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.
Power-law spectrum of random feature model is preserved in neural networks.
Large models follow power laws in performance with dataset size or parameters.
A hierarchical model shows how scaling laws emerge from sequential feature recovery.
Critical volatility triggers log-normal to power-law transitions in interconnected systems.
Ridge regression reveals surprising high-dimensional behaviors via random matrix theory.
Bayesian nonparametric CMS improves frequency estimation for power-law data.
SignSGD outperforms SGD in linear regression with optimal scaling laws under PLRF model.
Network data appear in a number of applications, such as online social networks and biological networks, and there is growing interest in both developing models for networks as well as studying the properties of such data. Since individual network datasets continue to grow in size, it is necessary to develop models tha…
Power laws detected in financial data, modeled with random multipliers.
We look at how asset exchange models can be mapped to random iterated function systems (IFS) giving new insights into the dynamics of wealth accumulation in such models. In particular, we focus on the "yard-sale" (winner gets a random fraction of the poorer players wealth) and the "theft-and-fraud" (winner gets a rando…
We present a model for random simple graphs with a degree distribution that obeys a power law (i.e., is heavy-tailed). To attain this behavior, the edge probabilities in the graph are constructed from Bertoin-Fujita-Roynette-Yor (BFRY) random variables, which have been recently utilized in Bayesian statistics for the c…
We investigate a class of feature allocation models that generalize the Indian buffet process and are parameterized by Gibbs-type random measures. Two existing classes are contained as special cases: the original two-parameter Indian buffet process, corresponding to the Dirichlet process, and the stable (or three-param…
We find a deterministic equivalent for random feature regression's test error, independent of feature map dimension.
The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from the Bernoulli process turns these into binary-valued features. Recent work has …
We uncover scaling laws and statistical structure in complex datasets.
Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in model-based clustering, population genetics, ecology or network analysis. While the exchangeability assumption is sensib…
Bayesian nonparametric approaches, in particular the Pitman-Yor process and the associated two-parameter Chinese Restaurant process, have been successfully used in applications where the data exhibit a power-law behavior. Examples include natural language processing, natural images or networks. There is also growing em…
Effects of randomness on non-integer power law tails in multiplicatively interacting stochastic processes are investigated theoretically. Generally, randomness causes decrease of the exponent of tails and the growth rate of processes. Explicit calculations are performed for two examples: uniformly distributed and two p…
How do individuals accumulate wealth as they interact economically? We outline the consequences of a simple microscopic model in which repeated pairwise exchanges of assets between individuals build the wealth distribution of a population. This distribution is determined for generic exchange rules --- transactions that…
Modeling financial returns as conditionally independent random variables explains power-law tails.
It is ubiquitous in natural and social sciences that two variables, recorded temporally or spatially in a complex system, are cross-correlated and possess multifractal features. We propose a new method called multifractal detrended cross-correlation analysis (MF-DXA) to investigate the multifractal behaviors in the pow…
Superposition accelerates training to a universal power-law exponent.
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 …
Study reveals a universal formula for knotting in random equilateral polygons.
We constructed an analog electrical circuit which generates fluctuations in which probability density function has power law tails. In the circuit fluctuations with an arbitrary exponent of the power law can be obtained by adjusting the resistance. With this low cost circuit the random fluctuations which have the simil…
We analyze the European transition economies and show that time series for most of major indices exhibit (i) power-law correlations in their values, power-law correlations in their magnitudes, and (iii) asymmetric probability distribution. We propose a stochastic model that can generate time series with all the previou…
Stock markets are complex systems exhibiting collective phenomena and particular features such as synchronization, fluctuations distributed as power-laws, non-random structures and similarity to neural networks. Such specific properties suggest that markets operate at a very special point. Financial markets are believe…
It is now well established empirically that financial price changes are distributed according to a power law, with cubic exponent. This is a fascinating regularity, as it holds for various classes of securities, on various markets, and on various time scales. The universality of this law suggests that there must be som…
We extend the model of rational bubbles of Blanchard and of Blanchard and Watson to arbitrary dimensions d: a number d of market time series are made linearly interdependent via d times d stochastic coupling coefficients. We first show that the no-arbitrage condition imposes that the non-diagonal impacts of any asset i…
In this paper we explain the wild fluctuations of financial prices from the intrinsic amplifying feedback of speculative supply and demand. Formally, we show that an asset return follows a multiplicative random growth with exogenous input, which is well-known to be a generic power-law generating process, and which coul…
We study here numerically the behavior of an ideal gas like model of markets having only one non-consumable commodity. We investigate the behavior of the steady-state distributions of money, commodity and total wealth, as the dynamics of trading or exchange of money and commodity proceeds, with local (in time) fluctuat…
Robust CD method for real-world time series with power-law distributions.
Unified theory for neural scaling laws in hierarchically compositional data.
The study analyzes deep linear networks from random initialization, capturing dynamics and hyperparameter effects.
The quotient of random variables with normal distributions is examined and proven to have have power law decay, with density , with the coefficient depending on the means and variances of the numerator and denominator and their correlation. We also obtain the conditional probability…
Stochastic block models (SBMs) have been playing an important role in modeling clusters or community structures of network data. But, it is incapable of handling several complex features ubiquitously exhibited in real-world networks, one of which is the power-law degree characteristic. To this end, we propose a new var…
Study reveals neural scaling laws in random graphs and natural language models.
We introduce and study a simple model of a limit order-driven market. Traders in this model can either trade at the market price or place a limit order, i.e. an instruction to buy (sell) a certain amount of the stock if its price falls below (raises above) a predefined level. The choice between these two options is pur…
A methodology is developed to identify, as units of study, each decrease in the value of a stock from a given maximum price level. A critical level in the amount of price declines is found to separate a segment operating under a random walk from a segment operating under a power law. This level is interpreted as a poin…
The observation of power laws in the time to extrema of volatility, volume and intertrade times, from milliseconds to years, are shown to result straightforwardly from the selection of biased statistical subsets of realizations in otherwise featureless processes such as random walks. The bias stems from the selection o…
Signatures of universality are detected by comparing individual eigenvalue distributions and level spacings from financial covariance matrices to random matrix predictions. A chopping procedure is devised in order to produce a statistical ensemble of asset-price covariances from a single instance of financial data sets…
Different models of capital exchange among economic agents have been proposed recently trying to explain the emergence of Pareto's wealth power law distribution. One important factor to be considered is the existence of risk aversion. In this paper we study a model where agents posses different levels of risk aversion,…
This work analyzes neural scaling laws using power-law data spectra and derives analytical expressions for generalization error.
Exact results on power-law distributions in systems with resets.
The persistence phenomenon is studied in the Japanese financial market by using a novel mapping of the time evolution of the values of shares quoted on the Nikkei Index onto Ising spins. The method is applied to historical end of day data from the Japanese stock market during 2002. By studying the time dependence of th…
Defines complexity measure for neural networks and feature representations, revealing scaling patterns.
A new model detects financial bubbles with high accuracy.
Study classifies stock price jumps as exogenous or endogenous using news data.