedding with near-optimal sparsity for high-dimensional data.
The random dot product graph (RDPG) is an independent-edge random graph that is analytically tractable and, simultaneously, either encompasses or can successfully approximate a wide range of random graphs, from relatively simple stochastic block models to complex latent position graphs. In this survey paper, we describ…