The paper proposes using k-means clustering to improve SMC algorithms by fighting degeneracy.
problem Degeneracy in SMC methods where particles collapse onto a single particle.
method Integrates k-means clustering to initialize centers and adjust weights to improve performance.
result The proposed Stochastic SMC algorithm outperforms vanilla algorithms in experiments.
Improves unsupervised clustering using deep generative models with a Gaussian mixture prior.
problem Cluster degeneracy in variational autoencoders (VAEs).
method Applying a heuristic called minimum information constraint to mitigate over-regularization in a VAE with a Gaussian mixture prior.
result Demonstrates improved performance in unsupervised clustering on synthetic and real datasets.
New approach corrects latent space degeneracy in Variational Autoencoders.
problem Degeneracy in latent space of Variational Autoencoders.
method Perturbation theory to correct degeneracy in latent space.
result Corrected latent space degeneracy, leading to interpretable embeddings.
Research on mixed polynomials, extending non-degeneracy concepts to complex variables.
problem Extending non-degeneracy concepts to mixed polynomials in complex variables.
method Generalization of Mondal's partial non-degeneracy to mixed polynomials, introducing new concepts and proving properties.
result Strong partial non-degeneracy implies isolated singularities, and mixed polynomials that are strongly inner non-degenerate satisfy the strong Milnor condition.
Classifies patterns of symmetry breaking and vacuum degeneracy in scalar and gauge fields.
problem Understanding patterns of symmetry breaking and vacuum degeneracy in complex field systems.
method Uses mathematical classification of singular foliations to encode and classify patterns of spontaneous symmetry breaking and vacuum degeneracy.
result Mathematical classification provides a qualitative understanding of possible patterns of vacuum degeneracy.
CP degeneracy affects tensor regression solutions, especially in high dimensions.
problem CP degeneracy in tensor regression.
method Analysis of CP degeneracy and development of a penalized strategy.
result A general penalized strategy to overcome CP degeneracy in tensor regression.
Note removes degeneracy in Kähler geometry estimates.
problem Estimating diameter and inequalities in Kähler geometry with degeneracy.
method Technical improvement of earlier results.
result Established diameter, Green's functions, and Sobolev inequalities without small degeneracy assumption.
We construct a complete convergent normal form for a real hypersurface in $\CC{N},\,N\geq 2$ at generic Levi degeneracy. This seems to be the first convergent normal form for a Levi-degenerate hypersurface. In particular, we obtain, in the spirit of the work of Chern and Moser \cite{chern}, distinguished curves in the …
Proves non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics.
problem Non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics.
method Analyzes linearised Einstein operator in TT-gauge for Kottler metrics. result Non-degeneracy of TT-gauge-fixed linearised Einstein operator for most Riemannian Kottler metrics. Network degeneracy affects training performance, especially in deep networks.
problem Degeneracy in deep neural networks leads to poor training performance.
method Predicted degeneracy level correlates with training dynamics using finite and infinite width networks.
result Degeneracy in neural networks correlates with training performance and can be predicted.
TAMD prevents degeneracy in finite mixtures, offering strong guarantees but modest practical improvements.
problem Degeneracy in maximum likelihood estimation of finite mixtures.
method Transcendental regularization with analytic barrier functions.
result Strong theoretical guarantees (identifiability, consistency, robustness) but modest practical improvements.
We analyze relations between BPS degeneracies related to Labastida-Marino-Ooguri-Vafa (LMOV) invariants, and algebraic curves associated to knots. We introduce a new class of such curves that we call extremal A-polynomials, discuss their special properties, and determine exact and asymptotic formulas for the correspond…
New cylindrical solutions found for Grushin-type problem.
problem Critical Grushin-type problem on CR sphere.
method Local Pohozaev identities for non-degeneracy, Lyapunov-Schmidt reduction for solutions.
result New type of multi-bubbling cylindrical solutions constructed.
Geometric regularisation improves statistical models by avoiding degeneracy loci.
problem Non-identifiability, singular information, and moment indeterminacy in statistical models.
method Develops the geometric regularisation of distribution-kernel pairs (T,φ) using Whitney, Thom, and Mather theorems. result Finite-dimensional weak transversality theorem for generic kernels, avoiding degeneracy strata of high codimension.
Study non-degeneracy of minimal hypersurfaces asymptotic to cones, proving Jacobi equation solvability.
problem Non-degeneracy properties of minimal hypersurfaces asymptotic to cones.
method Analysis of the Jacobi operator and construction of its right inverse.
result Proved solvability of the Jacobi equation under non-degeneracy assumptions.
