arXiv research

Low-index harmonic maps from $S^3$ to $S^2$ are simple.

Study on minimal surfaces with Y-singularities, proving rigidity for Morse index one.

Pruning is an efficient model compression technique to remove redundancy in the connectivity of deep neural networks (DNNs). Computations using sparse matrices obtained by pruning parameters, however, exhibit vastly different parallelism depending on the index representation scheme. As a result, fine-grained pruning ha…

This work introduces a novel nonparametric density index defined on graphs, the Sum-over-Forests (SoF) density index. It is based on a clear and intuitive idea: high-density regions in a graph are characterized by the fact that they contain a large amount of low-cost trees with high outdegrees while low-density regions…

p-index approach shows efficient-contrarian strategy outperforms others in low-sentiment periods

Gradient flow solves multi-index regression for high-dimensional Gaussian data.

Study efficient estimation of hidden subspaces in Gaussian Multi-index models.

The systole function has a universal index gap on moduli spaces.

Adversarial robustness in multi-index models is as easy as standard learning.

Adding linear layers to ReLU networks favors functions with low mixed variation.

For an immersed minimal surface in $\mathbb{R}^3$, we show that there exists a lower bound on its Morse index that depends on the genus and number of ends, counting multiplicity. This improves, in several ways, an estimate we previously obtained bounding the genus and number of ends by the index. Our new estimate resol…

Study proves rigidity of capillary surfaces in curved 3D spaces.

Study on CMC hypersurfaces with bounded index and area, proving multiplicity one convergence and bounds on genus.

The study examines how formal index insurance compares to informal risk sharing in managing natural disasters.

We develop a general structure theory for compact homogeneous Riemannian manifolds in relation to the co-index of symmetry. We will then use these results to classify irreducible, simply connected, compact homogeneous Riemannian manifolds whose co-index of symmetry is less or equal than three. We will also construct ma…

Kernel Quantization improves CNN compression without sacrificing performance.

Paper examines global Covid-19 data complexity and finds low intrinsic dimensions.

Randomly biased data makes complex models as easy to learn as simple ones.

Obesity is an important concern in public health, and Body Mass Index is one of the useful (and proliferant) measures. We use Convolutional Neural Networks to determine Body Mass Index from photographs in a study with 161 participants. Low data, a common problem in medicine, is addressed by reducing the information in …

Study spectral estimators for multi-index models to recover low-dimensional signal subspaces.

Motivated by the sampling problems and heterogeneity issues common in high- dimensional big datasets, we consider a class of discordant additive index models. We propose method of moments based procedures for estimating the indices of such discordant additive index models in both low and high-dimensional settings. Our …

This is an expository article. It discusses an approach to hypoelliptic Fredholm index theory based on noncommutative methods (groupoids, C*-algebras, K-theory). The paper starts with an explicit index theorem for scalar second order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-bro…

Paper introduces a new index to measure financial and workplace resilience of firms.

In this paper we show that the only properly immersed self--shrinkers $Σ$ in $\mathbb{R}^{m+1}$ with Morse index $1$ are the hyperplanes through the origin. Moreover, we prove that if $Σ$ is not a hyperplane through the origin then the index jumps and it is at least $m+2$, with equality if and only if $Σ$ is a cylinder…

A new stock index model simplifies high-dimensional stock data.

The main result of this paper is non-vanishing of the image of the index map from the $G$-equivariant $K$-homology of a proper $G$-compact $G$-manifold $X$ to the $K$-theory of the $C^{*}$-algebra of the group $G$. Under the assumption that the Kronecker pairing of a $K$-homology class with a low-dimensional cohomology…

Single Index Models (SIMs) are simple yet flexible semi-parametric models for classification and regression. Response variables are modeled as a nonlinear, monotonic function of a linear combination of features. Estimation in this context requires learning both the feature weights, and the nonlinear function. While met…

Index structures are important for efficient data access, which have been widely used to improve the performance in many in-memory systems. Due to high in-memory overheads, traditional index structures become difficult to process the explosive growth of data, let alone providing low latency and high throughput performa…

Study shows computational and statistical gaps in Gaussian Single-Index Models.

Transformers learn low-dimensional target functions efficiently in-context.

We study the estimation of the parametric components of single and multiple index volatility models. Using the first- and second-order Stein's identities, we develop methods that are applicable for the estimation of the variance index in the high-dimensional setting requiring finite moment condition, which allows for h…

This paper reviews and analyzes various modeling approaches for financial index tracking.

We introduce in this paper a new algorithm for Multi-Armed Bandit (MAB) problems. A machine learning paradigm popular within Cognitive Network related topics (e.g., Spectrum Sensing and Allocation). We focus on the case where the rewards are exponentially distributed, which is common when dealing with Rayleigh fading c…

The Chern classes of a K-theory class which is represented by a vector bundle with connection admit refinements to Cheeger-Simons classes in Deligne cohomology. In the present paper we consider similar refinements in the case where the classes in K-theory are represented by geometric families of Dirac operators. In low…

New algorithms learn multi-index models via harmonic analysis, achieving statistical and computational trade-offs.

DFR models dynamic distributional data with weighted Fréchet means.

Counterexample disproves Borde-Sorkin conjecture on causal continuity of Morse spacetimes.

New neural networks learn single-index models efficiently.

SGD trains NNs to learn low-dimensional representations efficiently.

For a knot $K\subset S^3$, its exterior $E(K) = S^3\backslashη(K)$ has a singular foliation by Seifert surfaces of $K$ derived from a circle-valued Morse function $f\colon E(K)\to S^1$. When $f$ is self-indexing and has no critical points of index 0 or 3, the regular levels that separate the index-1 and index-2 critica…

We study the parameter estimation problem for a varying index coefficient model in high dimensions. Unlike the most existing works that iteratively estimate the parameters and link functions, based on the generalized Stein's identity, we propose computationally efficient estimators for the high-dimensional parameters w…

Single Index Models (SIMs) are simple yet flexible semi-parametric models for machine learning, where the response variable is modeled as a monotonic function of a linear combination of features. Estimation in this context requires learning both the feature weights and the nonlinear function that relates features to ob…

Proves properties of CMC hypersurfaces in specific spaces.

Proposes a method for valid inference in GPLSIMs with longitudinal data.

Properties of low-variability periods in the time series are analysed. The theoretical approach is used to show the relationship between the multi-scaling of low-variability periods and multi-affinity of the time series. It is shown that this technically simple method is capable of reveling more details about time-seri…

In this short note, we prove that on the three-sphere with any bumpy metric there exist at least four solutions of the Allen-Cahn equation with spherical interface and index at most two. The proof combines several recent results from the literature.

The study analyzes macroeconomic factors affecting copper futures volatility and long-term correlation with S&P 500.

Biomedical text tagging systems are plagued by the dearth of labeled training data. There have been recent attempts at using pre-trained encoders to deal with this issue. Pre-trained encoder provides representation of the input text which is then fed to task-specific layers for classification. The entire network is fin…