arXiv research

The study predicts pass completion probability in NFL games.

Complete classification of links up to specific moves.

Proposes a new method for predicting missing relations in knowledge graphs.

Develops a Gaussian-based message-passing algorithm for noisy matrix completion.

Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as maximum a posteriori inference problems in a graphical model and present a message p…

A pass-move and a $#$-move are local moves on oriented links defined by L.H. Kauffman and H. Murakami respectively. Two links are self pass-equivalent (resp. self $#$-equivalent) if one can be deformed into the other by pass-moves (resp. $#$-moves), where non of them can occur between distinct components of the link. T…

The goal of this paper is to describe all local diffeomorphisms mapping a family of circles, in an open subset of $\r^3$, into straight lines. This paper contains two main results. The first is a complete description of the rectifiable collection of circles in $\r^3$ passing through one point. It turns out that to be r…

New theorem finds new minimal hypersurfaces in hyperbolic space.

Unified theory linking atom-centered and message-passing models for molecular properties.

I begin by giving a general discussion of completely integrable Hamiltonian systems in the setting of contact geometry. We then pass to the particular case of toric contact structures on the manifold $S^2\times S^3$. In particular we give a complete solution to the contact equivalence problem for a class of toric conta…

Given a hyperbolic surface $§$, a classic result of Birman and Series states that for each $K$, all complete geodesics with at most $K$ self-intersections can only pass through a certain nowhere dense, Hausdorff dimension 1 subset of $§$. We define a self-intersection function for each complete geodesic, which bounds t…

Sparse sampling method for tensor factorization and completion of high rank tensors.

Polar manifolds are Riemannian G-manifolds admitting a "section", i.e., a complete submanifold passing through every orbit and doing so orthogonally. We consider compact simply-connected polar manifolds and achieve an equivariantly diffeomorphic classification in dimensions 5 or less. As an application, we determine wh…

A genus-1 tangle G is an arc properly embedded in a standardly embedded solid torus S in the 3-sphere. We say that a genus-1 tangle embeds in a knot K in S^3 if the tangle can be completed by adding an arc exterior to the solid torus to form the knot K. We call K a closure of G. An obstruction to embedding a genus-1 ta…

Study nondegenerate singularities in mean curvature flow.

Study on nonlinear elliptic equations with variable exponents, proving existence and multiplicity of solutions.

A new single-pass algorithm improves sparse PCA under limited computational resources.

We consider matrix completion for recommender systems from the point of view of link prediction on graphs. Interaction data such as movie ratings can be represented by a bipartite user-item graph with labeled edges denoting observed ratings. Building on recent progress in deep learning on graph-structured data, we prop…

A new GNM model outperforms MLP for tabular data.

A {\em good drawing\/} of $K_n$ is a drawing of the complete graph with $n$ vertices in the sphere such that: no two edges with a common end cross; no two edges cross more than once; and no three edges all cross at the same point. Gioan's Theorem asserts that any two good drawings of $K_n$ that have the same rotations …

Researchers prove rigidity for log-Sobolev inequality on specific metric spaces.

The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a W…

We develop an efficient alternating framework for learning a generalized version of Factorization Machine (gFM) on steaming data with provable guarantees. When the instances are sampled from $d$ dimensional random Gaussian vectors and the target second order coefficient matrix in gFM is of rank $k$, our algorithm conve…

In this paper, we consider the streaming memory-limited matrix completion problem when the observed entries are noisy versions of a small random fraction of the original entries. We are interested in scenarios where the matrix size is very large so the matrix is very hard to store and manipulate. Here, columns of the o…

Google's Cloud TPUs are a promising new hardware architecture for machine learning workloads. They have powered many of Google's milestone machine learning achievements in recent years. Google has now made TPUs available for general use on their cloud platform and as of very recently has opened them up further to allow…

Improved single-pass streaming MAB regret bound to O(K^1/3T^2/3).

We analyze oversquashing in topological message-passing using relational structures.

Message passing is the key to graph neural networks, but new terms are needed to avoid confusion.

Optimizes reinforcement learning by prioritizing sets of samples over individual ones.

We construct a new spectral sequence beginning at the Khovanov homology of a link and converging to the Khovanov homology of the disjoint union of its components. The page at which the sequence collapses gives a lower bound on the splitting number of the link, the minimum number of times its components must be passed t…

DDEQs extend DEQs to discrete measure inputs using Wasserstein gradient flows.

This article is motivated by soccer positional passing networks collected across multiple games. We refer to these data as replicated spatial passing networks---to accurately model such data it is necessary to take into account the spatial positions of the passer and receiver for each passing event. This spatial regist…

ADMP-GNN dynamically adjusts message-passing layers for better graph learning performance.

A new knot move preserves pass-move equivalence and differs in count.

Every classical knot is band-pass equivalent to the unknot or the trefoil. The band-pass class of a knot is a concordance invariant. Every ribbon knot, for example, is band-pass equivalent to the unknot. Here we introduce the long virtual knot concordance group $\mathscr{VC}$. It is shown that for every concordance cla…

We prove: If a complete connected smooth surface M in euclidean 3-space has general position, intersects some plane along a clean figure-8 (a loop with total curvature zero) and all compact intersections with planes have central symmetry, then M is a (geometric) cylinder over some central figure-8. On the way, we estab…

In this paper we study constant mean curvature surfaces $Σ$ in a product space, $\mathbb{M}^2\times \mathbb{R}$, where $\mathbb{M}^2$ is a complete Riemannian manifold. We assume the angle function $ν= \meta{N}{\partial_t}$ does not change sign on $Σ$. We classify these surfaces according to the infimum $c(Σ)$ of the G…

We study generalizations of finite-type knot invariants obtained by replacing the crossing change in the Vassiliev skein relation by some other local move, analyzing in detail the band-pass and doubled-delta moves. Using braid-theoretic techniques, we show that, for a large class of local moves, generalized Goussarov's…

Study of minimal surfaces in 4D with specific ends.

New MCMC algorithm reduces subset selection passes to 2 for optimal $k$-dimensional subspace approximation.

A new model prices assets considering market microstructure effects.

Factor graphs have recently gained increasing attention as a unified framework for representing and constructing algorithms for signal processing, estimation, and control. One capability that does not seem to be well explored within the factor graph tool kit is the ability to handle deterministic nonlinear transformati…

CPS solves inverse problems using forward passes and constrained particle seeking.

New algorithm reduces memory-regret trade-off for bandits.

We consider stochastic gradient descent (SGD) for least-squares regression with potentially several passes over the data. While several passes have been widely reported to perform practically better in terms of predictive performance on unseen data, the existing theoretical analysis of SGD suggests that a single pass i…

New graph coarsening method preserves GNN message-passing signals.

Study on convergence of graph neural networks on random graphs.

Convex surfaces derived from specific Riemannian manifolds with high regularity.