相关论文: When does gradient descent with logistic loss find…

The function and performance of neural networks is largely determined by the evolution of their weights and biases in the process of training, starting from the initial configuration of these parameters to one of the local minima of the…

We analyse the convergence of one-hidden-layer ReLU networks trained by gradient flow on $n$ data points. Our main contribution leverages the high dimensionality of the ambient space, which implies low correlation of the input samples, to…

We study the overparametrization bounds required for the global convergence of stochastic gradient descent algorithm for a class of one hidden layer feed-forward neural networks, considering most of the activation functions used in…

Several recent works demonstrate that transformers can implement algorithms like gradient descent. By a careful construction of weights, these works show that multiple layers of transformers are expressive enough to simulate iterations of…

The ability of learning useful features is one of the major advantages of neural networks. Although recent works show that neural network can operate in a neural tangent kernel (NTK) regime that does not allow feature learning, many works…

Advanced machine learning methods, and more prominently neural networks, have become standard to solve inverse problems over the last years. However, the theoretical recovery guarantees of such methods are still scarce and difficult to…

A recent line of research on deep learning focuses on the extremely over-parameterized setting, and shows that when the network width is larger than a high degree polynomial of the training sample size $n$ and the inverse of the target…

Neural networks are very successful tools in for example advanced classification. From a statistical point of view, fitting a neural network may be seen as a kind of regression, where we seek a function from the input space to a space of…

We consider a deep ReLU / Leaky ReLU student network trained from the output of a fixed teacher network of the same depth, with Stochastic Gradient Descent (SGD). The student network is \emph{over-realized}: at each layer $l$, the number…

Deep neural networks are highly expressive machine learning models with the ability to interpolate arbitrary datasets. Deep nets are typically optimized via first-order methods and the optimization process crucially depends on the…

Natural gradient descent is a principled method for adapting the parameters of a statistical model on-line using an underlying Riemannian parameter space to redefine the direction of steepest descent. The algorithm is examined via methods…

Gradient descent (GD) type optimization schemes are the standard methods to train artificial neural networks (ANNs) with rectified linear unit (ReLU) activation. Such schemes can be considered as discretizations of gradient flows (GFs)…

We consider the problem of generalization of arbitrarily overparameterized two-layer ReLU Neural Networks with univariate input. Recent work showed that under square loss, flat solutions (motivated by flat / stable minima and Edge of…

We introduce a novel framework for learning in neural networks by decomposing each neuron's weight vector into two distinct parts, $W_1$ and $W_2$, thereby modeling contrastive information directly at the neuron level. Traditional gradient…

Stochastic gradient descent plays a fundamental role in nearly all applications of deep learning. However its ability to converge to a global minimum remains shrouded in mystery. In this paper we propose to study the behavior of the loss…

The dynamics of gradient-based training in neural networks often exhibit nontrivial structures; hence, understanding them remains a central challenge in theoretical machine learning. In particular, a concept of feature unlearning, in which…

We study the dynamics and implicit bias of gradient flow (GF) on univariate ReLU neural networks with a single hidden layer in a binary classification setting. We show that when the labels are determined by the sign of a target network with…

We present a theoretical and empirical study of the gradient dynamics of overparameterized shallow ReLU networks with one-dimensional input, solving least-squares interpolation. We show that the gradient dynamics of such networks are…

Overparameterized ML models, including neural networks, typically induce underdetermined training objectives with multiple global minima. The implicit bias refers to the limiting global minimum that is attained by a common optimization…

Any gradient descent optimization requires to choose a learning rate. With deeper and deeper models, tuning that learning rate can easily become tedious and does not necessarily lead to an ideal convergence. We propose a variation of the…