New algorithm improves regression error bounds and accelerates performance for low noise.
problem Nonparametric least square regression in RKHS with optimal error bounds.
method Kernel Truncated Randomized Ridge Regression (KTRRR) with optimal generalization error bounds.
result Faster finite-time and asymptotic rates on low noise problems.
Latent FxLMS accelerates ANC by adapting along low-dimensional filter weights.
problem Improving active noise control with neural adaptive filters.
method Training an auto-encoder on filter coefficients, constraining weights to latent variables, and updating in latent space.
result Latent FxLMS converges in fewer steps with comparable error to standard FxLMS.
Replica exchange Langevin diffusion accelerates nonconvex optimization.
problem Nonconvex optimization challenges in machine learning.
method Replica exchange Langevin diffusion, discretization analysis.
result Replica exchange accelerates convergence to global minima.
New algorithm reduces feature count and accelerates error convergence.
problem Exponential error convergence in data classification with optimized random features.
method Optimized random features accelerated by quantum machine learning.
result Achieves exponential error convergence under low-noise condition.
ScaledGD accelerates ill-conditioned low-rank estimation.
problem Slow convergence of gradient descent in ill-conditioned problems.
method Scaled gradient descent (ScaledGD) with preconditioning.
result Linear convergence rate independent of condition number.
AGNES accelerates gradient descent with noisy gradients.
problem Minimizing smooth convex and strongly convex functions with noisy gradients.
method Generalization of Nesterov's accelerated gradient descent algorithm for noisy conditions.
result AGNES achieves acceleration for noisy gradients with a constant of proportionality up to 1.
Dropout-based regularization methods can be regarded as injecting random noise with pre-defined magnitude to different parts of the neural network during training. It was recently shown that Bayesian dropout procedure not only improves generalization but also leads to extremely sparse neural architectures by automatica…
Low-precision computation is often used to lower the time and energy cost of machine learning, and recently hardware accelerators have been developed to support it. Still, it has been used primarily for inference - not training. Previous low-precision training algorithms suffered from a fundamental tradeoff: as the num…
Paper develops a new weighted low-rank matrix approximation technique.
problem Matrix completion with missing data.
method Element-wise weighted generalization of low-rank matrix approximation.
result Proposes an algorithm and acceleration techniques for solving the weighted problem.
Momentum methods such as Polyak's heavy ball (HB) method, Nesterov's accelerated gradient (AG) as well as accelerated projected gradient (APG) method have been commonly used in machine learning practice, but their performance is quite sensitive to noise in the gradients. We study these methods under a first-order stoch…
A new model reduces noise and speeds up subspace segmentation.
problem Subspace segmentation from noisy data.
method Group norm regularized factorization model (GNRFM) with AALM algorithm.
result The method is faster and more robust to noise.
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.
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.
Improved training of large-scale neural networks with reduced variance noise.
problem Training large-scale neural networks with high variance noise.
method Stochastic variance reduced Nesterov's Accelerated Quasi-Newton method (SVR-NAQ).
result Improved performance compared to conventional methods on benchmark problems.
Accelerates stochastic optimization for convex and strongly convex problems.
problem Improving convergence rates in noisy stochastic optimization.
method Extends Catalyst approach to stochastic settings, handles inexact proximal operators.
result Achieves optimal worst-case complexity for noise-dominated regions.
New methods accelerate distributed optimization in noisy networks.
problem Optimizing distributed stochastic gradient methods for noisy, connected networks.
method Developed a framework for choosing stepsize and momentum parameters, proving acceleration and providing performance bounds.
result Distributed accelerated methods achieve acceleration with optimal complexity, reducing bias and variance.
Preconditioned non-convex gradient descent improves noisy matrix estimation.
problem Estimating low-rank matrices from noisy measurements.
method Preconditioned non-convex gradient descent for noisy measurements.
result Preconditioned method converges to minimax optimal estimate at a linear rate.
Two new differentially private optimization algorithms derived from accelerated methods.
problem Improving privacy in optimization algorithms while maintaining convergence rates.
method Polyak's heavy ball method and Nesterov's accelerated gradient method with differential privacy.
result The proposed algorithms outperform existing differentially private optimization methods.
