A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
CKA with Gaussian RBF kernels converges linearly as bandwidth increases.
MKA incorporates manifold geometry into kernel alignment for more robust representation comparison.
New measures link neural representation geometry to decoding ability.
The object of our investigation is a point that gives the maximum value of a potential with a strictly decreasing radially symmetric kernel. It defines a center of a body in Rm. When we choose the Riesz kernel or the Poisson kernel as the kernel, such centers are called a radial center or an illuminating center, respec…
The study explains how neural networks align their kernels to target functions during training.
NKI integrates obfuscated datasets using nonlinear kernels for improved data collaboration.
Kernel alignment measures the degree of similarity between two kernels. In this paper, inspired from kernel alignment, we propose a new Linear Discriminant Analysis (LDA) formulation, kernel alignment LDA (kaLDA). We first define two kernels, data kernel and class indicator kernel. The problem is to find a subspace to …
The study investigates kernel-target alignment in tree ensemble kernels.
New estimator corrects bias in CKA for sparsely sampled neurons.
DHGAK aligns substructures for better graph kernel performance.
TKRR improves KRR performance by aligning target functions with kernels.
Correntropy is a local similarity measure defined in kernel space and the maximum correntropy criterion (MCC) has been successfully applied in many areas of signal processing and machine learning in recent years. The kernel function in correntropy is usually restricted to the Gaussian function with center located at ze…
This work incorporates the multi-modality of the data distribution into a Gaussian Process regression model. We approach the problem from a discriminative perspective by learning, jointly over the training data, the target space variance in the neighborhood of a certain sample through metric learning. We start by using…
Neural networks can learn kernel machines with a data-dependent kernel.
Paper proposes new costs for learning multiple centers in MDNs.
The purpose of this paper is to extend the explicit geometric evaluation of semisimple orbital integrals for smooth kernels for the Casimir operator obtained by the first author to the case of kernels for arbitrary elements in the center of the enveloping algebra.
Recently, considerable effort has been devoted to deep domain adaptation in computer vision and machine learning communities. However, most of existing work only concentrates on learning shared feature representation by minimizing the distribution discrepancy across different domains. Due to the fact that all the domai…
In this paper we introduce the deep kernelized autoencoder, a neural network model that allows an explicit approximation of (i) the mapping from an input space to an arbitrary, user-specified kernel space and (ii) the back-projection from such a kernel space to input space. The proposed method is based on traditional a…
The paper proposes a learning-theoretic perspective on representation alignment.
New framework assesses neural sensitivity to small perturbations.
Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical correlation analysis (CCA). We show that CCA belongs to a family of statistics for mea…
Unified understanding of neural representation similarity measures.
This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified technique is obtained by accounting for the bias in the regression problem resulti…
NTKs explain GNNs' alignment for graph prediction.
Many pattern recognition methods rely on statistical information from centered data, with the eigenanalysis of an empirical central moment, such as the covariance matrix in principal component analysis (PCA), as well as partial least squares regression, canonical-correlation analysis and Fisher discriminant analysis. R…
Regularization effect found in neural feature alignment.
We introduce a kernel method for manifold alignment (KEMA) and domain adaptation that can match an arbitrary number of data sources without needing corresponding pairs, just few labeled examples in all domains. KEMA has interesting properties: 1) it generalizes other manifold alignment methods, 2) it can align manifold…
Two methods solve kernel ridge regression problems efficiently.
As a novel similarity measure that is defined as the expectation of a kernel function between two random variables, correntropy has been successfully applied in robust machine learning and signal processing to combat large outliers. The kernel function in correntropy is usually a zero-mean Gaussian kernel. In a recent …
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when representing graphs. Some recent global graph kernels, which utilizes the align…
We consider two eigenvalue problems for Laplacian on some specific doubly connected domain. In particular, we study the following two eigenvalue problems. Let be an open ball in and be a ball contained in . Let be the outward unit normal on . Then the first eigenvalue o…
This paper uses MIO to select features for kernel SVM classification.
String kernels are attractive data analysis tools for analyzing string data. Among them, alignment kernels are known for their high prediction accuracies in string classifications when tested in combination with SVM in various applications. However, alignment kernels have a crucial drawback in that they scale poorly du…
Deconfounds neural network representation similarity metrics to improve consistency and accuracy.
End-to-end kernel learning using generative RFFs for improved performance.
The paper proves no positive weak solutions for a specific inequality on Riemannian manifolds.
New kernel interprets 3D anisotropic data with rotations and improved predictions.
This paper examines the impact of centering in PCA and SVD.
One obstacle to applying reinforcement learning algorithms to real-world problems is the lack of suitable reward functions. Designing such reward functions is difficult in part because the user only has an implicit understanding of the task objective. This gives rise to the agent alignment problem: how do we create age…
Autoencoders learn data representations (codes) in such a way that the input is reproduced at the output of the network. However, it is not always clear what kind of properties of the input data need to be captured by the codes. Kernel machines have experienced great success by operating via inner-products in a theoret…
Expressiveness and generalization of deep models was recently addressed via the connection between neural networks (NNs) and kernel learning, where first-order dynamics of NN during a gradient-descent (GD) optimization were related to gradient similarity kernel, also known as Neural Tangent Kernel (NTK). In the majorit…
FCA improves fair clustering by optimizing utility and fairness.
Centered Kernel Alignment (CKA) was recently proposed as a similarity metric for comparing activation patterns in deep networks. Here we experiment with the modified RV-coefficient (RV2), which has very similar properties as CKA while being less sensitive to dataset size. We compare the representations of networks that…
Study tests how U.S. equity prices align with global asset frequencies using financial variables.
The paper explains generalization in kernel regression and deep neural networks using spectral bias and task-model alignment.
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 optimization during training. Such analyses also provide upper bounds on the gener…
New framework to test neural network representation similarity measures.
Can neural networks learn to compare graphs without feature engineering? In this paper, we show that it is possible to learn representations for graph similarity with neither domain knowledge nor supervision (i.e.\ feature engineering or labeled graphs). We propose Deep Divergence Graph Kernels, an unsupervised method …