相关论文: Dimension reduction in recurrent networks by canon…

We show that recent results on randomized dimension reduction schemes that exploit structural properties of data can be applied in the context of persistent homology. In the spirit of compressed sensing, the dimension reduction is…

Despite their many appealing properties, kernel methods are heavily affected by the curse of dimensionality. For instance, in the case of inner product kernels in $\mathbb{R}^d$, the Reproducing Kernel Hilbert Space (RKHS) norm is often…

Interest in reinforcement learning (RL) for large-scale systems, comprising extensive populations of intelligent agents interacting with heterogeneous environments, has surged significantly across diverse scientific domains in recent years.…

Under mild assumptions on the kernel, we obtain the best known error rates in a regularized learning scenario taking place in the corresponding reproducing kernel Hilbert space (RKHS). The main novelty in the analysis is a proof that one…

The focus of this paper is the application of classical model order reduction techniques, such as Active Subspaces and Proper Orthogonal Decomposition, to Deep Neural Networks. We propose a generic methodology to reduce the number of layers…

We study dynamic regret in online convex optimization, where the objective is to achieve low cumulative loss relative to an arbitrary benchmark sequence. By observing that competing with an arbitrary sequence of comparators…

Quantum Annealing (QA) is one of the most promising frameworks for quantum optimization. Here, we focus on the problem of minimizing complex classical cost functions associated with prototypical discrete neural networks, specifically the…

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

This work presents a nonparametric framework for dissipativity learning in reproducing kernel Hilbert spaces, which enables data-driven certification of stability and performance properties for unknown nonlinear systems without requiring an…

We study distributed learning with the least squares regularization scheme in a reproducing kernel Hilbert space (RKHS). By a divide-and-conquer approach, the algorithm partitions a data set into disjoint data subsets, applies the least…

Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…

The goal of supervised representation learning is to construct effective data representations for prediction. Among all the characteristics of an ideal nonparametric representation of high-dimensional complex data, sufficiency, low…

Traditionally, kernel methods rely on the representer theorem which states that the solution to a learning problem is obtained as a linear combination of the data mapped into the reproducing kernel Hilbert space (RKHS). While elegant from…

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…

This study presents a novel model for invertible sentence embeddings using a residual recurrent network trained on an unsupervised encoding task. Rather than the probabilistic outputs common to neural machine translation models, our…

The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential…

When applying quantum computing to machine learning tasks, one of the first considerations is the design of the quantum machine learning model itself. Conventionally, the design of quantum machine learning algorithms relies on the…

Encoding classical data into quantum states is considered a quantum feature map to map classical data into a quantum Hilbert space. This feature map provides opportunities to incorporate quantum advantages into machine learning algorithms…

One of the fundamental problems within the field of machine learning is dimensionality reduction. Dimensionality reduction methods make it possible to combat the so-called curse of dimensionality, visualize high-dimensional data and, in…

Current deep learning architectures suffer from catastrophic forgetting, a failure to retain knowledge of previously learned classes when incrementally trained on new classes. The fundamental roadblock faced by deep learning methods is that…