Paper proposes a learning-based sparse Bayesian method for accurate off-grid DOA estimation.
problem One-bit off-grid direction of arrival (DOA) estimation in a single snapshot scenario.
method Formulated off-grid DOA estimation model, used Sparse Bayesian framework, proposed Learning-based Sparse Bayesian approach.
result Improved computational efficiency and accuracy in off-grid DOA estimation.
We present high-order compact schemes for a linear second-order parabolic partial differential equation (PDE) with mixed second-order derivative terms in two spatial dimensions. The schemes are applied to option pricing PDE for a family of stochastic volatility models. We use a non-uniform grid with more grid-points ar…
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 …
3D object recognition accuracy can be improved by learning the multi-scale spatial features from 3D spatial geometric representations of objects such as point clouds, 3D models, surfaces, and RGB-D data. Current deep learning approaches learn such features either using structured data representations (voxel grids and o…
Develops a framework for distilling flow models from few steps.
problem Improving few-step sampling in diffusion models for better performance.
method Local approximation errors and dynamical amplification controlled through analytical tractability.
result Deep residual compositions efficiently approximate long-horizon transport with controlled global error.
The paper simulates Lévy processes and their extremum and hitting time.
problem Simulating Lévy processes and their extremum and hitting time accurately and efficiently.
method Using characteristic functions and conditional characteristic functions, with conformal deformations and precalculated values on multi-grids.
result Accurate and fast simulation of Lévy processes and their extremum and hitting time.
High-order financial derivative pricing method using Radial Basis Functions.
problem Pricing financial derivatives with high accuracy and efficiency.
method Radial Basis Function generated Finite Differences for non-uniform node layouts.
result Fourth-order convergence in space with non-uniform node layouts.
New method models PDEs from noisy, limited data.
problem Modeling PDEs with incomplete, noisy data.
method Learned linear transformation of spatial grid points, followed by dynamics learning in a reduced basis, then back transformation.
result Rapid high-resolution simulations with smaller training data sets.
We propose to use Gaussian process regression to accurately estimate the diffusion MRI signal at arbitrary locations in q-space. By estimating the signal on a grid, we can do synthetic diffusion spectrum imaging: reconstructing the ensemble averaged propagator (EAP) by an inverse Fourier transform. We also propose an a…
Starfield optimizes satellite links for LEO mega-constellations by aligning ISLs with regional traffic patterns.
problem Forming a stable satellite topology in LEO mega-constellations with limited ISLs and unstable acquisition.
method Starfield uses a demand-aware heuristic algorithm based on traffic flows and Riemannian geometry to assign satellite links.
result Starfield reduces hop count and improves stretch factor by up to 30% compared to existing methods.
This work certifies non-uniform bounds against adversarial attacks for neural networks.
problem Certifying robust regions around data points against non-uniform adversarial attacks.
method Formulated as an optimization problem with nonlinear constraints, using the augmented Lagrangian method for general feedforward neural networks.
result Non-uniform bounds have larger volumes and better interpretability compared to uniform bounds.
Neural network solves BVPs with unstructured data.
problem Solving Boundary Value Problems (BVPs) with numerical methods.
method Neural Network based numerical method for solving BVPs.
result Validated the method for Laplace and Poisson equations.
Estimates graph process with high-frequency data, proving asymptotic properties.
problem Estimating graph process with high-frequency data.
method Discretized maximum likelihood estimators for GrOU process under high-frequency sampling.
result Asymptotic central limit theorems for estimators under finite and infinite jump activity.
The study finds non-uniform lattices with thin Hitchin representations in specific Lie groups.
problem Finding thin Hitchin representations in non-uniform lattices of Lie groups.
method Arithmetic methods to construct thin Hitchin representations.
result Infinitely many orbits of thin Hitchin representations in non-uniform lattices.
Enhances CEV model pricing with high-order scheme and adaptive time stepping.
problem Improving accuracy in pricing American CEV models with irregularities.
method High-order time adapted scheme, local mesh refinement, adaptive time stepping, fifth-order 5(4) Dormand-Prince method.
result Highly accurate solution with reduced computational runtime.
