New method improves random parameter generation in neural networks.
problem Standard method of generating random weights and biases in neural networks has drawbacks.
method Proposes a new method to generate random parameters ensuring nonlinear sigmoids remain in the input hypercube and uniformly distributed slope angles for activation functions.
result Ensures the most useful nonlinear fragments of sigmoids remain in the input hypercube.
Random features improve learning efficiency with optimal generalization.
problem Efficient learning with optimal generalization properties.
method Ridge regression with random features, focusing on O ( 1 / n ) O(1/\sqrt{n}) O ( 1/ n ) bounds and O ( n log n ) O(\sqrt{n}\log n) O ( n log n ) features. result Achieves O ( 1 / n ) O(1/\sqrt{n}) O ( 1/ n ) bounds with O ( n log n ) O(\sqrt{n}\log n) O ( n log n ) features, faster than previous results. Proposes semi-random features for nonlinear function approximation.
problem Nonlinear function approximation in machine learning.
method Semi-random features as a middle ground between deep learning and kernel methods.
result Proves universal approximation and generalization for deep semi-random features.
Random subgroups of free groups are invariant only by inner automorphisms.
problem Understanding the structure of random subgroups in free groups.
method Analyzing splittings and automorphisms of random subgroups.
result Random subgroups of free groups are invariant only by inner automorphisms.
GraphMoE generates random graphs using neural networks and graphlets.
problem Learning generative models for random graphs.
method GraphMoE uses a neural network trained with graphlets and subgraph counts to match the distribution of random graphs.
result GraphMoE can generate graphs that mimic various real-world datasets and fool graph classifiers.
Random polynomial dynamical systems often have negative Lyapunov exponents.
problem Understanding the behavior of random polynomial dynamical systems.
method Investigation of i.i.d. random complex dynamical systems generated by probability measures.
result For a generic system, the Lyapunov exponent of almost every sequence of maps is negative for most initial values.
Proposes a new method for generating random parameters in neural networks.
problem Improving randomized learning of feedforward neural networks.
method Randomly selects slope angles, rotates activation functions, and distributes them across the input space.
result The method gives better results than the common approach, especially for complex target functions.
Machine learning detects classical noise in quantum RNGs.
problem Classical noise compromises the randomness of quantum RNGs.
method Developed a machine learning model to analyze and detect correlations in QRNGs.
result Machine learning can identify and mitigate classical noise in QRNGs.
Transforms random forests into efficient neural networks using imitation learning.
problem Inefficient architectures of existing methods for transforming random forests into neural networks.
method Generates training data from a random forest and learns a neural network to imitate its behavior.
result Implicit transformation creates efficient neural networks with better generalization.
Sparse random features improve accuracy in data-scarce settings.
problem Limited accuracy of random feature methods in data-scarce applications.
method Sparse random feature expansion using compressive sensing.
result Improved generalization bounds for sparse random features.
New MBQC algorithm uses randomness for generative modeling.
problem Designing efficient quantum algorithms for generative modeling.
method Proposes a variational MBQC algorithm that treats randomness as a resource.
result Randomness in MBQC can lead to significant gains in generative modeling performance.
Method generates random numbers from sensor noise, improving accuracy and speed.
problem Improving accuracy and speed of Monte Carlo integration.
method Sampling a physical process in a controlled environment.
result Reduces error of Monte Carlo integration by 10^68 times while doubling speed.
Sharp asymptotics derived for phase retrieval and compressed sensing with random generative priors.
problem Phase retrieval and compressed sensing with random measurement matrices.
method Sharp asymptotics derived for optimal performance and polynomial algorithm for random generative priors.
result Compressed phase retrieval becomes tractable with random generative priors, unlike sparse priors.
Kernel ridgeless regression with random features shows good generalization without explicit regularization.
problem Generalization of kernel ridgeless regression without explicit regularization.
method Investigation of ridgeless regression with random features and stochastic gradient descent, exploring the effect of random features error and spectral density optimization.
result Random features error exhibits the double-descent curve, leading to improved generalization.
Random feature models can outperform a weak teacher with early stopping.
problem Generalization from a weak to a strong model in random feature networks.
method Random feature models, early stopping, proving weak-to-strong generalization.
result Random feature models can outperform a weak teacher with early stopping.
Develops a method for random manifolds and submanifolds, focusing on 3-ball knots.
problem Understanding random submanifolds in triangulated manifolds.
method Coloring vertices of triangulated manifolds to generate random submanifolds.
result Probability of generating an unknot decays exponentially in 3-ball with 3 colors.
