This paper studies the performance of a recently proposed preconditioned stochastic gradient descent (PSGD) algorithm on recurrent neural network (RNN) training. PSGD adaptively estimates a preconditioner to accelerate gradient descent, and is designed to be simple, general and easy to use, as stochastic gradient desce…
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48 results for “Digital Distributed Stochastic Gradient Descent”
Efficient Federated Learning over Multiple Access Channel with Differential Privacy Constraintscs.LG
Paper addresses FL over MAC with DP constraints, proposing a novel consensus scheme.
problem Federated learning over a multiple access channel with differential privacy constraints.
method Proposes a novel consensus scheme using digital distributed stochastic gradient descent (D-DSGD) with artificial noise to preserve DP.
result Demonstrates improved convergence rate and DP level for a given MAC capacity.
The paper studies stochastic gradient descent with infinite variance gradients.
problem Theoretical properties of SGD with infinite variance gradients.
method Establish asymptotic behavior of SGD with infinite variance gradients.
result Asymptotic distribution of SGD is characterized as a stationary distribution of an Ornstein-Uhlenbeck process driven by a stable Lévy process.
Paper addresses fault-tolerance in distributed machine learning with stochastic gradient descent.
problem Fault-tolerance in distributed stochastic gradient descent (D-SGD) for machine learning.
method Proposes norm-based comparative gradient elimination (CGE) to robustify D-SGD against Byzantine faulty agents.
result CGE guarantees fault-tolerance against a bounded fraction of Byzantine agents under standard stochastic assumptions.
New dynamics for SGD in small learning rate regime.
problem Improving stochastic gradient descent in small learning rate regime.
method Introducing stochastic modified flows and distribution dependent stochastic modified flows.
result Captures fluctuating dynamics of SGD in small learning rate - infinite width scaling regime.
SGD reduces test error by decorrelating updates.
problem Improving generalization error in machine learning models.
method Derive a formula for generalization gap change due to SGD updates, compare to GD, and show decorrelation effect.
result SGD implicitly regularizes generalization error by decorrelating updates.
New method optimizes SDE models using continuous-time gradient descent.
problem Optimizing over the stationary distribution of SDE models.
method Continuous-time stochastic gradient descent for SDE models.
result Asymptotic convergence to the direction of steepest descent.
In just three years, Variational Autoencoders (VAEs) have emerged as one of the most popular approaches to unsupervised learning of complicated distributions. VAEs are appealing because they are built on top of standard function approximators (neural networks), and can be trained with stochastic gradient descent. VAEs …
What enables Stochastic Gradient Descent (SGD) to achieve better generalization than Gradient Descent (GD) in Neural Network training? This question has attracted much attention. In this paper, we study the distribution of the Stochastic Gradient Noise (SGN) vectors during the training. We observe that for batch sizes …
Two novel algorithms improve distributed machine learning in the presence of Byzantine adversaries.
problem Improving distributed machine learning in the presence of Byzantine adversaries.
method Two novel stochastic gradient descent algorithms, ByGARS and ByGARS++, using reputation scores for gradient aggregation.
result Robust to any number of multiplicative noise Byzantine adversaries and converge for strongly convex loss functions.
A new stochastic algorithm approximates optimal distributions without requiring propagation of chaos.
problem Optimizing functionals over probability distributions using finite particle systems.
method Virtual particle stochastic approximation, viewed as a form of stochastic gradient descent in the Wasserstein space.
result The algorithm's output converges to the optimal distribution and produces i.i.d. samples.
We introduce Kalman Gradient Descent, a stochastic optimization algorithm that uses Kalman filtering to adaptively reduce gradient variance in stochastic gradient descent by filtering the gradient estimates. We present both a theoretical analysis of convergence in a non-convex setting and experimental results which dem…
We provide tight finite-time convergence bounds for gradient descent and stochastic gradient descent on quadratic functions, when the gradients are delayed and reflect iterates from rounds ago. First, we show that without stochastic noise, delays strongly affect the attainable optimization error: In fact, the error…
MT-SGD samples from multiple target distributions using gradient descent.
problem Sampling from multiple unnormalized target distributions.
method Proposes MT-SGD, a flow of intermediate distributions to sample from multiple target distributions.
result Asymptotic analysis shows MT-SGD reduces to multiple-gradient descent for multi-objective optimization.
