arXiv research

New cutoff phenomenon found for geodesic paths on hyperbolic manifolds.

New transport method simplifies cutoff phenomenon for Markov processes.

Non-negative curvature affects Markov chains' mixing and expansion properties.

High-dimensional curved diffusions show abrupt convergence at a critical time.

In this paper we study the common distance between points and the behavior of a constant length step discrete random walk on finite area hyperbolic surfaces. We show that if the second smallest eigenvalue of the Laplacian is at least 1/4, then the distances on the surface are highly concentrated around the minimal poss…

LLMs can memorize economic data and recall exact values before their training cutoff.

We determine the information-theoretic cutoff value on separation of cluster centers for exact recovery of cluster labels in a $K$-component Gaussian mixture model with equal cluster sizes. Moreover, we show that a semidefinite programming (SDP) relaxation of the $K$-means clustering method achieves such sharp threshol…

We show that Chern-Simons gauge theory with appropriate cutoffs is equivalent, term by term in perturbation theory, to a Fermionic theory with a nonlocal interaction term. When an additional cutoff is placed on the Fermi fields, this Fermionic theory gives rise to a convergent perturbation expansion. This leads us to c…

In this paper we revisit the hypothesis needed to define the "paracomposition" operator, an analogue to the classic pull-back operation in the low regularity setting, first introduced by S. Alinhac in [3]. More precisely we do so in two directions. First we drop the diffeomorphism hypothesis. Secondly we give estimates…

One of the main obstacles regarding Barky Emery curvature on graphs is that the results require a global uniform lower curvature bounds where no exception sets are allowed. We overcome this obstacle by introducing the perpetual cutoff method. As applications, we prove gradient estimates only requiring curvature bounds …

DatedGPT prevents lookahead bias in financial forecasting models.

Develops a tool to identify abnormal blood smear results based on CBC tests.

We introduce a new, high-throughput, synchronous, distributed, data-parallel, stochastic-gradient-descent learning algorithm. This algorithm uses amortized inference in a compute-cluster-specific, deep, generative, dynamical model to perform joint posterior predictive inference of the mini-batch gradient computation ti…

New models avoid lookahead bias by training on past data only.

A new calibration metric bridges testability and actionability.

Bayesian model estimates treatment effects near cutoffs in regression discontinuity designs.

Study challenges the necessity of data augmentation for improving predictions on imbalanced text datasets.

Blockchain markets with paid-priority trading can lead to biased prices and reduced liquidity.

We show that the Yang-Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction terms. When a further momentum cutoff is imposed, this Fermionic theory has a co…

The so-called Pareto-Levy or power-law distribution has been successfully used as a model to describe probabilities associated to extreme variations of worldwide stock markets indexes data and it has the form $Pr(X>x) ~ x**(-alpha) for gamma< x <infinity. The selection of the threshold parameter gamma$ from empirical d…

In this paper we tackle the problem of estimating the power-law tail exponent of income distributions by using the Hill's estimator. A subsample semi-parametric bootstrap procedure minimising the mean squared error is used to choose the power-law cutoff value optimally. This technique is applied to personal income data…

We detect lookahead bias in LLM forecasts using a novel statistical method.

AI bias arises from human-defined goals, not algorithmic flaws.

Optimal cutoff interval for risk scores improves binary classification accuracy.

Graph neural networks fail to distinguish certain 3D atom configurations.

New method calibrates uncertainty estimates for image classifiers without labeled data.

ChatGPT snapshots predict future stock returns.

The CGMY model's ATM call-price asymptotics are derived using characteristic function.

We prove precompactness in an orbifold Cheeger-Gromov sense of complete gradient Ricci shrinkers with a lower bound on their entropy and a local integral Riemann bound. We do not need any pointwise curvature assumptions, volume or diameter bounds. In dimension four, under a technical assumption, we can replace the loca…

In this paper, by employ the cutoff function and the maximum principle, some Hamilton-Souplet-Zhang type gradient estimates for porous medium type equation are deduced. As a special case, an Hamilton-Souplet-Zhang type gradient estimates of the heat equation is derived which is different from the result of Souplet-Zhan…

Proposes a method to detect anomalies in financial time series using PCA and neural networks.

This paper proposes BAT to balance accuracy and robustness in adversarial training.

We investigate Inverse Mean Curvature Flow (IMCF) of non-compact hypersurfaces in hyperbolic space. Specifically, we look at bounded graphs over horospheres in $\mathbb{H}^{n+1}$ and show long time existence of the flow. Along the way many important local estimates as well as global estimates are obtained. In addition,…

Some general features of kinetic multi-agent models are reviewed, with particular attention to the relation between the agent saving propensities and the form of the equilibrium wealth distribution. The effect of a finite cutoff of the saving propensity distribution on the corresponding wealth distribution is studied. …

The paper decomposes unsupervised learning's generalization error into model, data, and variance components.

The dynamics of generalized Lotka-Volterra systems is studied by theoretical techniques and computer simulations. These systems describe the time evolution of the wealth distribution of individuals in a society, as well as of the market values of firms in the stock market. The individual wealths or market values are gi…

The plateau phenomenon, wherein the loss value stops decreasing during the process of learning, has been reported by various researchers. The phenomenon is actively inspected in the 1990s and found to be due to the fundamental hierarchical structure of neural network models. Then the phenomenon has been thought as inev…

In this paper, by maximum principle and cutoff function, we investigate gradient estimates for positive solutions to two nonlinear parabolic equations under Ricci flow. The related Harnack inequalities are deduced. An result about positive solutions on closed manifolds under Ricci flow is abtained. As applications, gra…

Optimal timing for borrowing from a 457(b) plan to maximize returns.

Paper optimizes ES estimation under an $\ell_1$ constraint, reducing estimation errors.

The two phase behavior in financial markets actually means the bifurcation phenomenon, which represents the change of the conditional probability from an unimodal to a bimodal distribution. In this paper, the bifurcation phenomenon in Hang-Seng index is carefully investigated. It is observed that the bifurcation phenom…

New recursion formula for non-orientable surfaces resolves divergences.

Equivalence of norms on manifolds with curvature bounds established.

The paper explains how neural networks learn less salient frequency components during training.

A new method for virtual drug screening detects top treatments.

A low rank matrix X has been contaminated by uniformly distributed noise, missing values, outliers and corrupt entries. Reconstruction of X from the singular values and singular vectors of the contaminated matrix Y is a key problem in machine learning, computer vision and data science. In this paper we show that common…

We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log…

Large language models improve futures market factor models in China.