Precise computations of Dehn functions for subgroups of free group products.
problem Computing precise Dehn functions for subgroups of direct products of free groups.
method Analyzing specific subgroups and using algebraic methods to compute Dehn functions.
result Quartic and quadratic Dehn functions for specific subgroups of free group products.
Lower bounds set for infinite-precision transformers.
problem Understanding limitations of infinite-precision transformers.
method Used VC dimension technique to prove lower bounds.
result First lower bounds for two tasks: function composition and SUM2. Study identifies three quantization regimes for ReLU networks.
problem Approximation of Lipschitz functions by ReLU networks with finite-precision weights.
method Established through nonasymptotic tight lower and upper bounds on minimax approximation error.
result Memory-optimality achieved in proper quantization regime for deep networks.
Finite-precision learning of anh networks is limited by the Monte Carlo rate.
problem Learning anh neural networks under finite precision method Using iterated anh activations to construct localized bump functions result No adaptive randomized algorithm can achieve higher convergence rate than Monte Carlo rate in finite precision
Estimates precision matrix with confounding, improving over baselines.
problem Precision matrix estimation with extraneous confounding.
method Joint nonparametric estimator inspired by neuroscientific research.
result Consistent and efficient estimation of precision matrix with improved performance over baselines.
A new R package for high-dimensional regression and precision matrix estimation.
problem High-dimensional linear regression and precision matrix estimation challenges.
method flare package implements various regression methods and extensions for sparse precision matrix estimation.
result The flare package is efficient and scalable for large problems.
Study precise asymptotic behavior of functions in singular metric spaces.
problem Singular metric spaces with incomplete geometry.
method Expansions of quasi-harmonic and eigenfunctions.
result More precise description of asymptotic behavior at infinity.
We prove that any minimal (maximal) strongly regular surface in the three-dimensional Minkowski space locally admits canonical principal parameters. Using this result, we find a canonical representation of minimal strongly regular time-like surfaces, which makes more precise the Weierstrass representation and shows mor…
A new method quantizes neural networks to low-precision without STE, improving accuracy.
problem Quantization of neural networks to low-precision without a complete theoretical understanding.
method Alpha-blending (AB) using stochastic gradient descent (SGD) to quantize weights and gradually increase the coefficient α. result Improves top-1 accuracy by 0.9% on 1-bit BinaryNet, 0.82% on 8-bit MobileNet v1, and 2.93% on 4-bit ResNet_50 v1/2 compared to STE.
BOSH optimizes functions with stochastic evaluations more efficiently and precisely.
problem Optimizing functions with noisy evaluations can lead to suboptimal solutions.
method BOSH uses a hierarchical Gaussian process to generate a growing pool of realizations.
result BOSH provides more efficient and higher-precision optimization than standard BO.
Optimizes CM for stochastic convex optimization with progressive precision.
problem Stochastic nature of objective function in convex optimization.
method Iterative coordinate minimization with optimal precision control.
result Order-optimal regret performance for strongly convex and nonsmooth functions.
Paper explores low-precision SGLD for neural networks, reducing costs without sacrificing performance.
problem Infeasibility of low-precision sampling in large-scale scenarios.
method Developed low-precision SGLD with quantization function and full-precision gradient accumulators.
result Low-precision SGLD achieves comparable performance to full-precision SGLD with only 8 bits.
This article presents differential equations and solution methods for the functions of the form Q(x)=F−1(G(x)), where F and G are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples from one distribution into samples from another. The method may be developed an…
Low precision networks in the reinforcement learning (RL) setting are relatively unexplored because of the limitations of binary activations for function approximation. Here, in the discrete action ATARI domain, we demonstrate, for the first time, that low precision policy distillation from a high precision network pro…
Maximizing the speed and precision of communication while minimizing power dissipation is a fundamental engineering design goal. Also, biological systems achieve remarkable speed, precision and power efficiency using poorly understood physical design principles. Powerful theories like information theory and thermodynam…
Improved HGF networks avoid negative precision errors in volatility updates.
problem Negative posterior precision errors in volatility-coupled nodes of HGF networks.
method Introduced a modified quadratic approximation to variational energy.
result Robust update equations across parameter space that track posterior faithfully.
