arXiv research

Study confirms boundedness of certain singularities in log Fano geometry.

Characterizes toroidal and semi-toric compactifications as log minimal models and applies to weak K-moduli.

Sharp bound on smallest diameter of hyperbolic surfaces.

Study shows boundedness of klt singularities in 3D or with bounded Kollár components.

Log minimality proven for weak K-moduli compactifications of Calabi-Yau varieties.

Let $δ_{g,n}$ be the minimal dilatation of pseudo-Anosovs defined on an orientable surface of genus $g$ with $n$ punctures. Tsai proved that for any fixed $g \ge 2$, the logarithm of the minimal dilatation $\log δ_{g,n}$ is on the order of $\frac{\log n}{n}$. The main result of this paper is that if $2g+1$ is relativel…

New proof of harmonic map uniqueness with analytic targets.

We study surfaces in Euclidean space ${\mathbb R}^3$ that are minimal for a log-linear density $φ(x,y,z)=αx+βy+γy$, where $α,β,γ$ are real numbers not all zero. We prove that if a surface is $φ$-minimal foliated by circles in parallel planes, then these planes are orthogonal to the vector $(α,β,γ)$ and the surface must…

The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly convex minimization problems. Typical applications include many popular statistical…

Proposes CLUB for reliable MI minimization in high dimensions.

New method for robust distribution alignment using log-likelihood ratio and normalizing flows.

Thresholded Lasso bandit minimizes regret in sparse linear bandits.

We survey some recent topics on singularities, with a focus on their connection to the minimal model program. This includes the construction and properties of dual complexes, the proof of the ACC conjecture for log canonical thresholds and the recent progress on the `local stability theory' of an arbitrary Kawamata log…

We demonstrate that, in the classical non-stochastic regret minimization problem with $d$ decisions, gains and losses to be respectively maximized or minimized are fundamentally different. Indeed, by considering the additional sparsity assumption (at each stage, at most $s$ decisions incur a nonzero outcome), we derive…

After establishing suitable notions of stability and Chern classes for singular pairs, we use Kähler-Einstein metrics with conical and cuspidal singularities to prove the slope semistability of orbifold tangent sheaves of minimal log-canonical pairs of log general type. We then proceed to prove the Miyaoka-Yau inequali…

Study designs logging policies to minimize off-policy evaluation error.

Proves unique degeneration of log Fano fibration germs.

Proposes a new Huber loss combining absolute and quadratic properties.

We show that the minimal number of colors for all effective $n$-colorings of a link with non-zero determinant is at least $1+\log_2 n$.

SUMO provides unbiased log marginal likelihood estimation for latent variable models.

Estimates Schrödinger potentials with minimal sample size.

New framework improves EM algorithm convergence under log-Sobolev inequality.

New inequality shows energy growth and decay in geometric problems.

SVRN accelerates Newton methods by reducing variance and improving performance.

The paper improves sparse Gaussian processes by optimizing predictive loss.

Minimal geodesics on hyperbolic surfaces are long.

A new method combines online and offline learning to tackle contextual bandits with missing action support.

This paper concerns the set $\hat{\mathcal{M}}$ of pseudo-Anosovs which occur as monodromies of fibrations on manifolds obtained from the magic 3-manifold $N$ by Dehn filling three cusps with a mild restriction. We prove that for each $g$ (resp. $g \not\equiv 0 \pmod{6}$), the minimum among dilatations of elements (res…

We explain SSL objectives as log-likelihoods in a data curation model.

Paper extends SMM to weakly convex and multi-convex surrogates for non-convex optimization.

DLM for BNNs fails to improve over ELBO optimization.

New algorithms reduce matching regret by limiting frequent updates.

New algorithms reduce matching market regret to log(T) with improved stability.

A new VIS approach improves log-likelihood estimation in latent variable models.

Efficiently matches random graphs with inhomogeneous edge probabilities.

In this paper, we prove the openness of K-semistability in families of log Fano pairs by showing that the stability threshold is a constructible function on the fibers. We also prove that any special test configuration arises from a log canonical place of a bounded complement and establish properties of any minimizer o…

GN algorithm solves batched bandit for nondegenerate functions near-optimally.

Improves Gaussian process regression without bias.

Study proves uniqueness of Yang-Mills field tangent cones in arbitrary dimensions.

Equivalence proven between algebraic stability and geometric stability.

New privacy mechanism reduces error in query results.

We prove that the minimal diameter of a hyperbolic compact orientable surface of genus $g$ is asymptotic to $\log g$ as $g \to \infty$. The proof relies on a random construction, which we analyse using lattice point counting theory and the exploration of random trivalent graphs.

A new Bayesian filtering method speeds up stochastic Newton optimization.

A new estimator for evaluating policies in unknown environments.

This work improves regret minimization for logistic bandits by reducing dependence on a large constant.

Let X be a complex projective variety and D a reduced divisor on X. Under a natural minimal condition on the singularities of the pair (X, D), which includes the case of smooth X with simple normal crossing D, we ask for geometric criteria guaranteeing various positivity conditions for the log-canonical divisor K_X+D. …

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

For all $n$, we define the $n$-dimensional critical catenoid $M_n$ to be the unique rotationally symmetric, free boundary minimal hypersurface of non-trivial topology embedded in the closed unit ball in $\Bbb{R}^{n+1}$. We show that the Morse index $\text{MI}(n)$ of $M_n$ satisfies the following asymptotic estimate as …