Related papers: Natural Riemannian gradient for learning functiona…
In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…
Fractional gradient descent has been studied extensively, with a focus on its ability to extend traditional gradient descent methods by incorporating fractional-order derivatives. This approach allows for more flexibility in navigating…
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…
Learning to Rank (LTR) algorithms are usually evaluated using Information Retrieval metrics like Normalised Discounted Cumulative Gain (NDCG) or Mean Average Precision. As these metrics rely on sorting predicted items' scores (and thus, on…
In this paper, the Riemannian gradient algorithm and the natural gradient algorithm are applied to solve descent direction problems on the manifold of positive definite Hermitian matrices, where the geodesic distance is considered as the…
Federated learning (FL) has emerged as a powerful paradigm for collaborative model training across distributed clients while preserving data privacy. However, existing FL algorithms predominantly focus on unconstrained optimization problems…
Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…
We describe four algorithms for neural network training, each adapted to different scalability constraints. These algorithms are mathematically principled and invariant under a number of transformations in data and network representation,…
Recently, there has been a growing interest in efficient numerical algorithms based on tensor networks and low-rank techniques to approximate high-dimensional functions and solutions to high-dimensional PDEs. In this paper, we propose a new…
The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially…
We provide the first experimental results on non-synthetic datasets for the quasi-diagonal Riemannian gradient descents for neural networks introduced in [Ollivier, 2015]. These include the MNIST, SVHN, and FACE datasets as well as a…
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…
Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…
Enforcing orthonormal or isometric property for the weight matrices has been shown to enhance the training of deep neural networks by mitigating gradient exploding/vanishing and increasing the robustness of the learned networks. However,…
Value function learning plays a central role in many state-of-the-art reinforcement-learning algorithms. Many popular algorithms like Q-learning do not optimize any objective function, but are fixed-point iterations of some variant of…
Decision Trees (DTs) are commonly used for many machine learning tasks due to their high degree of interpretability. However, learning a DT from data is a difficult optimization problem, as it is non-convex and non-differentiable.…
In the recent years, Physics Informed Neural Networks (PINNs) have received strong interest as a method to solve PDE driven systems, in particular for data assimilation purpose. This method is still in its infancy, with many shortcomings…
The natural gradient allows for more efficient gradient descent by removing dependencies and biases inherent in a function's parameterization. Several papers present the topic thoroughly and precisely. It remains a very difficult idea to…
One of the most important parts of Artificial Neural Networks is minimizing the loss functions which tells us how good or bad our model is. To minimize these losses we need to tune the weights and biases. Also to calculate the minimum value…
The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The…