arXiv research

Hermite polynomials improve private data generation by reducing feature count.

Recent years have demonstrated that using random feature maps can significantly decrease the training and testing times of kernel-based algorithms without significantly lowering their accuracy. Regrettably, because random features are target-agnostic, typically thousands of such features are necessary to achieve accept…

Covariance pooling is a feature pooling method with good classification accuracy. Because covariance features consist of second-order statistics, the scale of the feature elements are varied. Therefore, normalizing covariance features using a matrix square root affects the performance improvement. When pooling methods …

Three-layer networks learn complex hierarchical polynomials of multiple nonlinear features.

The Hirzebruch $χ_y$-genus and Poincare polynomial share some similar features. In this article we investigate two of their similar features simultaneously. Through this process we shall derive several new results as well as reprove and improve some known results.

Three-layer neural networks learn hierarchical polynomial functions efficiently.

New algorithm learns sparse linear MDPs with polynomial interactions, improving sample complexity.

We define complex cobordism realizations of cohomological Thom polynomials and study their existence, uniqueness and other features. We show that problem is non-trivial on the example of $Σ^1$ singularity.

Q-SHAP efficiently calculates feature contributions in boosting trees.

Speech-driven facial animation involves using a speech signal to generate realistic videos of talking faces. Recent deep learning approaches to facial synthesis rely on extracting low-dimensional representations and concatenating them, followed by a decoding step of the concatenated vector. This accounts for only first…

Kernel approximation using randomized feature maps has recently gained a lot of interest. In this work, we identify that previous approaches for polynomial kernel approximation create maps that are rank deficient, and therefore do not utilize the capacity of the projected feature space effectively. To address this chal…

Paper conjectures Links-Gould invariant generalizes Alexander polynomial.

Jones polynomials for knots and links with many crossings calculated efficiently.

Extends A-type coefficient polynomials to B-type setting, introducing new invariants.

NGRC shows numerical instabilities with short lags and high-degree polynomials.

Gradient descent with growing learning rate enables learning non-linear features in neural networks.

New method improves Gaussian kernel approximations for high-frequency data.

Predicts the number of polynomial additions in Buchberger's algorithm using machine learning.

Study shows RFRR's effectiveness with nearly orthogonal data in overparameterized settings.

The colored HOMLFY polynomial is an important knot invariant depending on two variables $a$ and $q$. We give bounds on the degree in both $a$ and $q$ generalizing Morton's bounds \cite{Mo86} for the ordinary HOMFLY polynomial. Our bounds suggest that the degree detects certain incompressible surfaces in the knot comple…

Deep neural networks with piecewise-polynomial activations can approximate smooth functions and their derivatives.

Learning the kernel functions used in kernel methods has been a vastly explored area in machine learning. It is now widely accepted that to obtain 'good' performance, learning a kernel function is the key challenge. In this work we focus on learning kernel representations for structured regression. We propose use of po…

This work reconstructs knot invariants from Alexander polynomials, proving consistency with known theorems.

In this paper, we aim at introducing a new machine learning model, namely reconciled polynomial machine, which can provide a unified representation of existing shallow and deep machine learning models. Reconciled polynomial machine predicts the output by computing the inner product of the feature kernel function and va…

Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the interpretability of the features. We study the problem of constructing optimal sparse linear a…

Improves efficiency of random feature approximations for dot product kernels.

Study Alexander polynomials of modular knots, revealing finite and infinite coefficient properties.

Paper proposes an efficient RL algorithm for discounted MDPs using feature mapping.

New framework allows reinforcement learning with polynomial sample complexity.

In the era of big data, it is desired to develop efficient machine learning algorithms to tackle massive data challenges such as storage bottleneck, algorithmic scalability, and interpretability. In this paper, we develop a novel efficient classification algorithm, called fast polynomial kernel classification (FPC), to…

Kernel discriminant analysis uses nonlinear embeddings to improve classification.

Paper introduces algorithms for explaining monotonic classifiers.

Two-layer NN with channel attention learns low-degree spherical polynomials efficiently.

The Links-Gould invariant of alternating links has log-concave coefficients.

The paper improves bounds on skein tree depth and delta-crossing numbers for knots and links.

New method learns to generalize across different data domains efficiently.

New algorithms explain Naive Bayes classifiers in polynomial time and delay.

The colored Jones polynomial is a knot invariant that plays a central role in low dimensional topology. We give a simple and an efficient algorithm to compute the colored Jones polynomial of any knot. Our algorithm utilizes the walks along a braid model of the colored Jones polynomial that was refined by Armond from th…

This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the training sample. The estimated uncertainties can be propagated into the optimal…

New framework uses score-based priors to solve ill-conditioned polynomial equations, improving signal recovery from noisy data.

New kernel improves graph learning with fewer labeled data.

New method uses sparse random features for crashworthiness analysis.

Efficiently plans large MDPs with weak function approximations.

PDSim simulates and estimates commodity futures prices using polynomial diffusion models.

Polynomial networks and factorization machines are two recently-proposed models that can efficiently use feature interactions in classification and regression tasks. In this paper, we revisit both models from a unified perspective. Based on this new view, we study the properties of both models and propose new efficient…

Study shows polynomial-width neural networks can closely approximate infinite-width networks in polynomial time.

Spofe bridges statistical rigor and interpretability in feature extraction from tabular data.

Gradient Descent with Projection learns low-degree polynomials efficiently.