相关论文: Corridor Geometry in Gradient-Based Optimization

We study the implicit bias of gradient flow (i.e., gradient descent with infinitesimal step size) on linear neural network training. We propose a tensor formulation of neural networks that includes fully-connected, diagonal, and…

We introduce a machine-learning framework to learn the hyperparameter sequence of first-order methods (e.g., the step sizes in gradient descent) to quickly solve parametric convex optimization problems. Our computational architecture…

Stagewise training strategy is widely used for learning neural networks, which runs a stochastic algorithm (e.g., SGD) starting with a relatively large step size (aka learning rate) and geometrically decreasing the step size after a number…

We study gradient methods for optimizing $(L_0, L_1)$-smooth functions, a class that generalizes Lipschitz-smooth functions and has gained attention for its relevance in machine learning. We provide new insights into the structure of this…

Many modern learning tasks involve fitting nonlinear models to data which are trained in an overparameterized regime where the parameters of the model exceed the size of the training dataset. Due to this overparameterization, the training…

Herein the topics of (natural) gradient descent, data decorrelation, and approximate methods for backpropagation are brought into a common discussion. Natural gradient descent illuminates how gradient vectors, pointing at directions of…

Continual learning (CL) presents a fundamental challenge in training neural networks on sequential tasks without experiencing catastrophic forgetting. Traditionally, the dominant approach in CL has been gradient-based optimization, where…

In this paper, we study the implicit regularization of the gradient descent algorithm in homogeneous neural networks, including fully-connected and convolutional neural networks with ReLU or LeakyReLU activations. In particular, we study…

This paper shows that a wide class of effective learning rules -- those that improve a scalar performance measure over a given time window -- can be rewritten as natural gradient descent with respect to a suitably defined loss function and…

Recent progress on deep learning relies heavily on the quality and efficiency of training algorithms. In this paper, we develop a fast training method motivated by the nonlinear Conjugate Gradient (CG) framework. We propose the Conjugate…

Recent work across many machine learning disciplines has highlighted that standard descent methods, even without explicit regularization, do not merely minimize the training error, but also exhibit an implicit bias. This bias is typically…

Deep neural networks have been used in various machine learning applications and achieved tremendous empirical successes. However, training deep neural networks is a challenging task. Many alternatives have been proposed in place 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…

Despite the fact that the loss functions of deep neural networks are highly non-convex, gradient-based optimization algorithms converge to approximately the same performance from many random initial points. One thread of work has focused on…

Gradient-based iterative optimization methods are the workhorse of modern machine learning. They crucially rely on careful tuning of parameters like learning rate and momentum. However, one typically sets them using heuristic approaches…

We propose a computationally-friendly adaptive learning rate schedule, "AdaLoss", which directly uses the information of the loss function to adjust the stepsize in gradient descent methods. We prove that this schedule enjoys linear…

The success of deep learning is due, to a large extent, to the remarkable effectiveness of gradient-based optimization methods applied to large neural networks. The purpose of this work is to propose a modern view and a general mathematical…

We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system.…

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…

We study the gradient descent (GD) dynamics of a depth-2 linear neural network with a single input and output. We show that GD converges at an explicit linear rate to a global minimum of the training loss, even with a large stepsize --…