A new method identifies causal direction using dense functional classes.
problem Determining causal direction between two univariate, continuous-valued variables.
method Minimum Description Length (MDL) principle applied to cubic regression splines.
result LCUBE method achieves superior precision in identifying causal direction.
Introduces robust and decomposable AP for image retrieval.
problem Challenges in training deep neural networks with AP.
method Differentiable rank approximation and loss function design.
result ROADMAP outperforms AP approximation methods and deep models.
Active learning selects both observations and annotation precision for Gaussian Processes.
problem Costly annotation in supervised learning.
method Proposes an active learning algorithm that selects observations and annotation precision, using a modified BALD objective.
result Empirically shows the benefits of adjusting annotation precision in active learning.
Improved Thompson Sampling outperforms existing Bayesian optimization methods.
problem Thompson Sampling's performance in Bayesian optimization is suboptimal compared to other methods.
method Developed Stagger Thompson Sampler (STS), which more precisely samples the optimal arm with less computation.
result STS outperforms TS, PSS, and other acquisition methods in various optimization tasks.
Paper speeds up GP inference by reducing precision matrix computation.
problem High computational complexity in computing kernel precision matrices.
method Splitting precision matrix into Hankel-Toeplitz matrices and computing only unique entries.
result Precision matrix computation reduced from O(NM2) to O(NM). EasiCS improves neck function assessment by objectively classifying cervical spondylosis.
problem Subjective and coarse-grained neck function assessment methods.
method Developed clustering algorithms on sEMG data to objectively classify cervical spondylosis.
result EasiCS outperforms existing seven algorithms overall.
We are concerned about the coarse and precise aspects of a priori estimates for Green's function of a regular domain for the Laplacian-Betrami operator on any 3≤n-dimensional complete non-compact boundary-free Riemannian manifold through the square Sobolev/Nash/logarithmic-Sobolev inequalities plus the rough and s…
FQ-Conv quantizes CNNs for efficient inference with low-precision weights and activations.
problem Reducing precision in DNNs leads to reduced accuracy.
method Fully quantized convolutional neural networks (FQ-Conv) using novel quantization and training techniques.
result Ternary-weight CNNs perform nearly as well as full-precision networks.
A new algorithm improves GLasso for sparse precision matrix estimation.
problem Efficiently estimating sparse precision matrices in high-dimensional data.
method A new reparametrization and iterative block coordinate descent algorithm.
result Improved performance comparable to DP-GLasso with a simpler optimization target.
Expands statistical background for knee osteoarthritis treatment models.
problem Developing optimal exercise and weight loss treatments for knee osteoarthritis.
method Precision medicine models and jackknife cross-validation method.
result Jackknife estimator provides consistent value function estimation.
Kolmogorov neural networks can represent various types of functions.
problem Representing different types of functions with neural networks.
method Continuous, discontinuous bounded or unbounded activation functions in a two hidden layer model.
result Kolmogorov neural networks can represent continuous, discontinuous bounded and all unbounded multivariate functions.
We construct convergent and divergent lattices in negative curvature and give a precise asymptotic description of the behavior of their counting function.
The paper links set cuspidality to function regularity and flatness.
problem Linking set cuspidality to function regularity and flatness.
method Analyzes arc-smooth functions and their properties on various sets.
result Establishes a precise link between set cuspidality and function regularity.
New method optimizes individualized decision rules for precision medicine.
problem Heterogeneous patient responses to treatments.
method Proposes a decision-rule based optimized covariates dependent equivalent (CDE) for individualized decision making.
result Numerical experiments show improved performance in estimating optimal IDRs.
The paper shows how to infer conditional independence from non-Gaussian data.
problem Inferring conditional independence from non-Gaussian distributions.
method Developed a method to recover conditional independence structure from the precision matrix of generalized nonparanormal data.
result The conditional independence structure can be inferred from the precision matrix of generalized nonparanormal data.
The article analyzes high-dimensional classification using empirical risk minimization with precise error predictions.
problem Classifying high-dimensional data with Gaussian mixture models.
method Theoretical analysis of ridge-regularized and unregularized empirical risk minimization for high-dimensional Gaussian mixture separation.
result The square loss is optimal for high-dimensional classification in both ridge-regularized and unregularized cases.