This work estimates edge weights of edge-reinforced random walks using observed data.
problem Statistical estimation of edge weights in edge-reinforced random walks.
method Proposes an estimator based on the generalized method of moments using the magic formula and hyperbolic Gaussian structure.
result Analyzes the sample complexity of the proposed estimator.
Study on random Coxeter groups, extending Erdös-Rényi model.
problem Understanding random Coxeter groups and their properties.
method Extended Erdös-Rényi model to study random general Coxeter groups.
result Results on homology of nerve and hyperbolicity of random Coxeter groups.
A new method improves NetGAN's random walk initialization for graph generation.
problem NetGAN's random walk initialization leads to inconsistent and variable results, especially with short walks.
method Estimating node importance based on random walk influence over its neighborhood.
result Significantly better accuracy, less variance, and fewer outliers achieved.
New inequalities for subGaussian vectors, tighter than before.
problem Improving concentration inequalities for subGaussian random vectors.
method Deriving new concentration inequalities for subGaussian norm random vectors.
result Inequalities are tighter up to logarithmic factors.
Unified bounds for random subset generalization error and improved SGD Langevin dynamics.
problem Generalization error bounds for random subsets and stochastic gradient Langevin dynamics.
method Unified framework based on Hellström and Durisi's work, extending bounds for Langevin dynamics.
result Unified and refined bounds for generalization error in stochastic gradient Langevin dynamics.
Random permutations can offer faster convergence than with-replacement sampling for some functions.
problem Understanding when and how random permutations outperform with-replacement sampling in SGD convergence.
method Analyzing convergence rates for different function classes (1D strongly convex, general strongly convex, quadratic strongly convex).
result The optimal convergence gap between random and permutation-based SGD varies from exponential to nonexistent, depending on the function class.
A method for generating random weights and biases in neural networks with random hidden nodes.
problem The need for a method to control the generalization degree of neural networks with random hidden nodes.
method Proposes a method to generate random weights and biases that depend on input data range and activation function type.
result Improves the approximation performance of neural networks with random hidden nodes.
Flexible nonparametric models for density regression using NCoRM mixtures.
problem Density regression problems.
method Normalized compound random measure mixture models with a novel Metropolis-Hastings sampler.
result Illustrated on density regression problems, the approach makes unbiased estimation of Laplace functionals possible.
The paper tackles scalable simulation of discrete random variables.
problem Simulating discrete random variables with general and varying distributions in a scalable framework.
method Inspired by discrete choice models, the paper introduces parallelized randomness and a single associative operation for simulation.
result Characterization of algorithms for scalable simulation of discrete random variables.
EERF improves supervised learning by using data-dependent random features.
problem Improving generalization in supervised learning with fewer random features.
method EERF algorithm based on a data-dependent score function.
result EERF requires fewer random features to achieve a certain generalization error.
Study improves isoperimetric inequality for random groups.
problem Improving isoperimetric inequality for random groups.
method Generalizing the inequality to non-planar diagrams.
result Non-planar isoperimetric inequality established.
The paper generalizes product inequalities for random vectors and their applications.
problem Understanding concentration of measure for products of random vectors.
method Develops expressions for the concentration of functionals of random vectors based on product norms.
result Provides generalized Hanson-Wright inequalities and applications to random matrices.
This paper studies the probability of discrete groups generated by two parabolic elements in Kleinian groups.
problem Estimating the probability of discrete groups generated by two parabolic elements in Kleinian groups.
method Introduced geometrically natural probability measures and used computational investigation into the Riley slice.
result Identified the precise probability that a Fuchsian group generated by two parabolic Möbius transformations is discrete.
Free Random Projection enhances reinforcement learning by naturally incorporating hierarchical structure.
problem Improving reinforcement learning algorithms for better generalization and adaptability.
method Introduces Free Random Projection, a method that uses free probability theory to create random orthogonal matrices encoding hierarchical structure.
result Empirically shows consistent improvement in generalization over standard methods on multi-environment benchmarks.
Randomized neural networks improve deep RL agents' generalization.
problem Deep RL agents struggle to generalize to new, semantically similar environments.
method Introduce a randomized (convolutional) neural network to perturb input observations.
result Significantly outperforms various regularization and data augmentation methods.
Paper extends distributed learning with random features to non-attainable cases.
problem Generalization properties for distributed learning with random features under non-attainable conditions.
method Refined proof techniques, data-dependent generating strategy, additional unlabeled data.
result Remarkably reduces computational cost while preserving optimal generalization accuracy.
