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.
Paper discusses the Fisher metric and differentiability in statistical models.
Develops statistical guarantees for neural networks with regularization.
Novel power transform unifies various mathematical functions.
The paper derives Einstein tensors for a family of α-connections on quasi-statistical manifolds.
Study evaluates different mathematical models for three case studies using statistical fitting.
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical physics of fluctuating non-phantom rope-like objects. This new branch is called…
Paper proves mathematically that poisoning datasets can be detected.
Novel tests for genetic independence in high-dimensional data.
Abstract reviews mathematical fairness in machine learning.
We prove the eventological -theorem that complements the Boltzmann H-theorem from statistical mechanics and serves as a mathematical excuse (mathematically no less convincing than the Boltzmann H-theorem for the second law of thermodynamics) for what can be called "the second law of eventology", which justifies the …
Study quantifies how LLMs capture higher-order statistical structure using cumulant expansion.
Mathematical methods of population genetics and framework of exchangeability provide a Markov chain model for analysis and interpretation of stochastic behaviour of equity markets, explaining, in particular, market shape formation, statistical equilibrium and temporal stability of market weights.
The modern data analyst must cope with data encoded in various forms, vectors, matrices, strings, graphs, or more. Consequently, statistical and machine learning models tailored to different data encodings are important. We focus on data encoded as normalized vectors, so that their "direction" is more important than th…
Lecture notes on linear neural networks for deep learning optimization and generalization.
Abstract mathematical formulas for statistical structures and curvatures.
In these notes we describe heuristics to predict computational-to-statistical gaps in certain statistical problems. These are regimes in which the underlying statistical problem is information-theoretically possible although no efficient algorithm exists, rendering the problem essentially unsolvable for large instances…
The paper aims to mathematically define and learn abstractions from data.
Explains how geometry and statistics intertwine, focusing on information geometry.
Perceptrons have been known for a long time as a promising tool within the neural networks theory. The analytical treatment for a special class of perceptrons started in seminal work of Gardner \cite{Gar88}. Techniques initially employed to characterize perceptrons relied on a statistical mechanics approach. Many of su…
Paper explores the Jones polynomial and its impact on knot theory and related fields.
We propose a statistical mechanical derivation of Kahler-Einstein metrics, i.e. solutions to Einstein's vacuum field equations in Euclidean signature (with a cosmological constant) on a compact Kahler manifold X. The microscopic theory is given by a canonical free fermion gas on X whose one-particle states are plurican…
New method uses model comparison signals to improve LLM evaluation accuracy.
Paper reviews algebraic research in machine learning theory.
Experimental life sciences like biology or chemistry have seen in the recent decades an explosion of the data available from experiments. Laboratory instruments become more and more complex and report hundreds or thousands measurements for a single experiment and therefore the statistical methods face challenging tasks…
We develop a statistical framework to benchmark and select large language models based on their risks.
Novel Orlicz regrets consistently bound environmental variable statistics.
Deep learning uncovers patterns between knot types.
Paper analyzes shapes of brain arterial networks using statistical methods.
The paper explains how language models acquire complex skills through scaling laws and statistical analysis.
We describe in this note a new invariant of rooted trees. We argue that the invariant is interesting on it own, and that it has connections to knot theory and homological algebra. However, the real reason that we propose this invariant to readers is that we deal here with an elementary, interesting, new mathematics, an…
This paper develops a general framework for analyzing asymptotics of -statistics. Previous literature on limiting distribution mainly focuses on the cases when with fixed kernel size . Under some regularity conditions, we demonstrate asymptotic normality when grows with by utilizing existin…
New framework for managing medical risks using convex responses.
This paper develops a new mathematical-statistical approach to analyze a class of Flajolet-Martin algorithms (FMa), and provides analytical confidence intervals for the number F0 of distinct elements in a stream, based on Chernoff bounds. The class of FMa has reached a significant popularity in bigdata stream learning,…
Big data, data science, deep learning, artificial intelligence are the key words of intense hype related with a job market in full evolution, that impose to adapt the contents of our university professional trainings. Which artificial intelligence is mostly concerned by the job offers? Which methodologies and technolog…
Researchers study the normalizing constant of a continuous categorical distribution.
In this paper I give a brief introduction to a family of simple but non-trivial models designed to increase our understanding of collective processes in markets, the so-called Minority Games, and their non-equilibrium statistical mathematical analysis. Since the most commonly studied members of this family define disor…
Survey of mathematical foundations for reinforcement learning.
The need for new methods to deal with big data is a common theme in most scientific fields, although its definition tends to vary with the context. Statistical ideas are an essential part of this, and as a partial response, a thematic program on statistical inference, learning, and models in big data was held in 2015 i…
We introduce a toy probabilistic model to analyze job-matching processes in recent Japanese labor markets for university graduates by means of statistical physics. We show that the aggregation probability of each company is rewritten by means of non-linear map under several conditions. Mathematical treatment of the map…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here w…
Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior are derived from the model and compared with data. Deviations from Black-Scholes…
The paper reviews and improves concentration inequalities for statistical inference.
Independent component analysis (ICA) is a widely used BSS method that can uniquely achieve source recovery, subject to only scaling and permutation ambiguities, through the assumption of statistical independence on the part of the latent sources. Independent vector analysis (IVA) extends the applicability of ICA by joi…
We have measured the dissimilarities among several printed characters of a single page in the Gutenberg 42-line bible and we prove statistically the existence of several different matrices from which the metal types where constructed. This is in contrast with the prevailing theory, which states that only one matrix per…
Reasoning models generate differently based on problem difficulty, not just length.
We propose a paradigm to deep-learn the ever-expanding databases which have emerged in mathematical physics and particle phenomenology, as diverse as the statistics of string vacua or combinatorial and algebraic geometry. As concrete examples, we establish multi-layer neural networks as both classifiers and predictors …
Mathematical model audits social media algorithms to prevent bias.
New work shows FP potential monotonicity equals low-degree polynomial estimators limits.