arXiv research

Study evaluates thresholds for removing noise from DNN weights using random matrix theory.

Threshold found for hyperbolicity in random Coxeter groups.

Sharp threshold found for Frechet mean of inhomogeneous graphs.

Square percolation determines threshold for group divergence in random graphs.

Study on detecting and recovering hidden dense cycles in random graphs.

Analyzes biased random walks and corrupted intervals in adversarial settings.

Majority bit estimation in noisy random recursive DAGs.

Paper improves anomaly detection by using non-uniform random choices in isolation forests.

New local-search methods close the gap in sparse tensor PCA.

Critical volatility triggers log-normal to power-law transitions in interconnected systems.

The fundamental group of the $2$-dimensional Linial-Meshulam random simplicial complex $Y_2(n,p)$ was first studied by Babson, Hoffman and Kahle. They proved that the threshold probability for simple connectivity of $Y_2(n,p)$ is about $p\approx n^{-1/2}$. In this paper, we show that this threshold probability is at mo…

DaRE forests enable efficient data deletion from random forests.

We consider the community detection problem in sparse random hypergraphs. Angelini et al. (2015) conjectured the existence of a sharp threshold on model parameters for community detection in sparse hypergraphs generated by a hypergraph stochastic block model. We solve the positive part of the conjecture for the case of…

A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or "spike") is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughou…

Bayesian framework proves thresholds for multi-graph alignment feasibility.

Paper proves fair classification can be done via simple thresholding.

We study Linial-Meshulam random 2-complexes, which are two-dimensional analogues of Erdős-Rényi random graphs. We find the threshold for simple connectivity to be p = n^{-1/2}. This is in contrast to the threshold for vanishing of the first homology group, which was shown earlier by Linial and Meshulam to be p = 2 log(…

Shapelet is a discriminative subsequence of time series. An advanced shapelet-based method is to embed shapelet into accurate and fast random forest. However, it shows several limitations. First, random shapelet forest requires a large training cost for split threshold searching. Second, a single shapelet provides limi…

The labeled stochastic block model is a random graph model representing networks with community structure and interactions of multiple types. In its simplest form, it consists of two communities of approximately equal size, and the edges are drawn and labeled at random with probability depending on whether their two en…

We study two global structural properties of a graph $Γ$, denoted AS and CFS, which arise in a natural way from geometric group theory. We study these properties in the Erdös--Rényi random graph model G(n,p), proving a sharp threshold for a random graph to have the AS property asymptotically almost surely, and giving f…

We study Linial-Meshulam random 2-complexes, which are two-dimensional analogues of Erdős-Rényi random graphs. We find the threshold for simple connectivity to be p = n^{-1/2}. This is in contrast to the threshold for vanishing of the first homology group, which was shown earlier by Linial and Meshulam to be p = 2 log(…

Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix multiplication, that are robust to stragglers (i.e., machines that may perform slower …

Let $M$ be a compact, unit volume, Riemannian manifold with boundary. In this paper we study the homology of a random Čech-complex generated by a homogeneous Poisson process in $M$. Our main results are two asymptotic threshold formulas, an upper threshold above which the Čech complex recovers the $k$-th homology of $M…

HARFE approximates sparse additive functions using random features and ridge regression.

Random projections improve classifier generalization without needing to choose the best threshold.

Lower bound proves ridgeless regression performs poorly near interpolation threshold.

Graph matching in noisy environments with Markovian errors.

A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences. Baik, Ben Arous and Pé…

This paper resolves the all-or-nothing phase transition in graph matching.

We improve deep threshold networks' memorization capacity exponentially.

This work interprets GELU and related activations via a first-order loss function.

The paper studies phase transitions in random matrices and tensor unfolding for detecting signals.

We investigate the impact of available information on the estimation of the default probability within a generalized structural model for credit risk. The traditional structural model where default is triggered when the value of the firm's asset falls below a constant threshold is extended by relaxing the assumption of…

Study binary perceptrons' capacity using random duality theory.

Study sharpens threshold for matching correlated graphs without labels.

In the spirit of [Surya07'], we develop an average problem approach to prove the optimality of threshold type strategies for optimal stopping of Lévy models with a continuous additive functional (CAF) discounting. Under spectrally negative models, we specialize this in terms of conditions on the reward function and ran…

White matter hyperintensity (WMH) is commonly found in elder individuals and appears to be associated with brain diseases. U-net is a convolutional network that has been widely used for biomedical image segmentation. Recently, U-net has been successfully applied to WMH segmentation. Random initialization is usally used…

Polynomial-time algorithm solves random parity games with high probability.

Detects dense subhypergraphs in random hypergraphs using low-degree polynomials.

A simple model explains phase transition in large language models.

Fewer degrees of freedom can train deep networks, showing a sharp phase transition.

We prove overfitting in minimal and random NNs, tempering the effect.

Sharp threshold for exact recovery in non-uniform hypergraph stochastic block model.

Researchers identify critical protein residues using advanced graph theory.

This paper sets thresholds for recovering vertex correspondences in partially correlated graphs.

New method lowers spherical perceptron capacity using fully lifted random duality theory.

A new algorithm speeds up rerandomization for better experiment balance.

The paper extends risk measures to two-step approximations and studies log-concave distributions.