ALONE uses neural networks to accelerate cine MRI without needing ground truth.
problem Accelerated MRI reconstruction without using ground truth.
method Unsupervised learning of shallow CNNs to approximate MRI patches.
result ALONE outperforms TV and DIC methods in cine MRI reconstruction.
We formulate and study a general family of (continuous-time) stochastic dynamics for accelerated first-order minimization of smooth convex functions. Building on an averaging formulation of accelerated mirror descent, we propose a stochastic variant in which the gradient is contaminated by noise, and study the resultin…
Develops accelerated methods for optimization using low-dimensional projected-gradient information.
problem Optimization with low-dimensional projected-gradient information and Nesterov acceleration.
method Randomized-subspace Nesterov accelerated gradient methods for smooth convex and strongly convex optimization.
result Established accelerated oracle-complexity guarantees and unified basis for comparing sketch families.
New algorithms improve optimization under varying noise.
problem Optimizing under state-dependent noise in convex problems.
method Stochastic accelerated gradient descent (SAGD) and stochastic gradient extrapolation (SGE).
result Achieve optimal convergence rates and complexities.
Optimized method tackles convex optimization with heavy-tailed noise.
problem Convex optimization problems with noisy gradients.
method Vanilla stochastic proximal subgradient method without gradient clipping or normalization.
result Achieves optimal complexity for various convex optimization types under heavy-tailed noise.
In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of stochastic optimization methods as procedures that iteratively minimize a surrogate of th…
New method accelerates CNNs for mobile devices by approximating tensors and quantizing weights.
problem Efficiently compress and accelerate CNNs for mobile devices.
method Low-rank tensor approximation in Tucker format combined with quantization of weights and activations.
result Our method significantly improves CNN performance on various classification tasks.
We accelerate the power method for strong low-rank approximation using fast sketching.
problem Efficiency bottleneck in power method for large target ranks.
method Developed an algorithmic and theoretical framework for accelerating the power method using fast sketching.
result Simple and provably efficient methods for singular value decomposition, low-rank factorization, and Nyström approximation.
Improved optimization guarantees for deep learning models with Nesterov acceleration.
problem Optimization in non-convex deep learning landscapes.
method Analysis of Nesterov acceleration in benignly non-convex landscapes.
result Identical guarantees can be obtained in optimization problems with weak geometric assumptions, especially in overparametrized deep learning.
IRCUR accelerates RPCA by using CUR decomposition for efficient low rank estimation.
problem Dimension reduction in robust principal component analysis.
method IRCUR employs CUR decomposition to update the low rank component efficiently.
result IRCUR achieves significant computational efficiency compared to existing algorithms.
Paper proposes a new Bayesian optimisation method to handle aleatoric uncertainty.
problem Representing and minimizing aleatoric noise in Bayesian optimisation.
method Heteroscedastic Gaussian process (GP) surrogate model with AEI and ANPEI acquisition functions.
result Improved performance on toy problems and real-world datasets compared to homoscedastic methods.
We study the trade-offs between convergence rate and robustness to gradient errors in designing a first-order algorithm. We focus on gradient descent (GD) and accelerated gradient (AG) methods for minimizing strongly convex functions when the gradient has random errors in the form of additive white noise. With gradient…
Paper improves DNN accelerator robustness against bit errors with energy savings.
problem Bit errors in quantized DNN weights reduce energy efficiency.
method Combines robust fixed-point quantization, weight clipping, and random bit error training.
result Significantly improves robustness against random bit errors with high energy savings.
Stochastic gradient descent on manifolds improves low-rank approximation.
problem Efficiently approximate large matrices with lower rank.
method Stochastic gradient descent on a manifold.
result Algorithm outperforms Euclidean space methods on Netflix Prize data.
Unified approach for learning quantum operations from measurements.
problem Accurate reconstruction of unknown quantum operations from noisy measurements.
method Matrix sensing techniques, randomized measurement design, blockwise measurement design, alternating least squares (ALS).
result The proposed method provides theoretical guarantees for the identifiability and recovery of low-rank superoperators in the presence of noise.
Paper explores whether gradient normalization can replace clipping for SGD in heavy-tailed noise.
problem Ensuring convergence of SGD in heavy-tailed noise.
method Revisits gradient clipping and normalization, proving their sufficiency and effectiveness.
result Gradient normalization alone is sufficient for nonconvex SGD convergence under smoothness assumptions.
