arXiv research

New method uses graphene transistors for efficient non-uniform random number generation.

This work studies the robustness certification problem of neural network models, which aims to find certified adversary-free regions as large as possible around data points. In contrast to the existing approaches that seek regions bounded uniformly along all input features, we consider non-uniform bounds and use it to …

New rigidity theorem for product of lattices.

New method upsamples sparse, non-uniform point clouds more accurately.

Unified framework for non-uniform materials evolving over time.

The study finds non-uniform lattices with thin Hitchin representations in specific Lie groups.

New method detects communities in complex hypergraphs, matching theoretical limits.

New approach to adversarial robustness with non-uniform perturbations.

Sharp threshold for exact recovery in non-uniform hypergraph stochastic block model.

A groupoid $Ω\left( \mathcal{B} \right)$ called material groupoid is naturally associated to any simple body $\mathcal{B}$. The material distribution is introduced due to the (possible) lack of differentiability of the material groupoid. Thus, the inclusion of these new objects in the theory of material bodies opens th…

New approach finds minima of geodesic lengths for non-uniform fillings.

Two algorithms converge to dictionary learning with geometric rate for non-uniform data.

Study shows how non-uniform scaling affects persistence diagrams.

Non-uniform lattices in PU(n,1) cannot geometrically act on CAT(0) cube complexes.

We apply stochastic average gradient (SAG) algorithms for training conditional random fields (CRFs). We describe a practical implementation that uses structure in the CRF gradient to reduce the memory requirement of this linearly-convergent stochastic gradient method, propose a non-uniform sampling scheme that substant…

We study primal-dual type stochastic optimization algorithms with non-uniform sampling. Our main theoretical contribution in this paper is to present a convergence analysis of Stochastic Primal Dual Coordinate (SPDC) Method with arbitrary sampling. Based on this theoretical framework, we propose Optimality Violation-ba…

We present a novel method for neural network quantization that emulates a non-uniform $k$-quantile quantizer, which adapts to the distribution of the quantized parameters. Our approach provides a novel alternative to the existing uniform quantization techniques for neural networks. We suggest to compare the results as …

We prove that if $G$ is a non-uniform lattice in a rank-one semi-simple Lie group $\ne Isom(\H^2_\R)$ then $G$ is quasi-isometrically co-Hopf. This means that every quasi-isometric embedding $G\to G$ is coarsely onto and thus is a quasi-isometry.

Improved sampling accuracy in SG-MCMC methods via non-uniform gradient subsampling.

Spectral algorithm recovers community structure in sparse hypergraphs.

In this note, we study deformations of a non-uniform real hyperbolic lattice in quaternionic hyperbolic spaces. Specially we show that the representations of the fundamental group of the figure eight knot complement into PU(2,1) cannot be deformed in $PSp(2,1)$ out of PU(2,1) up to conjugacy.

We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are di…

A new method for matrix completion with model-free weights.

We consider stochastic gradient descent algorithms for minimizing a non-smooth, strongly-convex function. Several forms of this algorithm, including suffix averaging, are known to achieve the optimal $O(1/T)$ convergence rate in expectation. We consider a simple, non-uniform averaging strategy of Lacoste-Julien et al. …

Paper tackles non-uniform coverage planning for robots.

We study the effectiveness of non-uniform randomized feature selection in decision tree classification. We experimentally evaluate two feature selection methodologies, based on information extracted from the provided dataset: $(i)$ \emph{leverage scores-based} and $(ii)$ \emph{norm-based} feature selection. Experimenta…

Improved matrix completion for non-uniformly sampled data.

New loss function equivalence reveals PER's uniform sampling can be improved.

Frequency bias affects neural network training on non-uniform data.

Convolutional Neural Networks (CNN) has become more popular choice for various tasks such as computer vision, speech recognition and natural language processing. Thanks to their large computational capability and throughput, GPUs ,which are not power efficient and therefore does not suit low power systems such as mobil…

Proof shows volumes of certain geometric representations are always integers.

The paper proves Zimmer's conjecture for non-uniform lattices by controlling mass escape and Lyapunov exponents.

The study finds that certain hyperbolic manifolds contain subgroups isomorphic to surface groups.

Validates conformal prediction for network data under non-uniform sampling.

We study representations of lattices of PU(m,1) into PU(n,1). We show that if a representation is reductive and if m is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic m-space to complex hyperbolic n-space. This allows us to give a differential geometric proof of rigidity …

We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In our numerical study we obtain high-order numerical convergence also for non-zero …

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received …

Let $G$ and $G'$ be simple Lie groups of equal real rank and real rank at least $2$. Let $Γ<G$ and $Λ< G'$ be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of $Γ$ into $Λ$ is at bounded distance from a homomorphism. For example, any quasi-isometric embedding of $SL(n,\ma…

Study on Čech cohomology of Morse boundaries in hyperbolic manifolds.

Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the concept of an asymptotically linear estimator and the associated influence func…

The fundamental group of a Riemannian manifold with $δ$-pinched negative curvature, $δ>1/4$, cannot be the fundamental group of a quasicompact Kähler manifold. The proof also implies that a non-uniform lattice in $F_{4(-20)}$ cannot be the fundamental group of a quasicompact Kähler manifold. We also construct examples …

Generalizes smoothness conditions for optimization methods.

This letter presents an improved version of diffusion least mean ppower (LMP) algorithm for distributed estimation. Instead of sum of mean square errors, a weighted sum of mean square error is defined as the cost function for global and local cost functions of a network of sensors. The weight coefficients are updated b…

New method detects communities in hypergraphs by embedding them into a vector space.

Generative models characterized through learning theory.

Paper proposes a learning-based sparse Bayesian method for accurate off-grid DOA estimation.

New method learns from non-uniform data and partial physical knowledge.

The notion of expense in Bayesian optimisation generally refers to the uniformly expensive cost of function evaluations over the whole search space. However, in some scenarios, the cost of evaluation for black-box objective functions is non-uniform since different inputs from search space may incur different costs for …