arXiv research

Study connects Powell Conjecture to reducing sphere complex's connectivity.

The paper shows how reducible complexes affect local indicability.

Reduces connectivity problem for genus-4 Heegaard surface in 3-sphere.

Fixed point sets of certain group actions are contractible.

For a boundary-reducible $3$-manifold $M$ with $\partial M$ a genus $g$ surface, we show that if $M$ admits a genus $g+1$ Heegaard surface $S$, then the disk complex of $S$ is simply connected. Also we consider the connectedness of the complex of reducing spheres. We investigate the intersection of two reducing spheres…

New $Q$-learning method reduces variance and achieves optimal sample complexity.

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

Study reduces financial dynamics complexity using PCA for NASDAQ, oil, gold, and USD.

The Jones polynomial can be expressed in terms of spanning trees of the graph obtained by checkerboard coloring a knot diagram. We show there exists a complex generated by these spanning trees whose homology is the reduced Khovanov homology. The spanning trees provide a filtration on the reduced Khovanov complex and a …

In this paper a novel modification of the multilevel Monte Carlo approach, allowing for further significant complexity reduction, is proposed. The idea of the modification is to use the method of control variates to reduce variance at level zero. We show that, under a proper choice of control variates, one can reduce t…

This paper proposes a method to reduce complexity in GLMs with categorical predictors.

A new method reduces model complexity in DMD using LARS.

We apply L0 regularization to reduce neural network complexity and interpretability.

CDEFs reduce model complexity and uncover time correlations.

New framework reduces LLM complexity by directly finetuning in Boolean domain.

A new algorithm reduces time complexity for binary time series classification.

Improved BLS by reducing pseudoinverse complexity for added inputs.

Proposes a method to reduce parallel complexity of MLMC in SGD.

We show that the complex of weak reducing disks for the unknot in $3$-bridge position is contractible.

This paper explores the non-convex composition optimization in the form including inner and outer finite-sum functions with a large number of component functions. This problem arises in some important applications such as nonlinear embedding and reinforcement learning. Although existing approaches such as stochastic gr…

The paper analyzes reducing model complexity for better generalization.

The abstract describes a strategy to construct reduced Khovanov homology for links in lens spaces.

The paper describes the structure of injective LOT-complexes and proves they are aspherical.

Proposes DCADL for efficient image classification with reduced complexity.

Confirming the Powell Conjecture for genus-3 Heegaard splittings of the 3-sphere.

By the work of Harer, the reduced homology of the complex of curves is a fundamental cohomological object associated to all torsion free finite index subgroups of the mapping class group. We call this homology group the Steinberg module of the mapping class group. It was previously known that the curve complex has the …

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation by first embedding the trajectories in a reproducing kernel Hilbert space (RKHS…

VRL-SGD reduces communication complexity in non-identical data settings.

Reduced CNN complexity for exoplanet detection without significant loss in accuracy.

Neural networks have proven to be extremely powerful tools for modern artificial intelligence applications, but computational and storage complexity remain limiting factors. This paper presents two compatible contributions towards reducing the time, energy, computational, and storage complexities associated with multil…

Generalised contact structures are studied from the point of view of reduced generalised complex structures, naturally incorporating non-coorientable structures as non-trivial fibering. The infinitesimal symmetries are described in detail, with a geometric description given in terms of gerbes. As an application of the …

Paper applies FloatSD8 to LSTM networks, reducing complexity and power.

Cubic regularization (CR) is an optimization method with emerging popularity due to its capability to escape saddle points and converge to second-order stationary solutions for nonconvex optimization. However, CR encounters a high sample complexity issue for finite-sum problems with a large data size. %Various inexact …

Genus 3 Heegaard groups of lens space connected sums are finitely generated.

A second part of detailed elementary introduction into Khovanov homologies. This part is devoted to reduced Jones superpolynomials. The story is still about a hypercube of resolutions of a link diagram. Each resolution is a collection of non-intersecting cycles, and one associates a 2-dimensional vector space with each…

Computer experiments reveal complex knots that don't simplify.

We show that the Spivak normal fibration of an orientable 4-dimensional Poincaré complex has a vector bundle reduction.

Improved SVRC algorithm reduces complexity for nonconvex optimization.

Backward exploration reduces sample complexity in policy evaluation.

A hybrid model reduces graph complexity for improved classification accuracy.

Sliced Inverse Regression reduces parameter space for estimating complex financial models.

A new method reduces complexity and uncertainty in neural networks.

Active learning reduces spin network inference complexity by 10^6-fold.

New algorithm reduces matrix multiplication time for sparse matrices.

LeanResNet reduces CNN complexity without sacrificing accuracy.

VRCQ algorithm reduces variance in Q-learning for MDPs, achieving optimal sample complexity.

Paper tackles uncertainties in reduced-order modeling of complex systems.

Paper introduces probabilistic methods to approximate archetypal analysis, reducing complexity.