Related papers: General non-linear Bellman equations
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Hyperbolic space has become a popular choice of manifold for representation learning of various datatypes from tree-like structures and text to graphs. Building on the success of deep learning with prototypes in Euclidean and hyperspherical…
We apply scaling and the theory of the fundamental limits of the second-order molecular susceptibility to identify material classes with ultralarge nonlinear-optical response. Size effects are removed by normalizing all nonlinearities to…
Quantum Machine Learning algorithms based on Variational Quantum Circuits (VQCs) are important candidates for useful application of quantum computing. It is known that a VQC is a linear model in a feature space determined by its…
In this article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Cole) for systems of partial differentail equations. This…
The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…
In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…
Model explainability is crucial for human users to be able to interpret how a proposed classifier assigns labels to data based on its feature values. We study generalized linear models constructed using sets of feature value rules, which…
We propose a new approach to solving dynamic decision problems with rewards that are unbounded below. The approach involves transforming the Bellman equation in order to convert an unbounded problem into a bounded one. The major advantage…
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms.…
Ordinal regression is a classification task where classes have an order and prediction error increases the further the predicted class is from the true class. The standard approach for modeling ordinal data involves fitting parallel…
We consider the periodic dispersion generalized Benjamin-Ono equations with polynomial nonlinearity. We establish the nonlinear smoothing properties of these equations, according to which the difference between the solution and the linear…
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…
Machine learning algorithms use error function minimization to fit a large set of parameters in a preexisting model. However, error minimization eventually leads to a memorization of the training dataset, losing the ability to generalize to…
Linear models have shown great effectiveness and flexibility in many fields such as machine learning, signal processing and statistics. They can represent rich spaces of functions while preserving the convexity of the optimization problems…
One of the central challenges in modern machine learning is understanding how neural networks generalize knowledge learned from training data to unseen test data. While numerous empirical techniques have been proposed to improve…
New approaches to the theory of dynamic programming view dynamic programs as families of policy operators acting on partially ordered sets. In this paper, we extend these ideas by shifting from arbitrary partially ordered sets to ordered…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
Constructing good representations is critical for learning complex tasks in a sample efficient manner. In the context of meta-learning, representations can be constructed from common patterns of previously seen tasks so that a future task…