arXiv research

1-D CNNs classify pupil size variations in scotopic conditions.

The intensive care units (ICUs) are responsible for generating a wealth of useful data in the form of Electronic Health Record (EHR). This data allows for the development of a prediction tool with perfect knowledge backing. We aimed to build a mortality prediction model on 2012 Physionet Challenge mortality prediction …

LipKernel adds robustness to CNNs by enforcing Lipschitz bounds.

Generative Adversarial Networks create synthetic data for structural damage detection.

This paper characterizes stable polynomial mappings in a specific set.

Convolutional neural networks (CNNs) have achieved great success on grid-like data such as images, but face tremendous challenges in learning from more generic data such as graphs. In CNNs, the trainable local filters enable the automatic extraction of high-level features. The computation with filters requires a fixed …

Constructs a path integral for fermionic SPTs, solving anomalies in 2+1D topological orders.

New proof shows incremental flow models are essential for universal generation.

A classic problem in physics is the origin of fat tailed distributions generated by complex systems. We study the distributions of stock returns measured over different time lags $τ.$ We find that destroying all correlations without changing the $τ= 1$ d distribution, by shuffling the order of the daily returns, causes…

In this paper, we analyze L-space surgeries on two component L-space links. We show that if one surgery coefficient is negative for the L-space surgery, then the corresponding link component is an unknot. If the link admits very negative (i.e. $d_{1}, d_{2}\ll0$) L-space surgeries, it is the Hopf link. We also give a w…

The paper proves spectral convergence rates for graph Laplacian to manifold Laplace-Beltrami operator.

Study on surfaces in flag threefold with constraints on twistor fibers.

Improved algorithm for low-discrepancy colorings with practical time complexity.

Deep ReLU networks can approximate and learn smooth functions efficiently.

We extend the mixtures of Gaussians (MOG) model to the projected mixture of Gaussians (PMOG) model. In the PMOG model, we assume that q dimensional input data points z_i are projected by a q dimensional vector w into 1-D variables u_i. The projected variables u_i are assumed to follow a 1-D MOG model. In the PMOG model…

This paper is on the normal approximation of singular subspaces when the noise matrix has i.i.d. entries. Our contributions are three-fold. First, we derive an explicit representation formula of the empirical spectral projectors. The formula is neat and holds for deterministic matrix perturbations. Second, we calculate…

Power-law spectrum of random feature model is preserved in neural networks.

We introduce the class $Σ_k(d)$ of $k$-stellated (combinatorial) spheres of dimension $d$ ($0 \leq k \leq d + 1$) and compare and contrast it with the class ${\cal S}_k(d)$ ($0 \leq k \leq d$) of $k$-stacked homology $d$-spheres. We have $Σ_1(d) = {\cal S}_1(d)$, and $Σ_k(d) \subseteq {\cal S}_k(d)$ for $d \geq 2k - 1$…

New jet functors generalize classical notions in noncommutative geometry.

Modern audio source separation techniques rely on optimizing sequence model architectures such as, 1D-CNNs, on mixture recordings to generalize well to unseen mixtures. Specifically, recent focus is on time-domain based architectures such as Wave-U-Net which exploit temporal context by extracting multi-scale features. …

The hypercube's perimeter is significantly larger than expected near half volume.

The paper proves formulas and theorems for specific operators on manifolds.

New method beats volumetric barrier for manifold recovery.

New framework improves efficiency in low-rank matrix bandit problems.

Method estimates joint probability density from samples using low-rank decomposition and random projections.

A detailed version of preprint "Self-linking number of a real algebraic link" by the same author, alg-geom/9410030. For a nonsingular real algebraic curve in 3-dimensional projective space or 3-sphere, a new integer-valued characteristic is introduced. It is invariant under rigid isotopy and multiplied by -1 under mirr…

The study finds rational points on specific types of hypersurfaces.

This paper optimizes ReLU networks for approximating Hölder continuous functions.

We show that any $d$-Ahlfors regular subset of $\mathbb{R}^{n}$ supporting a weak $(1,d)$-Poincaré inequality with respect to surface measure is uniformly rectifiable.

Deep neural nets on 1-D data are convex Lasso models with reflection features.

Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a binary split of $[0, 1]^d$ and built up sequentially according to discrepancy crite…

Deep ReLU networks can efficiently approximate Sobolev and Besov functions.

For integers $d \geq 2$ and $ε= 0$ or 1, let $S^{1, d - 1}(ε)$ denote the sphere product $S^{1} \times S^{d - 1}$ if $ε= 0$ and the twisted $S^{d - 1}$ bundle over $S^{1}$ if $ε= 1$. The main results of this paper are: (a) if $d \equiv ε$ (mod 2) then $S^{1, d - 1}(ε)$ has a unique minimal triangulation using $2d + 3$ …

New approximative kernels improve PDE-G-CNNs for geometric deep learning.

In recent years, deep learning poses a deep technical revolution in almost every field and attracts great attentions from industry and academia. Especially, the convolutional neural network (CNN), one representative model of deep learning, achieves great successes in computer vision and natural language processing. How…

Where dealing with temporal sequences it is fair to assume that the same kind of deformations that motivated the development of the Dynamic Time Warp algorithm could be relevant also in the calculation of the dot product ("convolution") in a 1-D convolution layer. In this work a method is proposed for aligning the conv…

Sparse covariance estimation in the vertical-split model achieves exponential improvement over dense estimates.

Study robust learning of Lipschitz functions under corrupted binary signals.

We attempt to interpret how adversarially trained convolutional neural networks (AT-CNNs) recognize objects. We design systematic approaches to interpret AT-CNNs in both qualitative and quantitative ways and compare them with normally trained models. Surprisingly, we find that adversarial training alleviates the textur…

An electrocardiogram (ECG) is a time-series signal that is represented by one-dimensional (1-D) data. Higher dimensional representation contains more information that is accessible for feature extraction. Hidden variables such as frequency relation and morphology of segment is not directly accessible in the time domain…

In this paper, we give a quantum interpretation of the Bismut-Chern character form (the loop space lifting of the Chern character form) as well as the Chern character form associated to a complex vector bundle with connection over a smooth manifold in the framework of supersymmetric quantum field theories developed by …

Deep neural networks can approximate complex functions through repeated compositions of a fixed-size ReLU network.

While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry which treats the three objects in a unified manner, manifests not only diffeomorphism …

Convolutional Neural Networks (CNNs) have revolutionized performances in several machine learning tasks such as image classification, object tracking, and keyword spotting. However, given that they contain a large number of parameters, their direct applicability into low resource tasks is not straightforward. In this w…

2D CNNs approximate Korobov functions with near-optimal rates.

Improved adaptive rates for Lipschitz bandit problem.

In image classification, visual separability between different object categories is highly uneven, and some categories are more difficult to distinguish than others. Such difficult categories demand more dedicated classifiers. However, existing deep convolutional neural networks (CNN) are trained as flat N-way classifi…

Proposes a fixed smooth convolutional layer to reduce checkerboard artifacts in CNNs.