Related papers: Parametric Matrix Models
Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this…
We study and compare the learning dynamics of two universal learning algorithms, one based on Bayesian learning and the other on prediction with expert advice. Both approaches have strong asymptotic performance guarantees. When confronted…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
Numerical simulations are ubiquitous in science and engineering. Machine learning for science investigates how artificial neural architectures can learn from these simulations to speed up scientific discovery and engineering processes. Most…
Algorithms developed to solve many-body quantum problems, like tensor networks, can turn into powerful quantum-inspired tools to tackle problems in the classical domain. In this work, we focus on matrix product operators, a prominent…
The coincidence between polynomial neural networks and matrix Lie maps is discussed in the article. The matrix form of Lie transform is an approximation of the general solution of the nonlinear system of ordinary differential equations. It…
As deep learning applications continue to become more diverse, an interesting question arises: Can general problem solving arise from jointly learning several such diverse tasks? To approach this question, deep multi-task learning is…
Decision making algorithms are used in a multitude of different applications. Conventional approaches for designing decision algorithms employ principled and simplified modelling, based on which one can determine decisions via tractable…
We present a novel approach to modelling and learning vector fields from physical systems using neural networks that explicitly satisfy known linear operator constraints. To achieve this, the target function is modelled as a linear…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
There is a growing need for investigating how machine learning models operate. With this work, we aim to understand trained machine learning models by questioning their data preferences. We propose a mathematical framework that allows us to…
Differential equations are used in a wide variety of disciplines, describing the complex behavior of the physical world. Analytic solutions to these equations are often difficult to solve for, limiting our current ability to solve complex…
In the compressive learning theory, instead of solving a statistical learning problem from the input data, a so-called sketch is computed from the data prior to learning. The sketch has to capture enough information to solve the problem…
Data sets for fairness relevant tasks can lack examples or be biased according to a specific label in a sensitive attribute. We demonstrate the usefulness of weight based meta-learning approaches in such situations. For models that can be…
Due to the widespread use of complex machine learning models in real-world applications, it is becoming critical to explain model predictions. However, these models are typically black-box deep neural networks, explained post-hoc via…
Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models…
Networked data, in which every training example involves two objects and may share some common objects with others, is used in many machine learning tasks such as learning to rank and link prediction. A challenge of learning from networked…
Traditional models of climate change use complex systems of coupled equations to simulate physical processes across the Earth system. These simulations are highly computationally expensive, limiting our predictions of climate change and…
In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…
Artificial and natural neural network models are a new toolkit which could be potentially have been used for clarifying of complex brain functions. To attend this goal, such models need to be neurobiologically realistic. However, although…