arXiv research

New matrix ensembles better match deep neural network spectral densities.

PCA can detect a low-rank signal but is suboptimal for non-Gaussian matrices and synchronization problems.

PCA can detect a low-rank signal in spiked random matrix models, but not always optimally.

Researchers found the Wigner derivative and its inverse are equal for spherical tetrahedra.

SPQR improves Q-ensemble diversity in reinforcement learning.

The paper studies the geometry of Wigner caustics and decomposes curves into parallel arcs.

The paper examines singular points in Wigner caustics and affine equidistants of planar curves.

We show that, for each alpha in the interval (-1,1), the only Riemannian metrics on the space of positive definite matrices for which the alpha and -alpha-connections are mutually dual are matrix multiples fo the Wigner-Yanase-Dyson metric. If we further impose that the metric be monotone, then this set is reduced to s…

Wigner's theorem asserts that an isometric (probability conserving) transformation on a quantum state space must be generated by a Hamiltonian that is Hermitian. It is shown that when the Hermiticity condition on the Hamiltonian is relaxed, we obtain the following complex generalisation of Wigner's theorem: a holomorph…

Optimal spectral method found for inhomogeneous spiked Wigner model.

Study on eigenvalue distribution of correlated time series deforming the semi-circle law.

Generalizes JT gravity to time-reversal symmetric theories with fermions and supersymmetry.

Extends Wigner's representation to study super hyperbolic geometry.

A novel method computes Wigner kernels for atomic environments, achieving state-of-the-art accuracy.

We study random Morse functions on a Riemann manifold $(M^m,g)$ defined as a random Gaussian weighted superpositions of eigenfunctions of the Laplacian of the metric $g$. The randomness is determined by a fixed Schwartz function $w$ and a small parameter $\varepsilon>0$. We first prove that as $\varepsilon\to 0$ the ex…

Consistent model selection for spiked Wigner model via AIC-type criteria.

A test for weak signal detection in noisy data matrices.

Study detects signals in spiked Wigner models using log likelihood ratio.

Paper analyzes Birkhoff relaxation for graph alignment, providing theoretical guarantees.

Paper improves isoperimetric inequality with new curve properties.

Study on limits of detecting a rank-one perturbation in Wigner matrices.

Affine $λ$-equidistants of convex polygons with parallel opposite sides have applications to isoperimetric inequalities.

On the manifold of positive definite matrices, we investigate the existence of pairs of flat affine connections, dual with respect to a given monotone metric. The connections are defined either using the $α$-embeddings and finding the duals with respect to the metric, or by means of contrast functionals. We show that i…

Extends particle classification to curved space-times using groupoids.

Study of correlated Wigner matrices with BBP transitions.

Paper develops new method for detecting latent structure in large symmetric data matrices.

We present an original and novel method based on random matrix approach that enables to distinguish the respective role of temporal autocorrelations inside given time series and cross correlations between various time series. The proposed algorithm is based on properties of Wigner eigenspectrum of random matrices inste…

Study asymptotics of unitary matrix elements in quantum mechanics.

Signatures of universality are detected by comparing individual eigenvalue distributions and level spacings from financial covariance matrices to random matrix predictions. A chopping procedure is devised in order to produce a statistical ensemble of asset-price covariances from a single instance of financial data sets…

Study isoperimetric equalities for special closed curves.

Study optimal algorithms for recovering signals through inhomogeneous low-rank channels.

GRAMPA algorithm recovers latent vertex correspondence in correlated graphs with high probability.

Study finds spurious correlations in LIBOR rates due to bank manipulation.

We prove that either the images of the mapping class groups by quantum representations are not isomorphic to higher rank lattices or else the kernels have a large number of normal generators. Further we show that the images of the mapping class groups have nontrivial 2-cohomology, at least for small levels. For this pu…

Study on complexity of random polynomials with deterministic spikes, identifying phase transitions.

A new geometric approach to quantum mechanics simplifies time-dependent problems.

PPM improves graph matching for correlated Gaussian Wigner models with high probability.

Lower bounds on gradient queries for minimizing convex quadratic functions.

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

Optimal test for detecting signal in noisy matrix model.

Study Liouville action on quasi-Fuchsian groups, proving formulas and relating to holography.

The paper sets thresholds for testing correlation in hypergraphs, distinguishing between independent and correlated states.

Paper studies vertex correspondence recovery in correlated graphs with node features.

New research suggests deep networks converge to saddle points with high degeneracy.

Paper proposes new methods for improving interatomic potentials.

Simplified Ricci curvature for spherical fluid dynamics models.

Algorithm detects and estimates correlated signals in spiked matrices.

Paper solves graph matching problem using convex relaxation to the simplex.