One-bit quantization improves inference speed for Random Features models.
problem Efficient inference on resource-constrained devices.
method Analysis of one-bit quantization in Random Features model.
result Asymptotically, quantizing weights except the last incurs no loss in generalization error.
A new model combines diffusion and random features for better interpretability and comparable performance.
problem Lack of theoretical justification and computational expense in diffusion models, and limited interpretability in random feature models.
method Developed a deep random feature model inspired by diffusion models, derived generalization bounds using score matching.
result The model achieves comparable performance to fully connected neural networks and provides theoretical generalization bounds.
Analyzes the generalization and training errors of the random feature model over time.
problem Understanding the temporal behavior of generalization and training errors in deep learning.
method Uses Cauchy complex integral representations and random matrix methods based on linear pencils.
result Analytical solution of the full time-evolution path of generalization and training errors.
Generative neural networks enable quasi-random sampling for diverse multivariate distributions.
problem Generating quasi-random samples for complex multivariate distributions is challenging and restricted.
method Generative moment matching networks (GMMNs) for quasi-random sampling.
result GMMNs allow quasi-random sampling for a broader range of multivariate distributions.
Study loop corrections in random feature models affecting training and test errors.
problem Analyzing loop corrections in random feature models to understand training and test errors.
method Statistical physics and effective field theory approach to study loop corrections.
result Derived loop corrections to training error, test error, and generalization gap.
Generalizes randomized SVD for better matrix approximations using Gaussian vectors.
problem Computing accurate rank-k approximations of matrices with limited data.
method Extends randomized SVD to multivariate Gaussian vectors, incorporating prior knowledge and using Gaussian processes.
result Demonstrates improved accuracy in approximating matrices and Hilbert-Schmidt operators.
Generative model uses random convolutional features to create financial time series.
problem Generating realistic financial time series with limited data and avoiding overfitting.
method Train generators by matching random convolutional features of real and generated time series, using SOCK (SOft Competing Kernels) feature map.
result Generators trained with random SOCK features outperform baselines across various financial datasets.
We prove new concentration inequalities for random variables.
problem Concentration of random variables in nonlinear functions.
method Efron-Stein inequalities and PAC-Bayesian approach.
result User-friendly concentration bounds for various applications.
BC-GANs use randomness in generator for better unsupervised learning.
problem Improving unsupervised learning performance.
method Bayesian framework with random generator for deterministic input.
result BC-GANs outperform state-of-the-arts in experiments.
Kernel methods with random projections improve least-squares regression efficiency.
problem Efficiently solving least-squares regression problems in high-dimensional spaces.
method Kernel conjugate gradient methods with randomized sketches and Nyström subsampling.
result Optimal generalization and computational advantages with proportional projection dimensions.
New bounds on random quadratic forms hold under dependence, useful for adaptive modeling.
problem Need for independence in bounds on random quadratic forms.
method Uniform bounds on random quadratic forms of conditionally independent and sub-Gaussian stochastic processes.
result Bounds hold under general dependencies and sequential design.
Develops methods to construct exchangeable sequences of random multisets.
problem Creating models for random multisets with unknown base measures.
method Uses exchangeable sequences of point processes and conditional-i.i.d. negative binomial processes.
result Provides constructions for negative binomial processes with random base measures.
The paper examines random walks on metric spaces and finds commensurable subgroups.
problem Determining commensurable subgroups via stationary measures in metric spaces.
method Analyzing random walks on isometry groups of metric spaces with non-singular stationary measures.
result Subgroups generated by random walks are commensurable under mild conditions.
Random projections improve classifier generalization without needing to choose the best threshold.
problem Improving classifier generalization without choosing the best threshold.
method Thresholding a random one-dimensional feature after random projection of data.
result Generalization gap is significantly smaller than linear classifiers.
This study compares PRNG and QRNG in machine learning models, revealing significant differences in performance.
problem Implications of PRNG and QRNG on machine learning model performances.
method Used CPU and QPU to generate random numbers for various machine learning techniques.
result Quantum Random Number Generators (QRNG) outperform Pseudo Random Number Generators (PRNG) in certain tasks.
Random matrix theory predicts neural representations generalize well.
problem Understanding why neural representations generalize well in practice.
method Applied random matrix theory to kernel regression and neural networks.
result GCV estimator accurately predicts generalization risk in overparameterized settings.