arXiv research

Convolutional neural networks learn phase-dependent frequency representations.

Lowered regularity assumption for a phase-dependent Helfrich energy equation.

We describe a model for capturing the statistical structure of local amplitude and local spatial phase in natural images. The model is based on a recently developed, factorized third-order Boltzmann machine that was shown to be effective at capturing higher-order structure in images by modeling dependencies among squar…

New phase harmonic covariance models capture non-Gaussian properties of stationary processes.

New estimators improve efficiency in two-phase designs with coarsened data.

Clarifies method of phase synchronization for decoupling linear differential equations.

We consider a Canham-Helfrich-type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham-Helfrich energy, in which the bending rigidities and spontaneous curvatures…

The stability of money value is an important requisite for a functioning economy, yet it critically depends on the actions of participants in the market themselves. Here we model the value of money as a dynamical variable that results from trading between agents. The basic trading scenario can be recast into an Ising t…

New algorithm reduces regret by allowing free exploration in multi-armed bandits.

This research examines how the error rate of nearest neighbor classifiers varies with dataset size.

Study phase transitions in shuffled regression problems.

Spectral mixture (SM) kernels comprise a powerful class of generalized kernels for Gaussian processes (GPs) to describe complex patterns. This paper introduces model compression and time- and phase (TP) modulated dependency structures to the original (SM) kernel for improved generalization of GPs. Specifically, by adop…

Describes reconstructing Poisson structures from Lie group actions.

Yard-Sale (YS) is a stochastic multiplicative wealth-exchange model with two phases: a stable one where wealth is shared, and an unstable one where wealth condenses onto one agent. YS is here studied numerically on 1d rings, 2d square lattices, and random graphs with variable average coordination, comparing its propert…

Descending phase retrieval algorithms show a phase transition with increasing sample complexity.

Proves smoothness and estimates for special Lagrangian solutions with semi-convexity.

This paper presents a phase diagram for two-layer neural networks under different initialization scales.

Paper proposes an algorithm to learn DAGs with indirect dependencies.

We present a simple model of firm rating evolution. We consider two sources of defaults: individual dynamics of economic development and Potts-like interactions between firms. We show that such a defined model leads to phase transition, which results in collective defaults. The existence of the collective phase depends…

Large GD stepsizes improve margins and speed up training for non-homogeneous networks.

Modeling Bitcoin Lightning Network emergence as percolation process.

We find optimal learning rate schedules for a random feature model.

Paper eliminates warm-up phase for PO in linear MDPs, achieving optimal regret.

We analyze the stock prices of the S&P market from 1987 until 2012 with the covariance matrix of the firm returns determined in time windows of several years. The eigenvector belonging to the leading eigenvalue (market) exhibits in its long term time dependence a phase transition with an order parameter which can be in…

Characterizes RFF regression in large $n,p,N$ setting, providing precise learning phases and double descent curve.

The usual formulations of time-dependent mechanics start from a given splitting $Y=R\times M$ of the coordinate bundle $Y\to R$. From physical viewpoint, this splitting means that a reference frame has been chosen. Obviously, such a splitting is broken under reference frame transformations and time-dependent canonical …

We study the problem of approximate ranking from observations of pairwise interactions. The goal is to estimate the underlying ranks of $n$ objects from data through interactions of comparison or collaboration. Under a general framework of approximate ranking models, we characterize the exact optimal statistical error …

Inspired by the recent literature on aggregation theory, we aim at relating the long range correlation of the stocks return volatility to the heterogeneity of the investors' expectations about the level of the future volatility. Based on a semi-parametric model of investors' anticipations, we make the connection betwee…

We study the convolutional phase retrieval problem, of recovering an unknown signal $\mathbf x \in \mathbb C^n$ from $m$ measurements consisting of the magnitude of its cyclic convolution with a given kernel $\mathbf a \in \mathbb C^m$. This model is motivated by applications such as channel estimation, optics, and u…

In this note we revisit the subject of anomaly cancelation in string theory and M-theory on manifolds with String structure and give three observations. First, that on String manifolds there is no E8 x E8 global anomaly in heterotic string theory. Second, that the description of the anomaly in the phase of the M-theory…

PH-VAE models heavy-tailed data with flexible Phase-Type distributions.

A learning algorithm optimizes beamforming for holographic transceivers in far-field communication.

Proposes an online model for LLM cascading with adaptive API selection.

Study of two-layer ReLU neural network phase diagram at infinite-width limit.

New algorithm learns policies without explicit rewards for MDPs.

PolarBM models complex-valued audio signals in polar coordinates, improving over conventional methods.

Deep neural network estimates support of sparse signals for improved phase retrieval.

This article presents results from the first statistically significant study of causes of cost escalation in transport infrastructure projects. The study is based on a sample of 258 rail, bridge, tunnel and road projects worth US$90 billion. The focus is on the dependence of cost escalation on (1) length of project imp…

Probability Density Estimation (PDE) is a multivariate discrimination technique based on sampling signal and background densities defined by event samples from data or Monte-Carlo (MC) simulations in a multi-dimensional phase space. In this paper, we present a modification of the PDE method that uses a self-adapting bi…

Study reconstructs Riemannian metric from Cherenkov radiation in complex media.

New algorithm for safe bandits with unknown parameters and constraints.

The Gerber-Shiu function provides a way of measuring the risk of an insurance company. It is given by the expected value of a function that depends on the ruin time, the deficit at ruin, and the surplus prior to ruin. Its computation requires the evaluation of the overshoot/undershoot distributions of the surplus proce…

Noise can stabilize systemic risk models with uncertain robustness.

Study reveals phase transition in neural networks near interpolation.

DSTP-RNN improves long-term multivariate time series prediction using attention-based RNN.

Study on phase transitions on surfaces using Allen-Cahn equation.

We study the feasibility and noise sensitivity of portfolio optimization under some downside risk measures (Value-at-Risk, Expected Shortfall, and semivariance) when they are estimated by fitting a parametric distribution on a finite sample of asset returns. We find that the existence of the optimum is a probabilistic …

In this paper, we address the problem of reconstructing a time-domain signal (or a phase spectrogram) solely from a magnitude spectrogram. Since magnitude spectrograms do not contain phase information, we must restore or infer phase information to reconstruct a time-domain signal. One widely used approach for dealing w…