A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Polynomial decay of correlations shown for curved surfaces.
Study geodesic paths on flat surfaces, comparing length and singularity counts.
Theory predicts neural scaling exponents from language statistics.
New neural scaling law found for simple quadratic function.
This paper tightens the law of the iterated logarithm for empirical KL_inf, applicable to unbounded data.
Large models follow power laws in performance with dataset size or parameters.
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives are two important testing procedures for high-dimensional independence. However…
Study compares exponential and power-law kernels in modeling high-frequency trading data.
Sharp theory of neural network scaling laws for hierarchical targets.
We apply a suitable modification of the functional delta method to statistical functionals that arise from law-invariant coherent risk measures. To this end we establish differentiability of the statistical functional in a relaxed Hadamard sense, namely with respect to a suitably chosen norm and in the directions of a …
This work analyzes neural scaling laws using power-law data spectra and derives analytical expressions for generalization error.
Simplified kernel ridge regression with a conservation law.
Statistical properties of an order book and the effect they have on price dynamics were studied using the high-frequency NASDAQ Level II data. It was observed that the size distribution of marketable orders (transaction sizes) has power law tails with an exponent 1+mu_{market}=2.4 \pm 0.1. The distribution of limit ord…
Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper we generalize the model of interevent time to reproduce a variety of self-affine time series exhibiting power spec…
Pareto law, which states that wealth distribution in societies have a power-law tail, has been a subject of intensive investigations in statistical physics community. Several models have been employed to explain this behavior. However, most of the agent based models assume the conservation of number of agents and wealt…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus can not be used as a standard distribution. Normally professionals in the area …
Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents that may take values either less than and greater than two. Models based on various forms of exchangeability are able to capture power laws with , and admit tra…
The relevance of data quantifies learning efficiency.
We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One important property of these statistics is that they converge to zero for power laws o…
I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility function of the investor. The analytical solution of the problem gives insight on the origin of the recently empirically observed power law distribution of limit order prices. In the framewor…
Deviation inequalities and limit laws for random walks on metric spaces.
Unified model explains market dynamics, linking order flow, volatility, and impact.
NN-Turb generates turbulent velocity statistics using neural networks.
The study explains transformer scaling laws using statistical and approximation theories.
Modeling financial markets with a novel order flow model.
A fundamental problem in geostatistical modeling is to infer the heterogeneous geological field based on limited measurements and some prior spatial statistics. Semantic inpainting, a technique for image processing using deep generative models, has been recently applied for this purpose, demonstrating its effectiveness…
New insights into how depth and width affect in-context learning in deep models.
We provide an empirical investigation aimed at uncovering the statistical properties of intricate stock trading networks based on the order flow data of a highly liquid stock (Shenzhen Development Bank) listed on Shenzhen Stock Exchange during the whole year of 2003. By reconstructing the limit order book, we can extra…
The role of kernels is central to machine learning. Motivated by the importance of power-law distributions in statistical modeling, in this paper, we propose the notion of power-law kernels to investigate power-laws in learning problem. We propose two power-law kernels by generalizing Gaussian and Laplacian kernels. Th…
Following the work of Okuyama, Takayasu and Takayasu [Okuyama, Takayasu and Takayasu 1999] we analyze huge databases of Japanese companies' financial figures and confirm that the Zipf's law, a power law distribution with the exponent -1, has been maintained over 30 years in the income distribution of Japanese companies…
Superposition accelerates training to a universal power-law exponent.
We show that an economic system populated by multiple agents generates an equilibrium distribution in the form of multiple scaling laws of conditional PDFs, which are sufficient for characterizing the probability distribution. The existence of the double scaling law is demonstrated empirically for the sales and the lab…
This study reveals statistical patterns in ERC20 token transactions on Ethereum blockchain.
The paper studies scaling laws for associative memory mechanisms.
The paper proves local laws for non-separable sample covariance matrices.
Novel groups exhibit contradictory behaviors with respect to Burnside laws.
We uncover scaling laws and statistical structure in complex datasets.
Ridge regression reveals surprising high-dimensional behaviors via random matrix theory.
New formulae identify discrete probability laws without needing normalization constants.
We study the volume distribution of nodal domains of random band-limited functions on generic manifolds, and find that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the basic qualitative properties of this law, such as its support, monotonicity and…
New method uses sufficient statistics to infer causal relationships from observational data.
This paper improves the robustness of risk estimation for financial positions.
In this paper, we quantitatively investigate the statistical properties of a statistical ensemble of stock prices. We selected 1200 stocks traded on the Tokyo Stock Exchange, and formed a statistical ensemble of daily stock prices for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corr…
The paper connects neural networks to physics using probability theory.
Paper studies deep learning for solving elliptic PDEs, proving optimal bounds and neural scaling laws.
Study shows how anisotropic data affects learning dynamics in phase retrieval.
In the present work we demonstrate the application of different physical methods to high-frequency or tick-by-tick financial time series data. In particular, we calculate the Hurst exponent and inverse statistics for the price time series taken from a range of futures indices. Additionally, we show that in a limit orde…
We propose a series of simple models for the microstructure of a double auction market without intermediaries. We specialize to those markets, such interdealer broker markets, which are dominated by professional traders, who trade mainly through limit orders, watch markets closely, and move their limit order prices fre…