arXiv research

Unified geometric description of Kepler flow across all energies.

Investigates the rotating Kepler problem for energy values ≤ -3/2.

AIR-Net adapts low-rank regularization dynamically for better image completion.

A 6-regular triangulation for hyperbolic plane created.

Gradient descent implicitly regularizes neural networks by penalizing large loss gradients.

Choquet regularization improves exploration in RL.

The paper explores optimal regularizers for data sources, linking them to star bodies.

A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In…

In this article, we describe symplectic and complex toric spaces associated to the five regular convex polyhedra. The regular tetrahedron and the cube are rational and simple, the regular octahedron is not simple, the regular dodecahedron is not rational and the regular icosahedron is neither simple nor rational. We re…

The paper studies convergence rates of Tsallis entropic regularization in optimal transport.

Study uses property elicitation to understand how fairness regularizers affect optimal decisions.

Fiedler regularization uses spectral graph theory to improve neural network performance.

Study on convergence rates for optimal transport with regularization.

We establish continuous maximal regularity results for parabolic differential operators acting on sections of tensor bundles on Riemannian manifolds. As an application, we show that solutions to the Yamabe flow instantaneously regularize and become real analytic in space and time. The regularity result is obtained by i…

Improved optimal regularity for harmonic almost complex structures.

Dropout is a simple but effective technique for learning in neural networks and other settings. A sound theoretical understanding of dropout is needed to determine when dropout should be applied and how to use it most effectively. In this paper we continue the exploration of dropout as a regularizer pioneered by Wager,…

Regularization plays an important role in generalization of deep neural networks, which are often prone to overfitting with their numerous parameters. L1 and L2 regularizers are common regularization tools in machine learning with their simplicity and effectiveness. However, we observe that imposing strong L1 or L2 reg…

Study on the regularity of $p$-Gauss curvature flow near flat interfaces.

In this paper, we give a new generalization error bound of Multiple Kernel Learning (MKL) for a general class of regularizations, and discuss what kind of regularization gives a favorable predictive accuracy. Our main target in this paper is dense type regularizations including \ellp-MKL. According to the recent numeri…

In this work we study input gradient regularization of deep neural networks, and demonstrate that such regularization leads to generalization proofs and improved adversarial robustness. The proof of generalization does not overcome the curse of dimensionality, but it is independent of the number of layers in the networ…

We study the evolution equations for a regularized version of Dirac-geodesics, which are the one-dimensional version of Dirac-harmonic maps. We show that for the regularization being sufficiently large, the evolution equations subconverge to a regularized Dirac-geodesic. In the end, we discuss the limiting process of r…

Entropy-regularized NPG converges linearly with linear function approximation.

Regularized linear regression improves binary classification performance, especially with ridge and $\ell_1$ regularization.

New algorithm adds Hessian regularization to improve neural network robustness.

Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect. Although connection between Wasserstein DRO and regularization has been established in several settings, existin…

Study slice-regular polynomial functions via twistor space group actions.

Selective state-adaptive regularization improves offline RL performance.

New framework assesses regularization norms in ill-posed problems, revealing L2 instability and proposing adaptive fractional RKHS solutions.

New iterative regularization method tackles non-smooth, non-strongly convex functionals.

This study explores star-shaped regularizers learned from critic-based losses.

Regularizers change the geometric properties of loss functions in neural networks.

We investigate the learning rate of multiple kernel learning (MKL) with $\ell_1$ and elastic-net regularizations. The elastic-net regularization is a composition of an $\ell_1$-regularizer for inducing the sparsity and an $\ell_2$-regularizer for controlling the smoothness. We focus on a sparse setting where the total …

Introduces self-regularization for analyzing learning algorithms.

A connected combinatorial 2-manifold is called degree-regular if each of its vertices have the same degree. A connected combinatorial 2-manifold is called weakly regular if it has a vertex-transitive automorphism group. Clearly, a weakly regular combinatorial 2-manifold is degree-regular and a degree-regular combinator…

New framework for robust regularization under uncertain data distributions.

Sharp bounds on diameter and eigenvalues for amply regular graphs.

New regularizer improves neural network robustness and generalization.

The study limits how many parts regular simplicial partitions can overlap.

The use of convex regularizers allows for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones. However, the resultant optimization problem is much harder. In this paper, for a …

Proves $C^{1,1}$ regularity for multiple membrane solutions.

DRAG decreases regularization to accelerate semi-discrete OT convergence.

Paper finds essential regularity in singular connections.

Regularized mixtures improve inflation and interest rate forecasts, especially correcting overconfidence.

We formulate a principle for classification with the knowledge of the marginal distribution over the data points (unlabeled data). The principle is cast in terms of Tikhonov style regularization where the regularization penalty articulates the way in which the marginal density should constrain otherwise unrestricted co…

The study finds necessary and sufficient conditions for $C^1$-hypersurfaces to have nowhere $C^1$-regular parallel sets.

Study on regularity of optimal transport maps on convex domains with quadratic cost.

The paper studies how regularization parameters affect sparsity in deep neural networks.

Unified framework for sparse logistic regression with nonconvex regularization.