arXiv research

We introduce a new activation function using Chebyshev-Lagrange polynomials for improved neural network performance.

The paper proves Sard's theorem for polynomial maps in infinite dimensions.

New algorithm reduces dynamic regret for noisy gradient feedback with piecewise polynomial comparators.

PyChEst detects changes in non-stationary time series without distributional assumptions.

This paper proposes a method to approximate non-Gaussian likelihoods in Gaussian Processes.

Estimates change-points and graph structures in a time-varying Ising model.

New methods for calculating curvature in graph theory.

XOFM explains attribute effects in ordinal regression using piece-wise linear functions.

Bayesian method detects change points and clusters in piece-wise constant signals.

We consider billiard ball motion in a convex domain of the Euclidean plane bounded by a piece-wise smooth curve influenced by the constant magnetic field. We show that if there exists a polynomial in velocities integral of the magnetic billiard flow then every smooth piece $γ$ of the boundary must be algebraic and eith…

A new method for creating simpler models from complex ones.

Efficiently infers switching nonlinear systems with collapsed amortized variational inference.

L*ReLU improves deep learning for fine-grained image classification.

Deep nets' optima are surprisingly connected by simple paths.

Paper investigates a new type of elastica formed during beam rupture.

In this survey article, we review the relation between heat kernels and path integrals. In particular, we review recent results on the approximation of the Wiener measure on compact manifold by measures on (finite-dimensional) spaces of piece-wise geodesics.

DAMI uses interpretable regions to select informative samples for deep learning models.

CTR prediction in real-world business is a difficult machine learning problem with large scale nonlinear sparse data. In this paper, we introduce an industrial strength solution with model named Large Scale Piece-wise Linear Model (LS-PLM). We formulate the learning problem with $L_1$ and $L_{2,1}$ regularizers, leadin…

This paper extends depth separation results to piece-wise oscillatory functions.

This work simplifies adversarial attacks using neural networks, reducing computation and improving training convergence.

RUMBoost combines RUMs and deep learning for better choice modelling.

Neural models can realize decision trees with parameter sharing and improved performance.

Considering Wirtinger's inequality for piece-wise equipartite functions we find a discrete version of this classical inequality. The main tool we use is the theorem of classification of isometries. Our approach provides a new elementary proof of Wirtinger's inequality that also allows to study the case of equality. Mor…

Method to create rational Seifert surfaces for knots in Lens space.

It is shown that most of the well-known basic results for Sobolev-Slobodeckii and Bessel potential spaces, known to hold on bounded smooth domains in $\mathbb{R}^n$, continue to be valid on a wide class of Riemannian manifolds with singularities and boundary, provided suitable weights, which reflect the nature of the s…

Let S be a triangulated 2-sphere with fixed triangulation T. We apply the methods of thin position from knot theory to obtain a simple version of the three geodesics theorem for the 2-sphere [5]. In general these three geodesics may be unstable, corresponding, for example, to the three equators of an ellipsoid. Using a…

Given two points on a soup can or conical cup with lid, we find and classify all paths of minimal length connecting them. When the number of minimal paths is finite, there are at most four on a can and three on a cup. At worst, minimal paths are piece-wise smooth with three components, each of which is a classical geod…

The study examines generalization bounds for regression and classification tasks on adaptive input domains.

A new algorithm finds optimal solutions for constrained decision processes.

We investigate the functional determinant of the laplacian on piece-wise flat two-dimensional surfaces, with conical singularities in the interior and/or corners on the boundary. Our results extend earlier investigations of the determinants on smooth surfaces with smooth boundaries. The differences to the smooth case a…

Method finds differential equations for integrable billiard tables.

Optimal order execution strategies for brokers under reference benchmarks.

Study tackles inverse problems on low-dimensional manifolds, proving stability and proposing a reconstruction algorithm.

In many applications we seek to maximize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze existing solutions including finite-difference (FD) estimators and continuous relaxatio…

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by means of simplicial complexes. Th…

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including…

Paper proposes a novel SVM method for creating survival trees.

The functional determinant of an elliptic operator with positive, discrete spectrum may be defined as $e^{-Z'(0)}$, where $Z(s)$, the zeta function, is the sum $\sum_n^{\infty} λ_n^{-s}$ analytically continued to $s$ around the origin. In this paper $Z'(0)$ is calculated for the Laplace operator with Dirichlet boundary…

This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop the explicit solution for this class of problem. The revealed optimal control poli…

This paper proposes a novel Gaussian process approach to fault removal in time-series data. Fault removal does not delete the faulty signal data but, instead, massages the fault from the data. We assume that only one fault occurs at any one time and model the signal by two separate non-parametric Gaussian process model…

Gradient descent can use larger step sizes to avoid strict saddle points.

AdaPID optimizes diffusion-based samplers by dynamically adjusting schedules.

Intelligent behaviour in the real-world requires the ability to acquire new knowledge from an ongoing sequence of experiences while preserving and reusing past knowledge. We propose a novel algorithm for unsupervised representation learning from piece-wise stationary visual data: Variational Autoencoder with Shared Emb…

In this paper we analyze the asymptotic properties of l1 penalized maximum likelihood estimation of signals with piece-wise constant mean values and/or variances. The focus is on segmentation of a non-stationary time series with respect to changes in these model parameters. This change point detection and estimation pr…

We study the problem of estimating a temporally varying coefficient and varying structure (VCVS) graphical model underlying nonstationary time series data, such as social states of interacting individuals or microarray expression profiles of gene networks, as opposed to i.i.d. data from an invariant model widely consid…

Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy storage and computation requirements of a dictionary-matching (DM) step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. In this paper we study…

Motivated by an important insight from neural science, we propose a new framework for understanding the success of the recently proposed "maxout" networks. The framework is based on encoding information on sparse pathways and recognizing the correct pathway at inference time. Elaborating further on this insight, we pro…

We consider the detection of activations over graphs under Gaussian noise, where signals are piece-wise constant over the graph. Despite the wide applicability of such a detection algorithm, there has been little success in the development of computationally feasible methods with proveable theoretical guarantees for ge…