Paper tackles noisy neural networks and proposes a method to enhance their robustness.
problem Noisy neural networks struggle with random continuous noise in weights.
method Knowledge distillation combined with noise injection during training.
result Models achieve up to twice greater noise tolerance.
Accelerates data generation in score-based models.
problem Slow generation of realistic data by score-based models.
method Developed an adaptive step size SDE solver.
result Generates data 2-10 times faster with high quality.
Batch normalization makes neural networks more vulnerable to small adversarial perturbations.
problem Adversarial vulnerability of neural networks trained with batch normalization.
method Investigated the impact of batch normalization on adversarial robustness and compared it to weight decay.
result Substituting weight decay for batch norm nullifies adversarial vulnerability.
ScaledGD algorithm estimates low-rank tensors efficiently from corrupted data.
problem Estimating meaningful information from corrupted tensor data.
method Scaled gradient descent (ScaledGD) algorithm with tailored spectral initializations.
result ScaledGD achieves linear convergence at a constant rate independent of condition number.
This research accelerates sampling methods using Nesterov's Acceleration.
problem Improving sampling efficiency in MCMC methods.
method Developed a Hessian-Free High-Resolution ODE reformulation of NAG-SC, injected noise, and discretized the diffusion process.
result Quantified acceleration beyond underdamped Langevin in W2 distance for log-strongly-concave targets. Continuized Nesterov acceleration accelerates stochastic gradient descent and gossip algorithms.
problem Improving the convergence rate of stochastic gradient descent and gossip algorithms.
method Introducing a continuized variant of Nesterov acceleration, which mixes variables continuously and takes gradient steps at random times.
result The continuized Nesterov acceleration achieves convergence rates similar to Nesterov's original acceleration but with random parameters.
New quantum state reconstruction method accelerates convergence.
problem Quantum state reconstruction for larger systems.
method Momentum-Inspired Factored Gradient Descent (MiFGD) combining compressed sensing, non-convex optimization, and acceleration.
result Converges to true density matrix at an accelerated linear rate, provably close to the true matrix.
This work sets lower bounds on the number of score queries needed for diffusion sampling.
problem Establishing information-theoretic limits on the number of score evaluations required for diffusion sampling.
method Proving lower bounds on the number of adaptive score queries needed for sampling.
result Any sampling algorithm requires at least \(\widetilde{\Omega}(\sqrt{d})\) adaptive score queries for \(d\)-dimensional distributions.
New preconditioners speed up SGD on Lie groups.
problem Accelerating SGD convergence on Lie groups.
method Online updating of low-rank and matrix-free preconditioners.
result Preconditioners maintain symmetry and invariance.
Improved analysis of accelerated noisy power method for PCA.
problem Inexact matrix-vector products in PCA settings.
method Improved analysis of Accelerated Noisy Power Method under milder perturbation conditions.
result Worst-case optimal convergence rate with relaxed noise conditions.
New algorithm accelerates optimization in non-convex problems with heavy-tailed noise.
problem Optimizing non-convex functions with heavy-tailed noise.
method Proposes a variance-reduced accelerated algorithm for optimization problems in the form of F(x)=EΞ∼D[f(x,Ξ)]. result Achieves a high-probability convergence rate of O(log(T/δ)T2p−11−p), faster than the lower bound Ω(T3p−21−p). New study shows acceleration in hyperbolic spaces is impossible for strongly geodesically convex functions.
problem Acceleration in hyperbolic spaces for strongly geodesically convex functions is impossible.
method Perturbing hard functions with sums of bump functions chosen by a resisting oracle.
result Acceleration is unachievable for any deterministic algorithm in hyperbolic spaces for strongly geodesically convex functions.
Adapts SGD to noise and problem specifics for faster convergence.
problem Minimizing smooth, strongly-convex functions with varying noise and problem constants.
method Adaptive SGD with exponentially decreasing step-sizes, Nesterov acceleration, and stochastic line-search.
result Achieves near-optimal convergence rates without knowing noise or problem specifics.
SRFRN accelerates image super-resolution using shallow residual units.
problem High computational complexity and time in deep learning image super-resolution.
method SRFRN uses a bicubic interpolated low-resolution image and residual representative units (RFR) for faster and more efficient high-resolution image reconstruction.
result SRFRN achieves superior performance and faster execution time compared to existing methods.