arXiv research

Paper finds configurations for spherical curves with reductivity four and constructs a reduced curve without certain types of polygons.

The reductivity of a spherical curve represents how reduced the spherical curve is. It is unknown if there exists a spherical curve whose reductivity is four. In this paper we give an unavoidable set for spherical curves with reductivity four by considering 4-gons.

We show that we can obtain a reducible spherical curve from any non-trivial spherical curve by four or less inverse-half-twisted splices, i.e., the reductivity, which represents how reduced a spherical curve is, is four or less. We also discuss unavoidable sets of tangles for spherical curves.

Study on links formed by pseudocircle arrangements, focusing on three unavoidable cases.

Before the operation of a motor imagery based brain-computer interface (BCI) adopting machine learning techniques, a cumbersome training procedure is unavoidable. The development of a practical BCI posed the challenge of classifying single-trial EEG with a small training set. In this letter, we addressed this problem b…

New simplicial complexes show unavoidable link of spheres in high dimensions.

Bayesian CG reduces PDEs with random coefficients to cheaper models.

This paper provides lower bounds on the convergence rate of Derivative Free Optimization (DFO) with noisy function evaluations, exposing a fundamental and unavoidable gap between the performance of algorithms with access to gradients and those with access to only function evaluations. However, there are situations in w…

Paper bridges AI/ML and causal modeling to reduce bias.

Optimal regularity theory for stable minimal hypersurfaces with small singular set.

We give a necessary and sufficient geometric structural condition for a stable codimension 1 integral varifold on a smooth Riemannian manifold to correspond to an embedded smooth hypersurface away from a small set of generally unavoidable singularities; when this condition is satisfied, the singular set is empty if the…

Harmonization schemes limit accuracy due to domain information.

Contextual bandits study how reward variance affects regret bounds.

$L_1$ regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, $L_1$ regularization typically selects too many features and that so-called false positives are unavoidable. In this pape…

Structured missing data complicates machine learning, presenting new challenges.

We show that there exist infinitely many pairs of distinct knots in the 3-sphere such that each pair can yield homeomorphic lens spaces by the same Dehn surgery. Moreover, each knot of the pair can be chosen to be a torus knot, a satellite knot or a hyperbolic knot, except that both cannot be satellite knots simultaneo…

Study sparsity benefits in infinite feature contextual bandits.

Cosine similarity can force points to grow in magnitude, causing convergence issues.

Defines crisis transitions in pure exchange economies rigorously.

Develops a parameter-free SGD algorithm with optimal convergence rate.

Study of Willmore energy on sphere sublevel sets and flow singularities.

The paper explores robustness in linear regression models under adversarial attacks.

New algorithm recovers graph structure from noisy data.

New algorithms achieve logarithmic regret in learning linear quadratic control systems.

Machine learning's predictive power is limited by sample size, as shown by the Limits-to-Learning Gap.

The paper uses EVT to improve tail risk measures under ambiguity sets.

Understanding the nature of dark energy, the mysterious force driving the accelerated expansion of the Universe, is a major challenge of modern cosmology. The next generation of cosmological surveys, specifically designed to address this issue, rely on accurate measurements of the apparent shapes of distant galaxies. H…

FTPL with Fréchet perturbation achieves near optimal regret bounds for m-set semi-bandit problems.

Paper warns of metric deformation in manifold learning, leading to incorrect answers.

Study on signal detection in sparse additive models with nonasymptotic minimax rates.

Abstract: Study of surface transitions and IDE inflections via contact geometry.

The interest rates (or nominal yields) can be negative, this is an unavoidable fact which has already been visible during the Great Depression (1929-39). Nowadays we can find negative rates easily by e.g. auditing. Several theoretical and practical ideas how to model and eventually overcome empirical negative rates can…

Two supervised methods classify single-molecule patterns from X-ray imaging.

A new method for handling missing values in data.

We study singularities of Lagrangian mean curvature flow in $\C^n$ when the initial condition is a zero-Maslov class Lagrangian. We start by showing that, in this setting, singularities are unavoidable. More precisely, we construct Lagrangians with arbitrarily small Lagrangian angle and Lagrangians which are Hamiltonia…

New method predicts model performance under selection bias in healthcare.

Paper adapts CVS method for TL in functional linear regression.

This work explains GAN mode collapse and convergence issues via optimal transportation theory.

New research shows invariant networks can approximate any continuous function.

The paper sets bounds on how much regret is unavoidable in adaptive LQR with unknown B-matrix.

Enhanced LSTM with multiple kernels and attention improves video action recognition.

The paper provides PAC bounds for estimating causal effects using covariate adjustment with a valid set.

Adversarial examples arise from computational constraints in high-dimensional spaces.

Momentum SGD fails to track nonstationary optima due to drift amplification.

Study shows multi-distribution learning has slower rates than single-task learning.

The paper studies how to make machine learning models robust to adversarial attacks.

Paper tackles domain adaptation in object detection, improving accuracy.

Thompson Sampling's performance degrades with approximate inference, especially under $α$-divergence.