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.
The S&P500 daily values and log-returns fail to conform to Benford's laws, revealing underlying trends.
The yearly aggregated tax income data of all, more than 8000, Italian municipalities are analyzed for a period of five years, from 2007 to 2011, to search for conformity or not with Benford's law, a counter-intuitive phenomenon observed in large tabulated data where the occurrence of numbers having smaller initial digi…
Among econophysics investigations, studies of religious groups have been of interest. On one hand, the present paper concerns the Antoinist community financial reports, - a community which appeared at the end of the 19-th century in Belgium. Several growth-decay regimes have been previously found over different time sp…
Study tests UK FTSE-listed companies' financial data for Benford's Law conformity.
We discuss a common suspicion about reported financial data, in 10 industrial sectors of the 6 so called "main developing countries" over the time interval [2000-2014]. These data are examined through Benford's law first significant digit and through distribution distances tests. It is shown that several visually anoma…
In this paper, we search whether the Benford's law is applicable to monitor daily changes in sovereign Credit Default Swaps (CDS) quotes, which are acknowledged to be complex systems of economic content. This test is of paramount importance since the CDS of a country proxy its health and probability to default, being a…
Benford's law states that in data sets from different phenomena leading digits tend to be distributed logarithmically such that the numbers beginning with smaller digits occur more often than those with larger ones. Particularly, the law is known to hold for different types of financial data. The Illicit Financial Flow…
We explore the possibility of using machine learning to identify interesting mathematical structures by using certain quantities that serve as fingerprints. In particular, we extract features from integer sequences using two empirical laws: Benford's law and Taylor's law and experiment with various classifiers to ident…
This paper explores a real-world fundamental theme under a data science perspective. It specifically discusses whether fraud or manipulation can be observed in and from municipality income tax size distributions, through their aggregation from citizen fiscal reports. The study case pertains to official data obtained fr…
Suppose you look at today's stock prices and bet on the value of the first digit. One could guess that a fair bet should correspond to the frequency of for each digit from 1 to 9. This is by no means the case, and one can easily observe a strong prevalence of the small values over the large ones. The fir…
The paper contains a short review of techniques examining regional wealth inequalities based on recently published research work but is also presenting unpublished features. The data pertains to Italy (IT), over the period 2007-2011: the number of cities in regions, the number of inhabitants in cities and in regions, a…
Paper introduces PHI to identify structurally distinct payment patterns in UK municipal procurement.
This work explains scaling laws as redundancy laws in deep learning.
Study on RL on volatility surfaces, proving no free lunch for law-seeking methods.
A new scaling law predicts optimal batch size for training models.
Space exploration technology advances exponentially, consistent with Moore's and Wright's laws.
This work analyzes neural scaling laws using power-law data spectra and derives analytical expressions for generalization error.
An Atlas model is a rank-based system of continuous semimartingales for which the steady-state values of the processes follow a power law, or Pareto distribution. For a power law, the log-log plot of these steady-state values versus rank is a straight line. Zipf's law is a power law for which the slope of this line is …
Large models follow power laws in performance with dataset size or parameters.
Conservation law for weakly harmonic mappings in high dimensions.
Survey on conservation laws for geometric PDEs.
Dynamic risk measures follow law invariance principles over time.
Unified theory for neural scaling laws in hierarchically compositional data.
Defines formal vertex laws related to Lie conformal algebras.
We summarize a book under publication with his title written by the three present authors, on the theory of Zipf's law, and more generally of power laws, driven by the mechanism of proportional growth. The preprint is available upon request from the authors. For clarity, consistence of language and conciseness, we disc…
New concept of partial law invariance connects decision theory and financial risk management.
This work extends the scaling law to multiple and kernel regression, challenging traditional machine learning principles.
Study on eigenvalue distribution of correlated time series deforming the semi-circle law.
The article discusses conservation laws for polyharmonic maps and their applications.
Power laws detected in financial data, modeled with random multipliers.
By using numerical simulation, we confirm that Takayasu--Sato--Takayasu (TST) model which leads Pareto's law satisfies the detailed balance under Gibrat's law. In the simulation, we take an exponential tent-shaped function as the growth rate distribution. We also numerically confirm the reflection law equivalent to the…
Empirical law predicts accuracy of Google Translate's translation chains.
Browsing and finding relevant information for Bangladeshi laws is a challenge faced by all law students and researchers in Bangladesh, and by citizens who want to learn about any legal procedure. Some law archives in Bangladesh are digitized, but lack proper tools to organize the data meaningfully. We present a text vi…
Machine learning finds new natural laws from noisy data.
I consider the existence and structure of conservation laws for the general class of evolutionary scalar second-order differential equations with parabolic symbol. First I calculate the linearized characteristic cohomology for such equations. This provides an auxiliary differential equation satisfied by the conservatio…
Employing profits data of Japanese companies in 2002 and 2003, we identify the non-Gibrat's law which holds in the middle profits region. From the law of detailed balance in all regions, Gibrat's law in the high region and the non-Gibrat's law in the middle region, we kinematically derive the profits distribution funct…
New SDE model from machine learning optimization with unique stationary distribution.
Study reveals neural scaling laws in random graphs and natural language models.
New framework reveals thermodynamic principles for LLM training.
Develops a simple model to understand learning curves for arbitrary power laws.
Non-trivial conservation law found for a specific system.
Study explains Zipf's law using geometric mechanisms from a finite alphabet.
New scaling laws explain deep learning performance growth.
Derives Weyl law for volume spectrum using parametric inequalities.
We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected thre…
We show that there is a common mode of origin for the power laws observed in two different models: (i) the Pareto law for the distribution of money among the agents with random saving propensities in an ideal gas-like market model and (ii) the Gutenberg-Richter law for the distribution of overlaps in a fractal-overlap …
Superposition accelerates training to a universal power-law exponent.
The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation law has a unique representative. The structure of this subspace naturally gives …