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.
Dynamic risk measures follow law invariance principles over time.
New SDE model from machine learning optimization with unique stationary distribution.
Study shows how anisotropic data affects learning dynamics in phase retrieval.
Superposition accelerates training to a universal power-law exponent.
Machine learning recently has been used to identify the governing equations for dynamics in physical systems. The promising results from applications on systems such as fluid dynamics and chemical kinetics inspire further investigation of these methods on complex engineered systems. Dynamics of these systems play a cru…
This paper explains how predictable order flow can lead to Brownian motion in financial prices.
New scaling laws explain deep learning performance growth.
Distributions derived from non-extensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker-Planck equation. The combination shows promise in describing stochastic processes with power-law distributions and superdiffusive dynamics. We investigate intra-day price changes in the S&P500…
Study on SGD dynamics and scaling laws for training quadratic neural networks in high dimensions.
In this paper we analyze a dynamic recursive extension of the (static) notion of a deviation measure and its properties. We study distribution invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive is the variance. We also solve the problem of optimal risk-sha…
Method extracts governing laws from non-Gaussian stochastic systems data.
Framework learns stochastic dynamics from endpoint and intermediate distributions using soft energy constraints.
Study classifies stock price jumps as exogenous or endogenous using news data.
We study the growth dynamics of the size of manufacturing firms considering competition and normal distribution of competency. We start with the fact that all components of the system struggle with each other for growth as happened in real competitive bussiness world. The detailed quantitative agreement of the theory w…
Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two characteristic regimes. For large values of wealth it takes the form of a Pareto style…
Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We propose a non-parametric statistical learning approach to estimate the governing laws of distance-based interactions, with no reference or a…
We discover scaling laws for kernel regression loss under various learning rate schedules.
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 …
New mechanism found for power laws including Zipf's law.
The relaxation dynamics of aftershocks after large volatility shocks are investigated based on two high-frequency data sets of the Shanghai Stock Exchange Composite (SSEC) index. Compared with previous relevant work, we have defined main financial shocks based on large volatilities rather than large crashes. We find th…
We analyse the dynamics of the Warsaw Stock Exchange index WIG at a daily time horizon before and after its well defined local maxima of the cusp-like shape decorated with oscillations. The rising and falling paths of the index peaks can be described by the Mittag-Leffler function superposed with various types of oscil…
New framework reveals thermodynamic principles for LLM training.
We study finite sample properties of estimators of power-law cross-correlations -- detrended cross-correlation analysis (DCCA), height cross-correlation analysis (HXA) and detrending moving-average cross-correlation analysis (DMCA) -- with a special focus on short-term memory bias as well as power-law coherency. Presen…
Employing data on the assessed value of land in 1983 -- 2005 Japan, we investigate the dynamical behavior in the high scale region of non-equilibrium systems. From the detailed quasi-balance and Gibrat's law, we derive a relation between the change of Pareto index and a symmetry in the detailed quasi-balance. The relat…
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated Lévy distribution. For both (i) and (ii), we find that due to the correlations in the variance,…
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…
Paper approximates risk measures using SGD with Langevin dynamics.
Develops a new method to discover stochastic systems with non-Gaussian noise.
An interesting toy model has recently been proposed on Schumpeterian economic dynamics by Thurner {\it et al.} following the idea of economist Joseph Schumpeter. Punctuated equilibrium dynamics is shown to emerge from this model and some detail analyses of the time series indicate SOC kind of behaviours. The focus in t…
Tensor networks help learn complex physical laws from data.
This work proves that large models can be compressed significantly without losing performance.
Analyzes symmetries in neural networks to predict learning dynamics.
The paper synthesizes the mathematics of modeling the future.
New law predicts first extinction in resampling processes.
Stabilized neural differential equations enforce constraints on dynamical systems.
Defines -expectation of distributions and its applications.
Model predicts neural network performance scaling laws across various factors.
Symmetry-regularized Neural ODEs improve model stability and interpretability.
We introduce a deterministic dealer model which implements most of the empirical laws, such as fat tails in the price change distributions, long term memory of volatility and non-Poissonian intervals. We also clarify the causality between microscopic dealers' dynamics and macroscopic market's empirical laws.
New model uses symmetries and scaling laws to predict consumer advertising response.
The dynamical behavior of the currency exchange rate after its large-scale catastrophe is discussed through a case study of the rate of Russian rubles to US dollars after its crash in 2014. It is shown that, similarly to the case of the stock market crash, the relaxation is characterized by a power law, which is in ana…
Aioli unifies language model data mixing methods and improves performance.
Revisiting Trade-sign Long-memory and Square-root Law price impact
Advocates a local feedback approach for RL in unknown systems.
The paper uncovers two key laws of market impact influenced by volume and participation rate.
We show some fundamental results concerning -dimensional foliated dynamical systems (FDS for short) introduced by Deninger. Firstly, we give a decomposition theorem for an FDS, which yields a classification of FDS's. Secondly, for each type of the classification, we construct concrete examples of FDS…
Research activities of Kyoto Econophysics Group is reviewed. Strong emphasis has been placed on real economy. While the initial stage of research was a first high-definition data analysis on personal income, it soon progressed to firm dynamics, growth rate distribution and establishment of Pareto's law and Gibrat's law…
Volatility models must be rough to match market skew.