arXiv research

Reduces Nambu-Poisson manifolds by regular distributions, ensuring reduction unless distribution is zero.

Adaptive reduction scheme approximates optimal policy in regularized MDPs.

Paper develops reduction theory for controlled Lagrangian systems with symmetry and momentum map.

We demonstrate that almost all non-parametric dimensionality reduction methods can be expressed by a simple procedure: regularized loss minimization plus singular value truncation. By distinguishing the role of the loss and regularizer in such a process, we recover a factored perspective that reveals some gaps in the c…

New method reduces high-dimensional data to low-dimensional space with sparse regularization.

Reduces LCS manifolds with symplectic actions, preserving conformal structure.

Regularly reduces CMH systems with Heisenberg group symmetry.

RMDA trains structured neural networks with regularization and variance reduction.

The not-quite-Hamiltonian theory of singular reduction and reconstruction is described. This includes the notions of both regular and collective Hamiltonian reduction and reconstruction.

The purpose of this paper is to generalize the regular Optimal Reduction Theorem to general proper Dirac actions, formulated both in terms of point and orbit reduction. A comparison to general standard singular Dirac reduction is given emphasizing the desingularization role played by optimal reduction.

Reduces constructing multiplicative connections to simpler tasks.

Graph regularized autoencoder improves anomaly detection performance.

Improved LDA method for better classification and dimensionality reduction.

Study etale modules for reductive groups with 1D center, finding constraints on their irreducible submodules.

We investigate one-point reduction methods of finite topological spaces. These methods allow one to study homotopy theory of cell complexes by means of elementary moves of their finite models. We also introduce the notion of h-regular CW-complex, generalizing the concept of regular CW-complex, and prove that the h-regu…

For a possibly singular subset of a regular Poisson manifold we construct a deformation quantization of its algebra of Whitney functions. We then extend the construction of a deformation quantization to the case where the underlying set is a subset of a not necessarily regular Poisson manifold which can be written as t…

Reduces cotangent bundles using symplectic methods.

New methods reduce variance in stochastic dual averaging for sparse solutions.

Study on $p$-Kähler structures on fibrations and Lie groups.

The regular reduction of a Dirac manifold acted upon freely and properly by a Lie group is generalized to a nonfree action. For this, several facts about $G$-invariant vector fields and one-forms are shown.

RSAC improves lightweight continuous learning efficiency.

Paper proposes an algorithm to reduce hypothesis space for faster convergence in high-dimensional settings.

Survey of recent developments in symmetric reductions and controls for Hamiltonian systems.

A new algorithm reduces bias and variance in distributionally robust optimization.

A new algorithm reduces Hessian computation for nonconvex optimization.

The paper explores the geometrical structures of phase spaces for controlled Hamiltonian systems with symmetry.

A method to identify important features without solving the full problem.

This paper concerns model reduction of dynamical systems using the nuclear norm of the Hankel matrix to make a trade-off between model fit and model complexity. This results in a convex optimization problem where this trade-off is determined by one crucial design parameter. The main contribution is a methodology to app…

We realise the first and second Grushin distributions as symmetry reductions of the 3-dimensional Heisenberg distribution and 4-dimensional Engel distribution respectively. Similarly, we realise the Martinet distribution as an alternative symmetry reduction of the Engel distribution. These reductions allow us to derive…

A new algorithm screens negligible components to efficiently approximate optimal transport distances.

Drop-Activation reduces overfitting by randomly setting activations to identity.

In this paper, we first give the regular point reduction and the two types of Hamilton-Jacobi equation for a regular controlled Hamiltonian (RCH) system with symmetry and momentum map on the generalization of a semidirect product Lie group. Next, as an application of the theoretical results, we consider the underwater …

Adam optimizes DNNs to induce weight sparsity.

We show how to reduce, under certain regularities conditions, a Poisson-Nijenhuis Lie algebroid to a symplectic-Nijenhuis Lie algebroid with nondegenerate Nijenhuis tensor. We generalize the work done by Magri and Morosi for the reduction of Poisson-Nijenhuis manifolds. The choice of the more general framework of Lie a…

A general study of symmetries in optimal control theory is given, starting from the presymplectic description of this kind of system. Then, Noether's theorem, as well as the corresponding reduction procedure (based on the application of the Marsden-Weinstein theorem adapted to the presymplectic case) are stated both in…

Flipout decorrelates mini-batch weights for more variance reduction.

A trisymplectic structure on a complex 2n-manifold is a triple of holomorphic symplectic forms such that any linear combination of these forms has constant rank 2n, n or 0, and degenerate forms in $Ω$ belong to a non-degenerate quadric hypersurface. We show that a trisymplectic manifold is equipped with a holomorphic 3…

We accelerate CNF by reducing ODE truncation errors with polynomial regularization.

Self-calibrating neural networks adaptively determine dimensionality reduction.

Adaptive step sizes improve optimization for convex and nonconvex problems.

New stochastic CG algorithm with variance reduction converges faster and is more efficient.

VRSMD improves SMD convergence and has implicit regularization.

A new method bypasses regularization for disentangled latent variables without tuning.

Eigen-stratified models reduce model size and improve performance.

Accelerates Cox partial-likelihood optimization with improved SGD.

Bi-Lipschitz Autoencoder ensures robust manifold preservation.

A new DR method for HSI classification improves accuracy with limited samples.

Isometry regularizer improves autoencoder performance on manifold learning.