Related papers: Dual-to-kernel learning with ideals
We study the finite generation of the intersection algebra of two principal ideals I and J in a unique factorization domain R. We provide an algorithm that produces a list of generators of this algebra over R. In the special case that R is…
At the interface of machine learning and quantum computing, an important question is what distributions can be learned provably with optimal sample complexities and with quantum-accelerated time complexities. In the classical case, Klivans…
We apply local laws of random matrices and free probability theory to study the spectral properties of two kernel-based sensor fusion algorithms, nonparametric canonical correlation analysis (NCCA) and alternating diffusion (AD), for two…
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…
We show a duality of branes in the topological B-model by inserting two kinds of the non-compact branes simultaneously. We explicitly derive the integral formula for the matrix model partition function describing this situation, which…
Macaulay dual spaces provide a local description of an affine scheme and give rise to computational machinery that is compatible with the methods of numerical algebraic geometry. We introduce eliminating dual spaces, use them for computing…
Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…
Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between…
Continual learning (CL) learns a sequence of tasks incrementally. This paper studies the challenging CL setting of class-incremental learning (CIL). CIL has two key challenges: catastrophic forgetting (CF) and inter-task class separation…
Suppose we are given black-box access to a finite ring R, and a list of generators for an ideal I in R. We show how to find an additive basis representation for I in poly(log |R|) time. This generalizes a quantum algorithm of Arvind et al.…
Many recursive functions can be defined elegantly as the unique homomorphisms, between two algebras, two coalgebras, or one each, that are induced by some universal property of a distinguished structure. Besides the well-known applications…
Despite the effectiveness of Convolutional Neural Networks (CNNs) for image classification, our understanding of the relationship between shape of convolution kernels and learned representations is limited. In this work, we explore and…
Generalization performance of classifiers in deep learning has recently become a subject of intense study. Deep models, typically over-parametrized, tend to fit the training data exactly. Despite this "overfitting", they perform well on…
In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…
This paper investigates the foundations of deep learning through insight of geometry, algebra and differential calculus. At is core, artificial intelligence relies on assumption that data and its intrinsic structure can be embedded into…
Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated…
This paper introduces kernel continual learning, a simple but effective variant of continual learning that leverages the non-parametric nature of kernel methods to tackle catastrophic forgetting. We deploy an episodic memory unit that…
Recent results on optimization and generalization properties of neural networks showed that in a simple two-layer network, the alignment of the labels to the eigenvectors of the corresponding Gram matrix determines the convergence of the…
Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework.…
Kernel methods are of current interest in quantum machine learning due to similarities with quantum computing in how they process information in high-dimensional feature (Hilbert) spaces. Kernels are believed to offer particular advantages…