Investigates metric degeneracies on symplectic leaves using a generalized gradient flow.
problem Degeneracies in metrics on symplectic leaves of Poisson manifolds.
method Introduces the generalized double bracket (GDB) vector field to generalize gradient dynamics.
result Identifies admissible regions where the double bracket metric remains non-degenerate on symplectic leaves, enabling GDB as a gradient flow.
Improves machine translation by learning from user feedback.
problem Avoid showing inferior translations to users.
method Analyze degeneracies of counterfactual learning methods.
result Relates degeneracies to recent counterfactual learning techniques.
Study families of Morse functions for manifolds with boundary.
problem Characterize degeneracies in 1-parameter families of Morse functions.
method List all possible degeneracies in generic 1-parameter families.
result Identified all degeneracies in generic 1-parameter families.
The spectral properties of p-forms on the fundamental domains of regular tesselations of the d-dimensional sphere are discussed. The degeneracies for all ranks, p, are organised into a double Poincare series which is explicitly determined. In the particular case of coexact forms of rank (d-1)/2, for odd d, it is shown …
Investigates conditions for spectral sequence degeneracy in holomorphic Poisson structures.
problem Conditions for spectral sequence degeneracy in holomorphic Poisson structures.
method Uses Lie bi-algebroids, generalized complex structures, and hypercohomology of bi-complexes.
result Investigates conditions for spectral sequence degeneracy on the first page.
A method to automatically and symbolically detect and resolve degenerate parameter combinations from parameter-data pairs.
problem Identifying degenerate parameter combinations in physical models or real-world datasets.
method The degeneracy distillery method detects and resolves degenerate parameter combinations from parameter-data pairs.
result The method reduces the simulation budget required for downstream neural posterior estimation.
Study non-degenerate singular points of Poisson-Nijenhuis structures.
problem Non-degenerate singular points of Poisson-Nijenhuis structures.
method Completely describe pairs of compatible Poisson structures near singular points.
result Pairs of compatible Poisson structures near singular points are completely described.
Study proves non-degeneracy of certain metrics in linearized gravity.
problem Proving non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics.
method Analyzing solutions of the linearized Einstein equations around Kottler metrics.
result Linearized Einstein operator is non-degenerate for open ranges of mass parameter.
Study on automorphisms of complex bk-manifolds, extending previous work.
problem Investigate automorphisms of complex bk-manifolds with higher-order degeneracies. method Extend Mendoza's definition of complex b-manifolds to complex bk-manifolds and study their local and global automorphisms. result Propose bk-analogues for classical spaces of holomorphic functions. Holomorphic residue formula for complex supermanifolds.
problem Residue localization on complex supermanifolds.
method Holomorphic residue localization formula for odd vector fields.
result Explicit local residue formula under isolated non-degeneracy hypotheses.
Integral inequalities for holomorphic maps prove rigidity and degeneracy theorems.
problem Rigidity and degeneracy theorems for holomorphic maps without curvature sign assumptions.
method Integral inequalities derived from holomorphic maps between complex manifolds.
result Proves rigidity and degeneracy theorems for holomorphic maps.
Generalizing some results from R. Leung's thesis, we compute, in rational cohomology, the Poincare dual of the degeneracy locus of the family of Dirac operators parameterized by the moduli space of projectively anti-self-dual $\SO(3)$ connections. This is the first step in a program to derive a relation between the Don…
Study on existence of p-Kähler structures on nilmanifolds with nilpotent complex structures.
problem Existence of p-Kähler structures on nilmanifolds with nilpotent complex structures. method Determine optimal p for existence of p-Kähler structures and analyze the relationship between balanced metrics and degeneracy steps of the Frölicher spectral sequence. result No p-Kähler structures exist for an optimal p on nilmanifolds with nilpotent complex structures. Proves existence of proper solutions for inverse mean curvature flow.
problem Existence of proper solutions for inverse mean curvature flow.
method Proves existence theorem assuming non-degeneracy conditions on isoperimetric profile.
result No curvature assumption in existence theorem.
Tian's theorem connects Chern classes of bundles to random section zeros and degeneracy sets.
problem Understanding the distribution of zeros and degeneracy sets of random holomorphic sections.
method Analyzing the pullback of Chern classes and computing currents of integration.
result The limit distribution of zeros of random sections is determined by the Chern form.
Unified Morse-Bott-Smale chain complex, resolves well-definedness issue.
problem Well-definedness of Morse-Bott-Smale chain complex.
method Unified five degeneracy relations into a single condition.
result Quasi-isomorphic to Morse-Smale-Witten chain complex, alternative proof of Morse Homology Theorem.
