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The largely successful method of training neural networks is to learn their weights using some variant of stochastic gradient descent (SGD). Here, we show that the solutions found by SGD can be further improved by ensembling a subset of the…

Pretraining language models on large text corpora is a common practice in natural language processing. Fine-tuning of these models is then performed to achieve the best results on a variety of tasks. In this paper, we investigate the…

In this manuscript, we investigate the problem of how two-layer neural networks learn features from data, and improve over the kernel regime, after being trained with a single gradient descent step. Leveraging the insight from (Ba et al.,…

Learning relies on coordinated synaptic changes in recurrently connected populations of neurons. Therefore, understanding the collective evolution of synaptic connectivity over learning is a key challenge in neuroscience and machine…

Recent works have partly attributed the generalization ability of over-parameterized neural networks to frequency bias -- networks trained with gradient descent on data drawn from a uniform distribution find a low frequency fit before high…

The utilization of residual learning has become widespread in deep and scalable neural nets. However, the fundamental principles that contribute to the success of residual learning remain elusive, thus hindering effective training of plain…

Recent studies revealed complex convergence dynamics in gradient-based methods, which has been little understood so far. Changing the step size to balance between high convergence rate and small generalization error may not be sufficient:…

We study the supervised learning problem under either of the following two models: (1) Feature vectors ${\boldsymbol x}_i$ are $d$-dimensional Gaussians and responses are $y_i = f_*({\boldsymbol x}_i)$ for $f_*$ an unknown quadratic…

In this paper, we first identify activation shift, a simple but remarkable phenomenon in a neural network in which the preactivation value of a neuron has non-zero mean that depends on the angle between the weight vector of the neuron and…

The adaptive learning capabilities seen in biological neural networks are largely a product of the self-modifying behavior emerging from online plastic changes in synaptic connectivity. Current methods in Reinforcement Learning (RL) only…

The results of training a neural network are heavily dependent on the architecture chosen; and even a modification of only its size, however small, typically involves restarting the training process. In contrast to this, we begin training…

"Deep Learning"/"Deep Neural Nets" is a technological marvel that is now increasingly deployed at the cutting-edge of artificial intelligence tasks. This dramatic success of deep learning in the last few years has been hinged on an enormous…

Modern machine learning models often employ a huge number of parameters and are typically optimized to have zero training loss; yet surprisingly, they possess near-optimal prediction performance, contradicting classical learning theory. We…

Deep neural networks' remarkable ability to correctly fit training data when optimized by gradient-based algorithms is yet to be fully understood. Recent theoretical results explain the convergence for ReLU networks that are wider than…

Deep learning involves navigating a high-dimensional loss landscape over the neural network parameter space. Over the course of training, complex computational structures form and re-form inside the neural network, leading to shifts in…

In recent years, deep neural networks have found success in replicating human-level cognitive skills, yet they suffer from several major obstacles. One significant limitation is the inability to learn new tasks without forgetting previously…

Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the…

Deep neural networks have long training and processing times. Early exits added to neural networks allow the network to make early predictions using intermediate activations in the network in time-sensitive applications. However, early…

We consider optimizing two-layer neural networks in the mean-field regime where the learning dynamics of network weights can be approximated by the evolution in the space of probability measures over the weight parameters associated with…

Over-parameterized residual networks (ResNets) are amongst the most successful convolutional neural architectures for image processing. Here we study their properties through their Gaussian Process and Neural Tangent kernels. We derive…