arXiv research

A new sampler for FLMs improves token-level decoding controls.

3MSBM learns smooth trajectories from multiple snapshots.

Neural networks can approximate high-dimensional classifiers with ReLU networks under margin conditions.

Study minimax rates for binary classifier estimation with margin conditions.

Study shows exponential error reduction in multiclass classification without bias-variance trade-off.

Risk bounds for Classification and Regression Trees (CART, Breiman et. al. 1984) classifiers are obtained under a margin condition in the binary supervised classification framework. These risk bounds are obtained conditionally on the construction of the maximal deep binary tree and permit to prove that the linear penal…

Active learning can't improve over passive in certain settings.

Paper shows SVM can achieve super fast convergence rates.

Researchers expand on best subset selection theory, identifying key complexities.

Develops a Best-of-Both-Worlds algorithm for linear contextual bandits with Tsallis entropy.

New test for conditional independence using GNNs avoids estimating conditional distributions.

New algorithm reduces regret in GLM bandits with tighter bounds.

Proposes methods to identify and estimate counterfactual distributions with confounding.

Study online learning of neural networks with margin condition.

A new policy learning method allows policies to abstain when uncertain, improving safety and applicability.

Paper solves nonparametric contextual bandit with unbounded contexts.

Thresholded Lasso bandit minimizes regret in sparse linear bandits.

Empirical risk minimization (ERM) is a fundamental learning rule for statistical learning problems where the data is generated according to some unknown distribution $\mathsf{P}$ and returns a hypothesis $f$ chosen from a fixed class $\mathcal{F}$ with small loss $\ell$. In the parametric setting, depending upon $(\ell…

This paper is devoted to the bipartite ranking problem, a classical statistical learning task, in a high dimensional setting. We propose a scoring and ranking strategy based on the PAC-Bayesian approach. We consider nonlinear additive scoring functions, and we derive non-asymptotic risk bounds under a sparsity assumpti…

In this paper we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation conditional to a rare eve…

Post-training optimizes model performance beyond base model limits.

We consider the stochastic contextual bandit problem with additional regularization. The motivation comes from problems where the policy of the agent must be close to some baseline policy which is known to perform well on the task. To tackle this problem we use a nonparametric model and propose an algorithm splitting t…

New examples of knots with special bridge positions found.

The paper provides examples of keen weakly reducible bridge spheres for links in b-bridge position.

We compute the bridge spectra of cables of 2-bridge knots. We also give some results about bridge spectra and distance of Montesinos knots.

Any 2-bridge knot in the 3-sphere has a bridge sphere from which any other bridge surface can be obtained by stabilization, meridional stabilization, perturbation and proper isotopy.

Suppose a knot in a $3$-manifold is in $n$-bridge position. We consider a reduction of the knot along a bridge disk $D$ and show that the result is an $(n-1)$-bridge position if and only if there is a bridge disk $E$ such that $(D, E)$ is a cancelling pair. We apply this to an unknot $K$, in $n$-bridge position with re…

We define and compare several natural ways to compute the bridge number of a knot diagram. We study bridge numbers of crossing number minimizing diagrams, as well as the behavior of diagrammatic bridge numbers under the connected sum operation. For each notion of diagrammatic bridge number considered, we find crossing …

Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and hard to approximate in the presence of negative correlations, DPPs offer efficie…

New method finds infinitely many surface knots with specific bridge numbers.

Researchers found infinite links with specific bridge positions.

We show that if $K$ is a knot in $S^3$ and $Σ$ is a bridge sphere for $K$ with high distance and $2n$ punctures, the number of perturbations of $K$ required to interchange the two balls bounded by $Σ$ via an isotopy is $n$. We also construct a knot with two different bridge spheres with $2n$ and $2n-1$ bridges respecti…

We show that for every integer $b\geq 3$, there exists a link in a $b$-bridge position with respect to a critical bridge sphere. In fact, for each $b$, we construct an infinite family of links which we call square whose bridge spheres are critical.

Two-bridge ribbon knots have symmetric union presentations.

We give a locally minimal, but not globally minimal bridge position of a knot, that is, an unstabilized, nonminimal bridge position of a knot. It implies that a bridge position cannot always be simplified so that the bridge number monotonically decreases to the minimal.

Paper explores link and plat presentations, showing equivalence under bridge isotopy.

We give a complete characterization of those essential simple loops on 2-bridge spheres of 2-bridge links which are null-homotopic in the link complements. By using this result, we describe all upper-meridian-pair-preserving epimorphisms between 2-bridge link groups.

Bridge positions of handlebody-knots are equivalent when stable.

Paper refines generating function for 2-bridge knot groups.

The study calculates braid indices for two-bridge knots and proves inequalities.

We show that there exists an infinite family of knots, each of which has, for each integer k>=0, a destabilized (2k+5)-bridge sphere. We also show that, for each integer n>=4, there exists a knot with a destabilized 3-bridge sphere and a destabilized n-bridge sphere.

For any given number of crossings $c$, there exists a formula to determine the number of 2-bridge knots of $c$ crossings, and indeed it is a simple matter to actually construct presentations of these knots. However, the determination of whether a given (prime) knot is a 2-bridge knot remains a nontrivial exercise, and …

A new generative adversarial network is developed for joint distribution matching. Distinct from most existing approaches, that only learn conditional distributions, the proposed model aims to learn a joint distribution of multiple random variables (domains). This is achieved by learning to sample from conditional dist…

In this paper and its prequel, we give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in an even Heckoid orbifold for a 2-bridge link to be homotopic in the orbifold. We also give a necessary and sufficient condition for an essential simple loop on a 2-bridge sphere in an even …

Perturbing non-minimal bridge positions of a knot ensures similar behavior for its cable links.

The author, in her previous paper, constructed an infinite family of 3-bridge links each of which admits infinitely many 3-bridge spheres up to isotopy. In this paper, we prove that if a prime, unsplittable link $L$ in $S^3$ admits infinitely many 3-bridge spheres up to isotopy then $L$ belongs to the family.

The purpose of this note is to announce complete answers to the following questions. (1) For an essential simple loop on a 2-bridge sphere in a 2-bridge link complement, when is it null-homotopic in the link complement? (2) For two distinct essential simple loops on a 2-bridge sphere in a 2-bridge link complement, when…

In this paper and its sequel, we give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in an even Heckoid orbifold for a 2-bridge link to be homotopic in the orbifold. We also give a necessary and sufficient condition for an essential simple loop on a 2-bridge sphere in an even H…