arXiv research

Holonomy-preserving transformations help recover Alexander polynomials from graph zeta functions.

In this paper, we introduce a definition of $λ$-hypersurfaces of weighted volume-preserving mean curvature flow in Euclidean space. We prove that $λ$-hypersurfaces are critical points of the weighted area functional for the weighted volume-preserving variations. Furthermore, we classify complete $λ$-hypersurfaces with …

Pion optimizes LLMs by preserving weight matrix singular values.

A new index rebalancing strategy reduces large constituent weights without undesirable effects.

The use of inverse probability weighting (IPW) methods to estimate the causal effect of treatments from observational studies is widespread in econometrics, medicine and social sciences. Although these studies often involve sensitive information, thus far there has been no work on privacy-preserving IPW methods. We add…

Econometric framework integrates heavy-tailed distributions with behavioral probability weighting for better asset pricing.

In this paper we consider a class of weighted-volume preserving curvature flows acting on hypersurfaces that are trapped within two parallel hyperplanes and satisfy an orthogonal boundary condition. In the author's thesis the stability of cylinders under the flows was considered; it was found that they are stable provi…

Continuous-time interpolation of volatility surfaces preserving mixtures and arbitrage-free.

Smoothly conjugate Anosov flows on 3D manifolds are actually smoothly conjugate.

Weighted Monte Carlo prices exotic options calibrating the probabilities of previously generated paths by a regular Monte Carlo to fit a set of option premiums. When only vanilla call and put options and forward prices are considered, the Martingale condition might not be preserved. This paper shows that this is indeed…

In this paper, we study the complete bounded $λ$-hypersurfaces in weighted volume-preserving mean curvature flow. Firstly, we investigate the volume comparison theorem of complete bounded $λ$-hypersurfaces with $|A|\leqα$ and get some applications of the volume comparison theorem. Secondly, we consider the relation amo…

New method improves tensor completion by selectively preserving important elements.

New federated method preserves privacy and estimates treatment effects.

Flow preserves curvature sharpness on weighted graphs.

In this work we study the properties of deep neural networks (DNN) with random weights. We formally prove that these networks perform a distance-preserving embedding of the data. Based on this we then draw conclusions on the size of the training data and the networks' structure. A longer version of this paper with more…

Study preserves metrics with positive Bakry-Émry Ricci curvature via surgery.

BiTAT improves neural network quantization for edge devices by focusing on weight dependencies and disentangling them.

Before training a neural net, a classic rule of thumb is to randomly initialize the weights so the variance of activations is preserved across layers. This is traditionally interpreted using the total variance due to randomness in both weights \emph{and} samples. Alternatively, one can interpret the rule of thumb as pr…

We study the interplay between sequential decision making and avoiding discrimination against protected groups, when examples arrive online and do not follow distributional assumptions. We consider the most basic extension of classical online learning: "Given a class of predictors that are individually non-discriminato…

It was shown by Kaup that every origin-preserving automorphism of quasi-circular domains is a polynomial mapping. In this paper, we study how the weight of quasi-circular domains and the degree of such automorphisms are related. By using the Bergman mapping, we prove that every origin-preserving automorphism of normal …

The study shows finite measure-preserving isometry groups for certain metric measure spaces.

Study mass transport in low-diffusivity using Lagrangian coordinates.

A framework for privacy-preserving DNN pruning and acceleration.

In a recently published paper [1], it is shown that deep neural networks (DNNs) with random Gaussian weights preserve the metric structure of the data, with the property that the distance shrinks more when the angle between the two data points is smaller. We agree that the random projection setup considered in [1] pres…

Improved diffusion models for image synthesis with better training dynamics.

TransNet improves community detection on target networks using privacy-preserved source networks.

The paper generalizes K-stability results to singular and weighted settings.

New method preserves privacy by aggregating feature-vectors with weighted sums, ensuring label differential privacy.

We propose a novel approach to addressing the vanishing (or exploding) gradient problem in deep neural networks. We construct a new architecture for deep neural networks where all layers (except the output layer) of the network are a combination of rotation, permutation, diagonal, and activation sublayers which are all…

A new algorithm improves federated learning by combining knowledge distillation and weighted combination loss.

This paper solves aggregation of Pareto optimal models by using Bayesian priors and weighted averaging.

We consider a smooth Euclidean solid cone endowed with a smooth homogeneous density function used to weight Euclidean volume and hypersurface area. By assuming convexity of the cone and a curvature-dimension condition we prove that the unique compact, orientable, second order minima of the weighted area under variation…

Given a compact Riemannian manifold (M, g) and two positive functions $ρ$ and $σ$, we are interested in the eigenvalues of the Dirichlet energy functional weighted by $σ$, with respect to the L 2 inner product weighted by $ρ$. Under some regularity conditions on $ρ$ and $σ$, these eigenvalues are those of the operator …

We show that from an even degree symplectic NQ-manifold, whose homological vector field Q preserves the symplectic form, one can construct a weight system for tri-valent graphs with values in the Q-cohomology ring, satisfying the IHX relation. Likewise, given a representation of the homological vector field, one can co…

New methods reduce bias in synthetic data for machine learning.

The study examines stable regions in weighted manifolds with boundary properties.

R2D2-Net improves Bayesian neural networks by preventing over-shrinkage of important weights.

Incorporation of a new knowledge into neural networks with simultaneous preservation of the previous one is known to be a nontrivial problem. This problem becomes even more complex when new knowledge is contained not in new training examples, but inside the parameters (connection weights) of another neural network. Her…

The study preserves lower bounds of total scalar curvature under specific metric convergence.

We introduce a quotient of the affine Temperley-Lieb category that encodes all weight-preserving linear maps between finite-dimensional sl(2)-representations. We study the diagrammatic idempotents that correspond to projections onto extremal weight spaces and find that they satisfy similar properties as Jones-Wenzl pro…

Constructs a support-preserving homotopy for differential forms with boundary decay estimates.

Cautious Weight Decay modifies weight decay for better optimization.

New mechanism protects neural network weights from privacy attacks during self-supervised learning.

Binary autoencoder with sparse hidden layer preserves information and zero reconstruction error.

Since $n$-dimensional $λ$-hypersurfaces in the Euclidean space $\mathbb {R}^{n+1}$ are critical points of the weighted area functional for the weighted volume-preserving variations, in this paper, we study the rigidity properties of complete $λ$-hypersurfaces. We give a gap theorem of complete $λ$-hypersurfaces with po…

Higher-order proximity preserved network embedding has attracted increasing attention. In particular, due to the superior scalability, random-walk-based network embedding has also been well developed, which could efficiently explore higher-order neighborhoods via multi-hop random walks. However, despite the success of …

One of the difficulties of training deep neural networks is caused by improper scaling between layers. Scaling issues introduce exploding / gradient problems, and have typically been addressed by careful scale-preserving initialization. We investigate the value of preserving scale, or isometry, beyond the initial weigh…

This paper considers the scenario that multiple data owners wish to apply a machine learning method over the combined dataset of all owners to obtain the best possible learning output but do not want to share the local datasets owing to privacy concerns. We design systems for the scenario that the stochastic gradient d…