arXiv research

New method improves smoothness of robot learning.

Deep neural networks are susceptible to adversarial manipulations in the input domain. The extent of vulnerability has been explored intensively in cases of $\ell_p$-bounded and $\ell_p$-minimal adversarial perturbations. However, the vulnerability of DNNs to adversarial perturbations with specific statistical properti…

Greedy algorithm nearly outperforms exploration in contextual bandits.

Randomized exploration in linear bandits achieves optimal regret bounds.

Bandit learning algorithms typically involve the balance of exploration and exploitation. However, in many practical applications, worst-case scenarios needing systematic exploration are seldom encountered. In this work, we consider a smoothed setting for structured linear contextual bandits where the adversarial conte…

The study explores smooth structures on specific four-manifolds with cyclic groups, finding many admit infinitely many smooth structures.

Reinforcement learning algorithms rely on exploration to discover new behaviors, which is typically achieved by following a stochastic policy. In continuous control tasks, policies with a Gaussian distribution have been widely adopted. Gaussian exploration however does not result in smooth trajectories that generally c…

Paper explores using 0-surgery to find exotic 4-manifolds.

Kernel-UCBVI algorithm balances exploration and exploitation in metric state-action spaces.

The paper explores conditions for homology spheres to bound acyclic smooth manifolds and symplectic fillings.

New neural network smoothness constraints improve model performance.

ASE safely explores unknown MDPs with unknown dynamics, improving sample efficiency.

This study improves scalability of randomized smoothing for certifying classifier robustness.

The study explores conditions for $h$-cobordisms between smooth 4-manifolds.

The paper explores complex Poisson structures on smooth functions in complex manifolds.

This is the first version of a submission made to vixra back in August 2009. It is concerned with the exploration of various ideas due to Roy Frieden of the University of Arizona in his manuscript "Physics from Fisher Information", which was originally published in December 1998 by Cambridge University Press. In additi…

The paper analyzes the intrinsic exploration terms in policy-gradient algorithms.

New heat dispersion laws established for smooth compact manifolds.

Smooth KANs improve model reliability in computational biomedicine.

The paper investigates exotic smooth structures on manifolds with group actions.

The paper explores different smooth map notions on convex sets and their relationships.

The abstract explores Artin presentations and their connection to 4-manifolds using triangle groups.

Study perturbations of submodules in Drury-Arveson space, finding smooth vector bundles with Hermitian connections.

This paper improves convergence guarantees for SGD algorithms in non-convex smooth functions.

New method improves RL in continuous spaces with kernel smoothing.

The paper explores the structure of Reeb spaces for smooth functions on manifolds.

This paper analyzes MORL and proposes efficient algorithms to learn Pareto optimal policies.

The paper explores various stationarity concepts in non-smooth optimization.

SANE improves exploration of noisy, multimodal functions by finding multiple optima.

Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving stochastic gradient methods named predictive local smoothness (PLS). First, we …

Regularized MFPCA smooths multivariate functional data for clearer patterns.

Two new algorithms improve online clustering of bandits by accelerating cluster identification without strong assumptions.

Book on infinite-dimensional Lie groups, covering basics and various classes.

We present a 1-parameter family of finite action solutions to the $S0(2,1)$ Hitchin's equations and explore some of its basic properties. For a fixed value of the parameter, the solution is smooth. We conclude by showing a multi-particle generalization of our basic solutions.

New framework certifies robustness for regression models.

New algorithm reduces regret bounds for Bayesian optimization with unknown hyperparameters.

Improved Gibbs sampler speeds up Bayesian exponential smoothing model.

Random forests are a powerful method for non-parametric regression, but are limited in their ability to fit smooth signals, and can show poor predictive performance in the presence of strong, smooth effects. Taking the perspective of random forests as an adaptive kernel method, we pair the forest kernel with a local li…

This paper gives a review and synthesis of methods of evaluating dimensionality reduction techniques. Particular attention is paid to rank-order neighborhood evaluation metrics. A framework is created for exploring dimensionality reduction quality through visualization. An associated toolkit is implemented in R. The to…

We describe a general method to construct completely bounded idempotent mappings on operator spaces, starting from amenable semigroups of completely bounded mappings. We then explore several applications of that method to injective operator spaces, fixed points of completely contractive mappings, Toeplitz operators, dy…

Many real-world objects are designed by smooth curves, especially in the domain of aerospace and ship, where aerodynamic shapes (e.g., airfoils) and hydrodynamic shapes (e.g., hulls) are designed. To facilitate the design process of those objects, we propose a deep learning based generative model that can synthesize sm…

Using tools and results from geometric measure theory, we give a simple new proof of the main result (Theorem 1.3) in K. Kondo and M. Tanaka, Approximation of Lipschitz Maps via Immersions and Differentiable Exotic Sphere Theorems, \textit{Nonlinear Anal.} \textbf{155} (2017), 219--249, as well as the converse statemen…

This paper solves PDEs for embedding discrete lattices into smooth manifolds.

Recent advances in machine learning (ML) algorithms, especially deep neural networks (DNNs), have demonstrated remarkable success (sometimes exceeding human-level performance) on several tasks, including face and speech recognition. However, ML algorithms are vulnerable to \emph{adversarial attacks}, such test-time, tr…

We consider the class of curves of finite total curvature, as introduced by Milnor. This is a natural class for variational problems and geometric knot theory, and since it includes both smooth and polygonal curves, its study shows us connections between discrete and differential geometry. To explore these ideas, we co…

We explore a connection between the Finslerian area functional and well-investigated Cartan functionals to prove new Bernstein theorems, uniqueness and removability results for Finsler-minimal graphs, as well as enclosure theorems and isoperimetric inequalities for minimal immersions in Finsler spaces. In addition, we …

Study on Santaló point for convex bodies in normed spaces.

NAS-X improves inference and model learning for SLVMs.