Related papers: Inherent Noise in Gradient Based Methods
We study high-probability convergence in online learning, in the presence of heavy-tailed noise. To combat the heavy tails, a general framework of nonlinear SGD methods is considered, subsuming several popular nonlinearities like sign,…
Systematic generalization is the ability to combine known parts into novel meaning; an important aspect of efficient human learning, but a weakness of neural network learning. In this work, we investigate how two well-known modeling…
Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…
Applying Differentially Private Stochastic Gradient Descent (DPSGD) to training modern, large-scale neural networks such as transformer-based models is a challenging task, as the magnitude of noise added to the gradients at each iteration…
The challenge of overfitting, in which the model memorizes the training data and fails to generalize to test data, has become increasingly significant in the training of large neural networks. To tackle this challenge, Sharpness-Aware…
For infinitesimal learning rates, stochastic gradient descent (SGD) follows the path of gradient flow on the full batch loss function. However moderately large learning rates can achieve higher test accuracies, and this generalization…
Background: Deep learning models are typically trained using stochastic gradient descent or one of its variants. These methods update the weights using their gradient, estimated from a small fraction of the training data. It has been…
Stochastic gradient descent (SGD) is a pillar of modern machine learning, serving as the go-to optimization algorithm for a diverse array of problems. While the empirical success of SGD is often attributed to its computational efficiency…
In this paper, we provide a theoretical study of noise geometry for minibatch stochastic gradient descent (SGD), a phenomenon where noise aligns favorably with the geometry of local landscape. We propose two metrics, derived from analyzing…
Very large deep learning models trained using gradient descent are remarkably resistant to memorization given their huge capacity, but are at the same time capable of fitting large datasets of pure noise. Here methods are introduced by…
In the era of large-scale neural network models, optimization algorithms often struggle with generalization due to an overreliance on training loss. One key insight widely accepted in the machine learning community is the idea that wide…
We present a novel methodology based on a Taylor expansion of the network output for obtaining analytical expressions for the expected value of the network weights and output under stochastic training. Using these analytical expressions the…
Recent empirical work on stochastic gradient descent (SGD) applied to over-parameterized deep learning has shown that most gradient components over epochs are quite small. Inspired by such observations, we rigorously study properties of…
In machine learning, stochastic gradient descent (SGD) is widely deployed to train models using highly non-convex objectives with equally complex noise models. Unfortunately, SGD theory often makes restrictive assumptions that fail to…
The simplicity of gradient descent (GD) made it the default method for training ever-deeper and complex neural networks. Both loss functions and architectures are often explicitly tuned to be amenable to this basic local optimization. In…
In the current quantum computing paradigm, significant focus is placed on the reduction or mitigation of quantum decoherence. When designing new quantum processing units, the general objective is to reduce the amount of noise qubits are…
We consider the dynamics of gradient descent (GD) in overparameterized single hidden layer neural networks with a squared loss function. Recently, it has been shown that, under some conditions, the parameter values obtained using GD achieve…
The great success neural networks have achieved is inseparable from the application of gradient-descent (GD) algorithms. Based on GD, many variant algorithms have emerged to improve the GD optimization process. The gradient for…
In statistical learning theory, generalization error is used to quantify the degree to which a supervised machine learning algorithm may overfit to training data. Recent work [Xu and Raginsky (2017)] has established a bound on the…
Despite much research, Graph Neural Networks (GNNs) still do not display the favorable scaling properties of other deep neural networks such as Convolutional Neural Networks and Transformers. Previous work has identified issues such as…