arXiv research

The study examines 3-manifolds with slow scalar curvature decay and finds Whitehead manifold properties.

In this paper we investigate the life-span of classical solutions to the hyperbolic geometric flow in two space variables with slow decay initial data. By establishing some new estimates on the solutions of linear wave equations in two space variables, we give a lower bound of the life-span of classical solutions to th…

We show that there are topological obstructions for a noncompact manifold to admit a Riemannian metric with quadratic curvature decay and a volume growth which is slower than that of Euclidean space of the same dimension.

Weight decay stabilizes training dynamics by slowing progressive sharpening.

Study shows slow decay of impact in equity markets after metaorders.

Gradient flow with weight decay shows grokking effect in deep learning.

We study asymptotic behavior of positive smooth solutions of the conformal scalar curvature equation in ${\bf R}^n$. We consider the case when the scalar curvature of the conformal metric is bounded between two positive numbers outside a compact set. It is shown that the solution has slow decay if the radial change is …

New ensemble method improves model stability exponentially.

A self-organized model with social percolation process is proposed to describe the propagations of information for different trading ways across a social system and the automatic formation of various groups within market traders. Based on the market structure of this model, some stylized observations of real market can…

The study confirms positivity of Q-curvatures for specific conformal metrics.

Tian and Yau constructed a complete Ricci-flat Kähler metric on the complement of an ample and smooth anticanonical divisor. We inquire into the behaviour of this metric towards the boundary divisor and prove a slow decay rate of the difference to an appropriate explicitely given referential metric.

SignSGD outperforms SGD in linear regression with optimal scaling laws under PLRF model.

New framework improves GAN training by controlling weight spectra.

We construct unbounded positive $C^2$-solutions of the equation $Δu + K u^{(n + 2)/(n - 2)} = 0$ in ${\R}^n$ (equipped with Euclidean metric $g_o$) such that $K$ is bounded between two positive numbers in ${\R}^n$, the conformal metric $g = u^{4/(n - 2)} g_o$ is complete, and the volume growth of $g$ can be arbitrarily…

New magnetic memory effects found in gravitational waves and memory.

Using a proprietary dataset of meta-orders and prediction signals, and assuming a quasi-linear impact model, we deconvolve market impact from past correlated trades and a predictable return component to elicit the temporal dependence of the market impact of a single daily meta-order, over a ten day horizon in various e…

We consider the action of a pseudo-Anosov mapping class on $\mathcal{PML}(S)$. This action has north-south dynamics and so, under iteration, laminations converge exponentially to the stable lamination. We study the rate of this convergence and give examples of families of pseudo-Anosov mapping classes where the rate go…

The study uses the Merton model to estimate PD and finds a phase transition affecting convergence speed.

Continuous Hidden Markov Models for Equity Returns

Optimizes convex functions in finite vs infinite dimensions, revealing slow convergence rates.

Adaptive LR improves neural network Lipschitz regularity without slowing convergence.

Stock markets can be characterized by fat tails in the volatility distribution, clustering of volatilities and slow decay of their time correlations. For an explanation models with several mechanisms and consequently many parameters as the Lux-Marchesi model have been used. We show that a simple herding model with only…

In this article we study the dependence degree of the traded volume of the Dow Jones 30 constituent equities by using a nonextensive generalised form of the Kullback-Leibler information measure. Our results show a slow decay of the dependence degree as a function of the lag. This feature is compatible with the existenc…

We propose a simple stochastic volatility model which is analytically tractable, very easy to simulate and which captures some relevant stylized facts of financial assets, including scaling properties. In particular, the model displays a crossover in the log-return distribution from power-law tails (small time) to a Ga…

The L1 loss landscape of neural nets near local minima behaves differently, revealing exponential decay and increased vertex density.

Study of waves on Reissner-Nordström-AdS black holes, proving uniform boundedness and continuity.

In this paper, we use a database of around 400,000 metaorders issued by investors and electronically traded on European markets in 2010 in order to study market impact at different scales. At the intraday scale we confirm a square root temporary impact in the daily participation, and we shed light on a duration factor …

An analysis of the stylized facts in financial time series is carried out. We find that, instead of the heavy tails in asset return distributions, the slow decay behaviour in autocorrelation functions of absolute returns is actually directly related to the degree of clustering of large fluctuations within the financial…

The statistical properties of the increments x(t+T) - x(t) of a financial time series depend on the time resolution T on which the increments are considered. A non-parametric approach is used to study the scale dependence of the empirical distribution of the price increments x(t+T) - x(t) of S&P Index futures, for time…

New theory sharpens Q-learning with LDTZ rate, proving it's best of both worlds.

For an integer $n \ge 3$ and any positive number $ε$ we establish the existence of smooth functions K on $R^n \setminus \{0 \}$ with $|K - 1| \le ε$, such that the equation $Δu + n (n - 2) K u^{{n + 2}\over {n - 2}} = 0$ in $R^n \setminus \{0 \}$ has a smooth positive solution which blows up at the origin (i.e., u does…

Study shows how anisotropic data affects learning dynamics in phase retrieval.

We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed stock price return as a function of the return and time. The behavior of this fu…

Spectral feature learning improves IV regression for causal effect estimation.

This work studies learning curves for revenue maximization algorithms.

A phase transition affects loss landscape and generalization in neural networks.

This article derives prognostic expressions for the evolution of globally aggregated economic wealth, productivity, inflation, technological change, innovation and growth. The approach is to treat civilization as an open, non-equilibrium thermodynamic system that dissipates energy and diffuses matter in order to sustai…

Adafactor optimizes neural networks with less memory and similar performance.

We discuss the distribution of commuting distances and its relation to income. Using data from Denmark, the UK, and the US, we show that the commuting distance is (i) broadly distributed with a slow decaying tail that can be fitted by a power law with exponent $γ\approx 3$ and (ii) an average growing slowly as a power …

We prove a global smooth isometric immersion for negatively curved surfaces with finite total curvature.

SKI speeds up Toeplitz Neural Networks by avoiding explicit decay bias and using frequency response.

The concepts of scale invariance, self-similarity and scaling have been fruitfully applied to the study of price fluctuations in financial markets. After a brief review of the properties of stable Levy distributions and their applications to market data we indicate the shortcomings of such models and describe the trunc…

Paper analyzes convergence of FedAvg on non-iid data and provides theoretical guarantees.

Bounds on chemical reaction network relaxation rates using convex analysis.

Study on model collapse in regression models, proposing a mitigation strategy.

Machine learning speeds up FLIM analysis in biomedical research.

PCA-Net combines PCA and neural networks for operator approximation, with new bounds on complexity.

Paper explores universal rates of ERM in machine learning.