Log-Normal Multiplicative Dynamics improves low-precision training of neural networks.
problem Training large neural networks with low precision is unstable.
method Derive a Bayesian learning rule with log-normal posterior distributions and multiplicative updates.
result LMD achieves stable and accurate training for Vision Transformer and GPT-2.
rags2ridges simplifies graphical modeling of high-dimensional data.
problem Graphical modeling of high-dimensional precision matrices.
method Modular framework for extraction, visualization, and analysis of Gaussian graphical models.
result Provides a one-stop-shop for graphical modeling of high-dimensional precision matrices.
Constructs native Banach spaces for spline operators, enabling precise function reproduction.
problem Developing native Banach spaces for spline-admissible operators.
method Systematic construction involving test functions and completion processes.
result Native spaces ensure precise function reproduction with arbitrary precision.
Study compares different covariance estimation methods for portfolio allocation.
problem Comparing methods for estimating covariance and precision matrices in portfolio allocation.
method Gaussian Graphical Model (GGM), Shrinkage, Thresholding, Random Matrix Theory (RMT) methods.
result GGM methods outperform other methods in predictive ability for portfolio allocation.
Variant of previous work on smooth algebraic functions with compact and non-compact preimages.
problem Constructing smooth algebraic functions with specific preimage properties.
method Explicit construction of smooth real algebraic functions with controlled preimage compactness.
result New results in singularity theory and real algebraic geometry.
We describe the precise structure of the distributional Hessian of the distance function from a point of a Riemannian manifold. In doing this we also discuss some geometrical properties of the cutlocus of a point and we compare some different weak notions of Hessian and Laplacian.
Study on functional inequalities on simple edge spaces.
problem Whether classical functional inequalities hold in simple edge spaces.
method Analyzing Sobolev and Poincaré inequalities, proving optimality of Sobolev constant.
result Optimality result concerning the B-constant of the Sobolev inequality.
The paper approaches the task of handwritten text recognition (HTR) with attentional encoder-decoder networks trained on sequences of characters, rather than words. We experiment on lines of text from popular handwriting datasets and compare different activation functions for the attention mechanism used for aligning i…
We establish precise upper and lower bounds for the subelliptic heat kernel on nilpotent Lie groups G of H-type. Specifically, we show that there exist positive constants C1, C2 and a polynomial correction function Qt on G such that C1Qte−4td2≤pt≤C2Qte−4td2 wh…
New method estimates portfolio turnover using covariance matrix of returns.
problem Effective estimation of portfolio turnover for algorithmic trading strategies.
method Developed a mathematical model based on covariance matrix of returns.
result Proved a necessary condition for model applicability and suggested new estimations.
Study compares ML and DL methods for autism classification.
problem Classifying autism from healthy individuals using rs-fMRI data.
method Developed classification frameworks for rs-fMRI connectivity patterns.
result Best model achieved 71% accuracy on multisite ABIDE I data.
Study shows how to approximate functions using neural networks.
problem Approximating measurable functions on hypercube.
method Using affine neural networks to approximate measurable functions.
result Any measurable function can be approximated by a bounded number of neurons.
Distance function to a finite set is a topological Morse function.
problem Characterizing the topological Morse function of a finite set.
method Analyzing the distance function to a finite set in \(\mathbb{R}^n\).
result Distance function is a topological Morse function, with precise critical points and indices.
Generalized Precision Matrix for scalable estimation of nonparametric Markov networks.
problem Estimating conditional independence structure in general distributions for all data types.
method Generalized Precision Matrix (GPM) for mixed-type variables, regularized score matching framework for scalability.
result Validated theoretical results and demonstrated scalability in various settings.
We present a new method for estimating multivariate, second-order stationary Gaussian Random Field (GRF) models based on the Sparse Precision matrix Selection (SPS) algorithm, proposed by Davanloo et al. (2015) for estimating scalar GRF models. Theoretical convergence rates for the estimated between-response covariance…
Paper analyzes multi-attribute data to estimate differences in Gaussian graphical models.
problem Estimating differences in two Gaussian graphical models with similar structure.
method Group lasso penalized D-trace loss function and ADMM algorithm for optimization.
result Consistency in support recovery and estimation in high-dimensional settings established.