arXiv research

A novel 3D shape registration method using spectral graph embedding and probabilistic matching.

We present a parallelized bijective graph matching algorithm that leverages seeds and is designed to match very large graphs. Our algorithm combines spectral graph embedding with existing state-of-the-art seeded graph matching procedures. We justify our approach by proving that modestly correlated, large stochastic blo…

New matrix ensembles better match deep neural network spectral densities.

Graph matching aims at finding the vertex correspondence between two unlabeled graphs that maximizes the total edge weight correlation. This amounts to solving a computationally intractable quadratic assignment problem. In this paper we propose a new spectral method, GRAph Matching by Pairwise eigen-Alignments (GRAMPA)…

New method improves matrix completion accuracy, especially in noisy data.

Paper proposes a new method for training diffusion models using Markov operators.

A new method resolves permutation issues in shuffled linear regression for large-scale applications.

A novel method relaxes binary constraints to non-negative spheres for multi-matching and clustering.

New method controls linear systems with partial info and disturbances.

RFM simplifies generative modeling on complex geometries without simulation.

We analyze a new spectral graph matching algorithm, GRAph Matching by Pairwise eigen-Alignments (GRAMPA), for recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs. Extending the exact recovery guarantees established in the companion paper for Gaussian weights, in this work,…

New optimizer SF-NorMuon matches tuned AdamW across various horizons.

The paper introduces a quantum state system to count perfect matchings in graphs.

We present a solution to scale spectral algorithms for learning sequence functions. We are interested in the case where these functions are sparse (that is, for most sequences they return 0). Spectral algorithms reduce the learning problem to the task of computing an SVD decomposition over a special type of matrix call…

Spectral clustering achieves strong consistency in the stochastic block model under certain conditions.

Graph spectra have been successfully used to classify network types, compute the similarity between graphs, and determine the number of communities in a network. For large graphs, where an eigen-decomposition is infeasible, iterative moment matched approximations to the spectra and kernel smoothing are typically used. …

We introduce Courant algebroids, providing definitions, some historical notes, and some elementary properties. Next, we summarize basic properties of graded manifolds. Then, drawing on the work of Roytenberg and others, we introduce the graded or supergraded language demonstrating a cochain complex / cohomology for (ge…

Anosov diffeomorphisms with integrable subbundles have coherent dynamics and spectral rigidity.

Data vectors are obtained from multiple domains. They are feature vectors of images or vector representations of words. Domains may have different numbers of data vectors with different dimensions. These data vectors from multiple domains are projected to a common space by linear transformations in order to search clos…

We consider the problem of learning from a similarity matrix (such as spectral clustering and lowd imensional embedding), when computing pairwise similarities are costly, and only a limited number of entries can be observed. We provide a theoretical analysis using standard notions of graph approximation, significantly …

FAST selects coresets more efficiently by matching distributions in the frequency domain.

The strength of association between a pair of data vectors is represented by a nonnegative real number, called matching weight. For dimensionality reduction, we consider a linear transformation of data vectors, and define a matching error as the weighted sum of squared distances between transformed vectors with respect…

This paper tackles matching two complete graphs with correlated edge weights in geometric models.

Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.

SPECTRE uses spectral conditioning to generate larger graphs without mode collapse.

New spectral algorithm estimates random graph parameters robustly against corrupted nodes.

Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain from empirical trajectories. Through the lens of spectral decomposition, we study…

Paper tackles functional linear regression using spectral algorithms with discrete observations.

Consistent spectral clustering with fairness constraints on representation graphs.

Spectral clustering is one of the most effective clustering approaches that capture hidden cluster structures in the data. However, it does not scale well to large-scale problems due to its quadratic complexity in constructing similarity graphs and computing subsequent eigendecomposition. Although a number of methods h…

New algorithm finds sparse matrices on Stiefel manifold for optimisation.

In this work we study permutation synchronisation for the challenging case of partial permutations, which plays an important role for the problem of matching multiple objects (e.g. images or shapes). The term synchronisation refers to the property that the set of pairwise matchings is cycle-consistent, i.e. in the full…

Singular values of a data in a matrix form provide insights on the structure of the data, the effective dimensionality, and the choice of hyper-parameters on higher-level data analysis tools. However, in many practical applications such as collaborative filtering and network analysis, we only get a partial observation.…

Muon replaces matrix gradient with polar factor, optimizing flat spectrum updates

Improved spectral gap for MwG with adaptive RWM proposals.

Method detects neural network equivalence via matrix ensembles and spectral analysis.

In this paper, we consider low rank matrix estimation using either matrix-version Dantzig Selector $\hat{A}_λ^d$ or matrix-version LASSO estimator $\hat{A}_λ^L$. We consider sub-Gaussian measurements, $i.e.$, the measurements $X_1,\ldots,X_n\in\mathbb{R}^{m\times m}$ have $i.i.d.$ sub-Gaussian entries. Suppose $\textrm…

Spectral methods achieve near-optimal performance in orthogonal and permutation group synchronization.

While many multiple graph inference methodologies operate under the implicit assumption that an explicit vertex correspondence is known across the vertex sets of the graphs, in practice these correspondences may only be partially or errorfully known. Herein, we provide an information theoretic foundation for understand…

Adaptive spectral RL method enhances RL performance and interpretability.

Localizing targets of interest in a given hyperspectral (HS) image has applications ranging from remote sensing to surveillance. This task of target detection leverages the fact that each material/object possesses its own characteristic spectral response, depending upon its composition. As $\textit{signatures}$ of diff…

Improved spectral convergence bounds for diffusion maps on tori.

SC-Net learns interpretable filters for inverse problems, achieving optimal convergence and super-resolution.

We develop fast spectral algorithms for tensor decomposition that match the robustness guarantees of the best known polynomial-time algorithms for this problem based on the sum-of-squares (SOS) semidefinite programming hierarchy. Our algorithms can decompose a 4-tensor with $n$-dimensional orthonormal components in the…

In remote sensing, it is often challenging to acquire or collect a large dataset that is accurately labeled. This difficulty is usually due to several issues, including but not limited to the study site's spatial area and accessibility, errors in the global positioning system (GPS), and mixed pixels caused by an image'…

Analyzes how diffusion models learn, revealing a spectral bias in structure mastery.

Sharp pseudospectral bounds prevent transient amplification in coupled gradient descent.

Paper tackles robust graph matching in dense graphs with AMP type algorithm.