New material groupoid theory subdivides non-uniform bodies into smoothly uniform parts and isolated points.
problem Lack of differentiability in material bodies leads to non-uniformity.
method Introducing material groupoid and material distribution to study non-uniform bodies rigorously.
result Material bodies can be subdivided into smoothly uniform parts and isolated points.
New approach to adversarial robustness with non-uniform perturbations.
problem Real-world adversaries craft adversarial examples with non-uniform perturbations.
method Proposes non-uniform perturbations based on feature dependencies and data distribution.
result Shows improved robustness to real-world attacks compared to uniform perturbations.
New method upsamples sparse, non-uniform point clouds more accurately.
problem Suboptimal results from existing point cloud upsampling methods.
method Imposes manifold distribution constraints using Gaussian functions.
result Generates higher-quality, more uniformly distributed dense point clouds.
New approach finds minima of geodesic lengths for non-uniform fillings.
problem Finding minima of geodesic length functions for non-uniform fillings.
method Elementary optimization for 4-regular topological fillings, analysis of fat graphs and optimization techniques.
result Minima of geodesic length functions are found to be at triangle surfaces in both analyzed classes of non-uniform fillings.
New method uses graphene transistors for efficient non-uniform random number generation.
problem Generating non-uniform random variates efficiently.
method GFET-based hardware non-uniform random number generator.
result Demonstrated speedup of Monte Carlo integration by up to 2x.
Study shows how non-uniform scaling affects persistence diagrams.
problem Stability of persistence diagrams under non-uniform scaling.
method Explicit bounds on bottleneck distance derived for Euclidean scaling.
result Explicit bounds on the stability of persistence diagrams under non-uniform scaling.
Unified framework for non-uniform materials evolving over time.
problem Dealing with non-uniform materials evolving over time.
method Constructing a material groupoid and material distribution.
result Unified framework for general non-uniform evolution materials.
New rigidity theorem for product of lattices.
problem Understanding quasi-isometry of product lattices.
method Demonstrated rigidity for product of non-uniform rank one lattice and nilpotent lattice.
result Any quasi-isometric group is an extension of a non-uniform rank one lattice by a nilpotent lattice.
Non-uniform lattices in PU(n,1) cannot geometrically act on CAT(0) cube complexes.
problem Non-uniform lattices in PU(n,1) cannot geometrically act on CAT(0) cube complexes.
method Proving non-uniform lattices in PU(n,1) cannot geometrically act on CAT(0) cube complexes.
result 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…
New method detects communities in complex hypergraphs, matching theoretical limits.
problem Detecting communities in non-uniform hypergraphs with varying hyperedge sizes.
method Developed a spectral theory for weighted non-backtracking operators on non-uniform hypergraphs.
result Achieved the Kesten-Stigum bound for weak recovery in a general class of non-uniform HSBMs.
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 …
Sharp threshold for exact recovery in non-uniform hypergraph stochastic block model.
problem Community detection in random hypergraphs with non-uniform hyperedge probabilities.
method Sharp threshold established; two efficient algorithms for exact recovery.
result Sharp threshold for exact recovery; information-theoretic lower bound on misclassification.
Improved sampling accuracy in SG-MCMC methods via non-uniform gradient subsampling.
problem Computational inefficiency and sampling error in stochastic gradient MCMC methods.
method Proposes a non-uniform subsampling scheme to reduce sampling error in EWSG, a variant of SG-MCMC.
result EWSG reduces sampling error compared to uniform subsampling, improving accuracy without sacrificing convergence speed.
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→G is coarsely onto and thus is a quasi-isometry.
Efficient non-uniform quantizer improves CNN performance on FPGA.
problem Improving CNN performance on low-power systems like mobile devices.
method Custom hardware-friendly non-uniform quantizer for parameters and activations using a single scale integer representation.
result Little degradation in accuracy on CIFAR-10 and CIFAR-100 datasets.
