arXiv research

EagleEye detects localized density anomalies in multivariate data.

This work tackles sequential data learning challenges by improving neural network robustness to non-iid distribution shifts.

An important part of the classical theory of real or complex manifolds is the theory of (smooth, real analytic or complex analytic) vector bundles. With any vector bundle over a manifold (M,F) the sheaf of its (smooth, real analytic or complex analytic) sections is associated which is a locally free sheaf of F-modules,…

We define Radon transform and its inverse on the two-dimensional anti-de Sitter space over local fields using a novel construction through a quadratic equation over the local field. We show that the holographic bulk reconstruction of quantum fields in this space can be formulated as the inverse Radon transform, general…

Paper classifies pseudomanifolds over stratified spaces.

Investigate local Lie group structure of bisections over compact manifolds

Local convergence theory for mildly over-parameterized neural nets.

Let $A$ be a finite-dimensional local commutative algebra over $R$, $\dim_RA=n$. In this work we consider compact manifolds over $A$, and prove that the real part of an $A$-differentiable function is constant. Also we find estimates for the dimensions of some spaces of 1-form.

In this paper, we analyze the effects of depth and width on the quality of local minima, without strong over-parameterization and simplification assumptions in the literature. Without any simplification assumption, for deep nonlinear neural networks with the squared loss, we theoretically show that the quality of local…

Proposes a continuous, differentiable model from local adaptive models.

We examine the $L^2$-topology of the gauge orbits over a closed Riemann surface. We prove a subtle local slice theorem based on the div-curl Lemma of harmonic analysis, and deduce local pathwise connectedness and local uniform quasiconvexity of the gauge orbits. Using these, we generalize compactness results for anti-s…

We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results for systoles of local systems.

LES optimizes designs by sampling descent sequences, achieving strong sample efficiency.

Convolutional Neural Networks (CNN) and the locally connected layer are limited in capturing the importance and relations of different local receptive fields, which are often crucial for tasks such as face verification, visual question answering, and word sequence prediction. To tackle the issue, we propose a novel loc…

A new framework enhances generative modeling by learning local flows over complex manifolds.

Generalizes abelianization for framed local systems over surfaces.

We consider a distributed learning setup where a sparse signal is estimated over a network. Our main interest is to save communication resource for information exchange over the network and reduce processing time. Each node of the network uses a convex optimization based algorithm that provides a locally optimum soluti…

LSH methods extend to function spaces for efficient similarity search.

It is proved that the continuous bounded cohomology of SL_2(k) vanishes in all positive degrees whenever k is a non-Archimedean local field. This holds more generally for boundary-transitive groups of tree automorphisms and implies low degree vanishing for SL_2 over S-integers.

The study examines non-Kähler threefolds with specific metrics and finds they are quasi-bundles over surfaces.

Paper shows faster convergence to local-minimizers in over-parametrized models under interpolation-like conditions.

Paper addresses FL over MAC with DP constraints, proposing a novel consensus scheme.

We complete the quasi-isometric classification of irreducible lattices in semisimple Lie groups over nondiscrete locally compact fields of characteristic zero by showing that any quasi-isometry of a rank one S-arithmetic lattice in a semisimple Lie group over nondiscrete locally compact fields of characteristic zero is…

We study the Selberg zeta and the theta function associated to bundles over even-dimensional locally symmetric spaces of rank one.

Graphs can be smoothed or squashed too, study finds.

We characterize compact locally conformal parallel $G_2$ (respectively, $Spin(7)$) manifolds as fiber bundles over $S^1$ with compact nearly Kähler (respectively, compact nearly parallel $G_2$) fiber. A more specific characterization is provided when the local parallel structures are flat.

Improves multi-objective learning by adapting to local subintervals.

Homological algebra used to study local equivalence of complex rings.

We study an infinite dimensional ASD moduli space over the cylinder. Our main result is the formula of its local mean dimension. A key ingredient of the argument is the notion of non-degenerate ASD connections. We develop its deformation theory and show that there exist sufficiently many non-degenerate ASD connections …

Principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To every triangulated circle bundle over a simplex we associate a necklace (in combinatorial sense). We express rational local formulas for all…

We compute the local Lipschitz constant of ReLU networks precisely.

Distributed optimization often consists of two updating phases: local optimization and inter-node communication. Conventional approaches require working nodes to communicate with the server every one or few iterations to guarantee convergence. In this paper, we establish a completely different conclusion that each node…

A new method boosts graph neural networks by preventing over-smoothing and over-squashing.

Classifies limits of groups of involutions in SL(2,F) over local fields.

Paper proves stability of positive mass theorem for specific types of manifolds.

New Q-manifolds theory integrates Lie algebroids.

PF-LaCG removes the need for knowing smoothness and strong convexity parameters for locally accelerated CG.

In this paper we prove that over an asymptotically locally flat (ALF) Riemannian four-manifold the energy of an "admissible" SU(2) Yang--Mills is always integer. This result sharpens the previously known energy identity for such Yang--Mills instantons over ALF geometries. Furthermore we demonstrate that this statement …

A local monotonicity formula for the Yang-Mills-Higgs flow on $G$-bundles over $\mathbb{R}^{n}$ ($n>4$) is proved. It is shown that the monotone quantity coïncides on certain self-similar solutions with that appearing in existing non-local monotonicity formulæ for the Yang-Mills and Yang-Mills-Higgs flows.

InstantEmbedding efficiently generates node representations with less computation and memory.

We trained and evaluated a localization-based deep CNN for breast cancer screening exam classification on over 200,000 exams (over 1,000,000 images). Our model achieves an AUC of 0.919 in predicting malignancy in patients undergoing breast cancer screening, reducing the error rate of the baseline (Wu et al., 2019a) by …

We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed. Special attention is paid to the case of mappings between topological vector spaces ov…

Local search improves GFlowNets' ability to generate high-reward samples.

Study algebraic obstructions to knot-like complex realizability.

We introduce the notion of a {\vartheta}-summable Fredholm module over a locally convex dg algebra Ω and construct its Chern character as a cocycle on the entire cyclic complex of Ω, extending the construction of Jaffe, Lesniewski and Osterwalder to a differential graded setting. Using this Chern character, we prove an…

Proposes a framework to incorporate global sensitivity into local surrogate models.

Ricci flow smooths locally collapsing manifolds with controlled curvature.

The paper extends local h-principles to complex structures on Stein manifolds.