Stochastic gradient descent approximates Gaussian process posteriors efficiently.
problem Efficiently sampling from Gaussian process posteriors with limited computational resources.
method Developed stochastic gradient optimization objectives for sampling from Gaussian process posteriors.
result Stochastic gradient descent produces accurate predictive distributions, even in non-convergent cases.
Heavy-tailed distributions emerge in SGD's parameter evolution.
problem Understanding heavy-tailed distributions in SGD parameter evolution.
method Continuous diffusion approximation of SGD (homogenized SGD) analysis.
result Explicit upper and lower bounds on tail-index of homogenized SGD.
Asymptotic properties of one-layer artificial neural networks with sparse connectivitycond-mat.dis-nn
Law derived for neural networks with sparse connections.
problem Understanding the behavior of neural networks with sparse connections.
method Law of large numbers for empirical distribution of parameters derived.
result Law for neural networks with sparse connections derived.
New stochastic gradient descent with random search directions improves efficiency and convergence.
problem Efficiency and convergence of stochastic gradient descent methods.
method Developed a new class of stochastic gradient descent algorithms with random search directions.
result Established almost sure convergence and provided rates of convergence.
Variance reduction (VR) methods boost the performance of stochastic gradient descent (SGD) by enabling the use of larger, constant stepsizes and preserving linear convergence rates. However, current variance reduced SGD methods require either high memory usage or an exact gradient computation (using the entire dataset)…
Despite having various attractive qualities such as high prediction accuracy and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix Factorization has not been widely adopted because of the prohibitive cost of inference. In this paper, we propose a scalable distributed Bayesian matrix factorizat…
SGD improves DR by solving two-stage sampling problems.
problem Improving the learning properties of SGD for distribution regression.
method Applying SGD to two-stage sampling problems in distribution regression.
result Theoretical guarantees for SGD's performance in DR, with optimal bounds.
This paper develops a communication-efficient algorithm to solve the stochastic optimization problem defined over a distributed network, aiming at reducing the burdensome communication in applications such as distributed machine learning.Different from the existing works based on quantization and sparsification, we int…
SGD in DLNs reveals feature learning dynamics.
problem Understanding SGD dynamics in DLNs during saddle-to-saddle training.
method Stochastic Langevin dynamics with anisotropic, state-dependent noise; one-dimensional per-mode SDEs; Boltzmann distribution approximation.
result SGD noise encodes feature learning progression but does not alter saddle-to-saddle dynamics.
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.
Gradient descent and its many variants, including mini-batch stochastic gradient descent, form the algorithmic foundation of modern large-scale machine learning. Due to the size and scale of modern data, gradient computations are often distributed across multiple compute nodes. Unfortunately, such distributed implement…
Although stochastic gradient descent (SGD) is a driving force behind the recent success of deep learning, our understanding of its dynamics in a high-dimensional parameter space is limited. In recent years, some researchers have used the stochasticity of minibatch gradients, or the signal-to-noise ratio, to better char…
A new method improves stochastic gradient descent for faster and more efficient estimation.
problem Efficient and fast parametric estimation methods.
method Projected stochastic gradient descent corrected by Fisher scoring.
result The method is faster and more efficient than traditional methods.
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient descent, using Monte Carlo approximation for the gradients. This enables variatio…
Noise balance theory explains SGD's behavior in neural networks.
problem Understanding SGD's navigation in neural network loss landscapes.
method Analyzes minibatch noise and loss function symmetries.
result Derives the stationary distribution of SGD for deep networks.
Optimizes binary regression models with gradient ascent-descent methods.
problem Regression problems with binary weights in quantized learning and digital communication.
method Maximin optimization using gradient ascent-descent methods.
result The approach is optimal in linear regression with low noise and robust regression with few outliers.
A large class of machine learning techniques requires the solution of optimization problems involving spectral functions of parametric matrices, e.g. log-determinant and nuclear norm. Unfortunately, computing the gradient of a spectral function is generally of cubic complexity, as such gradient descent methods are rath…
FedAc accelerates Federated Averaging for distributed optimization.
problem Efficiently optimizing distributed machine learning models.
method Federated Accelerated Stochastic Gradient Descent (FedAc) using a potential-based perturbed iterate analysis.
result FedAc achieves faster convergence and lower communication costs than previous methods.