Study confirms C1 regularity for convex functionals with bounded degeneracy set.
problem Confirming C1 regularity for minimizers of convex functionals with small degeneracy set. method Building on previous work, confirms C1 regularity when D2F is positive and bounded away from finitely many points. Constructs a counterexample in R4 where F is strictly convex but D2F degenerates on a Simons cone intersection. result Confirms C1 regularity for minimizers of convex functionals with small degeneracy set. In this paper, we study the interplay between modules and sub-objects in holomorphic Poisson geometry. In particular, we define a new notion of "residue" for a Poisson module, analogous to the Poincaré residue of a meromorphic volume form. Of particular interest is the interaction between the residues of the canonical …
Compact K3 metrics derived from string theory vacua.
problem Finding Ricci-flat metrics on K3 surfaces.
method Using little string theory and BPS degeneracies.
result Systematic procedure for determining K3 metrics.
Study slopes in 3-manifolds, proving conjectures about knots.
problem Understanding slopes in 3-manifolds and their implications for knots.
method Upper bounds on distances between slopes, applications to knots and surgeries.
result Bounds on boundary and degeneracy slopes for knots in 3-manifolds.
New framework scales graph AE and VAE by training on a subset of nodes.
problem Training scalability and speed issues in graph AE and VAE models.
method Utilizes graph degeneracy to train on a dense subset of nodes, with a propagation mechanism.
result Empirically competitive results on large graphs (millions of nodes and edges).
A new method for neural network initialization using graph degeneracy.
problem Improving neural network performance through better initialization.
method Adapted k-hypercore decomposition for neural network initialization.
result k-hypercore outperforms state-of-the-art initialization methods.
The paper studies parallel surfaces of cuspidal cross caps and their degeneracy.
problem Investigating the geometry and singularities of parallel surfaces of cuspidal cross caps.
method Established a criterion for the degeneracy of the distance squared function using geometric invariants.
result Parallel surfaces degenerate into a degenerated cuspidal S1 singularity at specific distances.
The paper examines how the angle between inputs in ReLU networks decreases with depth, impacting training.
problem Depth degeneracy in neural networks, leading to constant function behavior on initialization.
method Combinatorial expansions and Monte Carlo experiments to analyze the angle between inputs in ReLU networks of increasing depth.
result The angle between inputs in ReLU networks decreases exponentially with depth, leading to constant function behavior on initialization.
UBVI improves variational inference by preventing degeneracy and improving scalability.
problem Degeneracy and scalability issues in variational inference.
method Exploits Hellinger metric geometry to prevent degeneracy, simplifies weight optimization, and uses scalable exponential family mixture components.
result Output of UBVI converges to best possible approximation in any mixture family, even when misspecified.
Local bifurcation theory typically deals with the response of a degenerate but isolated equilibrium state or periodic orbit of a dynamical system to perturbations controlled by one or more independent parameters, and characteristically uses tools from singularity theory. There are many situations, however, in which the…
Study of maximum likelihood under biased constraints reveals novel degeneracies and anomalous statistical behavior.
problem Investigating maximum likelihood under biased estimating equations.
method Analyzing the behavior of optimal distributions and log-likelihood statistics under mis-specification.
result Degeneracies in optimal distributions and anomalous behavior of log-likelihood statistics under mis-specification.
Unified interpretation of sub-Riemannian Gauss-Bonnet theorem for surfaces in 3D contact manifolds.
problem Proving a sub-Riemannian Gauss-Bonnet theorem for surfaces in 3D contact manifolds.
method Measure-theoretic perspective, focusing on singular measures and characteristic points.
result Unified interpretation of previous results and natural geometric conditions for the theorem.
The geography problem is usually stated for simply connected symplectic 4-manifolds. When the first cohomology is nontrivial, however, one can restate the problem taking into account how close the symplectic manifold is to satisfying the conclusion of the Hard Lefschetz Theorem, which is measured by a nonnegative integ…
This paper studies Poisson structures defined by divisor ideals.
problem Understanding Poisson structures with degeneracy captured by divisor ideals.
method Developed a framework using divisor ideals and Lie algebroids.
result Effective methods for studying Poisson structures of divisor-type.
The paper studies the distribution of random degeneracy sets on complex manifolds.
problem Distribution of random degeneracy sets on compact Kähler manifolds.
method Asymptotic expansion of induced Grassmannian Chern forms, meromorphic transforms, and Wishart distribution.
result Normalized currents converge to curvature forms with quantitative estimates.
New research suggests deep networks converge to saddle points with high degeneracy.
problem Understanding the convergence of deep neural networks to saddle points.
method Empirical studies and theoretical findings to validate the hypothesis.
result Deep neural networks converge to saddle points with high degeneracy, not just local minima.
This paper introduces a scalable benchmark for evaluating local posterior sampling in neural networks.
problem Degeneracy in neural network loss landscapes and its impact on SGMCMC algorithms.
method Development of a scalable benchmark for local posterior sampling.
result RMSProp-preconditioned SGLD is most effective at representing the local geometry of the posterior distribution.