PSLR classifies functional data with scalar covariates using path signatures.
problem Classical functional logistic regression models have limitations in capturing nonlinear and cross-channel dependencies.
method PSLR uses truncated path signatures to create a basis-free representation of functional data.
result PSLR outperforms traditional functional classifiers in accuracy and robustness, especially under non-uniform sampling.
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…
DA-LSTM adapts LSTM depth to non-uniform data, improving efficiency.
problem Non-uniform information distribution in sequential data cannot be accurately modeled by traditional LSTM.
method Developed DA-LSTM architecture that dynamically adjusts LSTM depth based on information distribution.
result DA-LSTM reduces computation resource usage and convergence time by 41.78% and 46.01% respectively.
We improve GANs by enforcing reproducibility and using non-uniform sampling.
problem Overrepresentation of certain samples in GANs' marginal log-likelihood.
method Enforce reproducibility through matching empirical distribution to prior, use non-uniform sampling for mini-batch selection.
result Improved quality and variety in generated samples, validated on CIFAR10, Fashion MNIST, and CelebA.
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…
We present a grid diagram analogue of Carter, Rieger and Saito's smooth movie theorem. Specifically, we give definitions for grid movies, grid movie isotopies and present a definition of grid planar isotopy as a particular subset of the grid diagram moves: stabilization, destabilization and commutation. We show that gr…
Improved matrix completion for non-uniformly sampled data.
problem Estimating unobserved entries in a matrix with varying sampling probabilities.
method Developed entry-specific bounds for low-rank matrix completion under structured non-uniform sampling.
result Error bounds for each entry match minimax lower bounds under certain conditions.
New loss function equivalence reveals PER's uniform sampling can be improved.
problem Improving Prioritized Experience Replay (PER) for better learning efficiency.
method Transforming non-uniformly sampled data loss functions into uniformly sampled ones.
result Some environments can replace PER with a new loss function without performance loss.
Two algorithms converge to dictionary learning with geometric rate for non-uniform data.
problem Dictionary learning for non-uniform data models.
method Derivation of convergence conditions for MOD and ODL.
result Both algorithms converge to the generating dictionary with geometric rate under certain conditions.
Proof shows volumes of certain geometric representations are always integers.
problem Integrality of volumes of specific geometric representations.
method Elementary, combinatorial-geometrical proof.
result Volumes of representations are integers when n≥2. Spectral algorithm recovers community structure in sparse hypergraphs.
problem Community detection in sparse random hypergraphs with community structure and higher-order interactions.
method Spectral algorithm with three steps: hyperedge selection, spectral partition, and correction/merging.
result Weak consistency achieved for weak signal-to-noise ratio.
The paper proves Zimmer's conjecture for non-uniform lattices by controlling mass escape and Lyapunov exponents.
problem Proving Zimmer's conjecture for non-uniform lattices in higher-rank semisimple Lie groups.
method Establishes finiteness of low-dimensional actions, introduces novel techniques to control mass escape and Lyapunov exponents.
result Proves Zimmer's conjecture for many non-uniform lattices, improving previous results.
The paper introduces triple grid diagrams to construct Lagrangian surfaces in complex projective space.
problem Constructing Lagrangian surfaces in complex projective space.
method Defining and analyzing triple grid diagrams to determine Lagrangian caps and surfaces.
result Triple grid diagrams can determine closed Lagrangian surfaces in CP2 under certain conditions. The study finds that certain hyperbolic manifolds contain subgroups isomorphic to surface groups.
problem The existence of thin surface subgroups in non-uniform arithmetic lattices.
method Analyzes arithmetic hyperbolic manifolds and their fundamental groups.
result Fundamental groups of non-compact arithmetic hyperbolic manifolds contain thin surface subgroups.
New algorithm improves online clustering of bandits with minimal frequency constraints.
problem Online clustering of bandits with non-uniform user frequencies.
method Proposes an efficient algorithm with simple set structures to represent clusters, proving a regret bound free of minimal frequency constraints.
result The new algorithm consistently outperforms existing methods in experiments on synthetic and real datasets.