Gravilon improves gradient descent for neural networks.
problem Improving efficiency and accuracy of gradient descent methods.
method Uses geometric modification of gradient step lengths.
result Promising experimental results on MNIST classification.
Recent work has argued that stochastic gradient descent can approximate the Bayesian uncertainty in model parameters near local minima. In this work we develop a similar correspondence for minibatch natural gradient descent (NGD). We prove that for sufficiently small learning rates, if the model predictions on the trai…
A new decentralized method solves minimax problems with reduced communication and sample complexity.
problem Solving minimax optimization problems in a distributed setting.
method Decentralized stochastic gradient descent ascent with variance reduction.
result Achieved optimal sample and communication complexities for nonconvex-strongly-concave problems.
New adaptive step-size method for convex optimization without tuning.
problem Optimizing convex functions efficiently with stochastic gradients.
method Adapted Adaptive Gradient Descent Without Descent to stochastic setting.
result Stochastic gradient descent converges under various assumptions.
Gradient descent with random weights in linear regression analyzed for various noise types.
problem Analyzing the impact of random noise on gradient descent in linear regression.
method Gradient descent with randomly weighted data points, various weighting distributions, geometric moment contraction.
result Characterization of implicit regularization and non-asymptotic convergence bounds.
This article suggests that deterministic Gradient Descent, which does not use any stochastic gradient approximation, can still exhibit stochastic behaviors. In particular, it shows that if the objective function exhibit multiscale behaviors, then in a large learning rate regime which only resolves the macroscopic but n…
New method reduces communication costs in distributed nonconvex optimization.
problem Large communication costs between central server and local workers in distributed learning.
method Communication-compressed AMSGrad for distributed nonconvex optimization.
result Converges to first-order stationary point with same iteration complexity as vanilla AMSGrad.
Stochastic gradient descent converges to universal limits in high dimensions.
problem Statistical tasks in high dimensions with specific data projections.
method Stochastic gradient descent applied to mixture distributions, proving universality of limits.
result The ODE limits are universal for mixtures of arbitrary product distributions.
Learning models with discrete latent variables using stochastic gradient descent remains a challenge due to the high variance of gradient estimates. Modern variance reduction techniques mostly consider categorical distributions and have limited applicability when the number of possible outcomes becomes large. In this w…
New bounds for M-SGD show its error distribution is nearly Gaussian.
problem Understanding the error distribution of M-SGD.
method Proved non-asymptotic bounds for M-SGD in Wasserstein distance.
result Error distribution of M-SGD is approximately Gaussian.
Researchers study heavy-tail properties of SGD using stochastic recurrence equations.
problem Analyzing heavy-tail properties of Stochastic Gradient Descent (SGD).
method Modeling SGD iterations as multivariate affine stochastic recursions and applying the theory of irreducible-proximal (i-p) matrices.
result Extended results of Gürbüzbalaban et al. (2020) by using the theory of i-p matrices.
We propose a novel robust aggregation rule for distributed synchronous Stochastic Gradient Descent~(SGD) under a general Byzantine failure model. The attackers can arbitrarily manipulate the data transferred between the servers and the workers in the parameter server~(PS) architecture. We prove the Byzantine resilience…
New bounds for model generalization under deterministic gradient descent.
problem Establishing generalization bounds for models trained with gradient descent methods.
method PAC-Bayesian bounds for deterministic optimisation algorithms.
result Fully computable bounds that depend on initial distribution and Hessian.
With the increase in the amount of data and the expansion of model scale, distributed parallel training becomes an important and successful technique to address the optimization challenges. Nevertheless, although distributed stochastic gradient descent (SGD) algorithms can achieve a linear iteration speedup, they are l…
Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an approximate Bayesian posterior inference algorithm. Specifically, we show how to adjust …
This paper deals with distributed finite-sum optimization for learning over networks in the presence of malicious Byzantine attacks. To cope with such attacks, most resilient approaches so far combine stochastic gradient descent (SGD) with different robust aggregation rules. However, the sizeable SGD-induced stochastic…