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.
The paper explains knowledge distillation by analyzing visual concepts in DNNs.
Ray-Singer torsion is a mathematical concept with applications in physics.
Prob2Vec embeds problems for adaptive tutoring, achieving high similarity accuracy.
Mathematical framework for differential machine learning in finance.
In this paper, we briefly discuss a mathematical concept that can be used in economics.
Mathematical analysis of Prytz planimeter using sub-Riemannian geometry.
The concept of closed trapped surface is of paramount importance in General Relativity and other gravitational theories. However, it is a purely geometrical object. With the aim of bringing this concept to closer attention by the mathematical community, I introduce the generalized idea of trapped submanifold by using t…
The concept of a symplectic structure first appeared in the works of Lagrange on the so-called "method of variation of the constants". These works are presented, together with those of Poisson, who first defined the composition law called today the "Poisson bracket". The method of variation of the constants is presente…
We review origins and main properties of the most important bracket operations appearing canonically in differential geometry and mathematical physics in the classical, as well as the supergeometric setting. The review is supplemented by a few new concepts and examples.
When people learn mathematical patterns or sequences, they are able to identify the concepts (or rules) underlying those patterns. Having learned the underlying concepts, humans are also able to generalize those concepts to other numbers, so far as to even identify previously unseen combinations of those rules. Current…
Study uses crochet to visualize non-Euclidean geometry.
Paper shows equivalence between MM and PH for n-D Morse functions.
Equivalence shown between two mathematical concepts for hyperbolic surfaces.
Proposes a simple method to represent and manipulate concepts using polynomials and moment statistics.
Survey on advanced gauge theory concepts.
The paper models and prices cyber insurance risks, distinguishing idiosyncratic, systematic, and systemic risks.
This paper is a tutorial on Formal Concept Analysis (FCA) and its applications. FCA is an applied branch of Lattice Theory, a mathematical discipline which enables formalisation of concepts as basic units of human thinking and analysing data in the object-attribute form. Originated in early 80s, during the last three d…
Mathematical framework for transfer learning feasibility and transfer risk.
Paper formalizes Simon's satisficing through FFSD, proving its equivalence to expected utility theory.
The paper applies math and physics to language models, introducing entropy and geometric concepts.
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in fact organized in the language topological quantum field theory.
We introduce the concept of singular values for the Riemann curvature tensor, a central mathematical tool in Einstein's theory of general relativity. We study the properties related to the singular values, and investigate five typical cases to show its relationship to the Ricci scalar and other invariants.
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…
Mathematical theory of super fiber bundles and connections developed.
Paper defines mathematical framework for neural network explainability.
The paper proves stability of the positive mass theorem using intrinsic flat convergence.
This paper introduces the concept of functional current as a mathematical framework to represent and treat functional shapes, i.e. sub-manifold supported signals. It is motivated by the growing occurrence, in medical imaging and computational anatomy, of what can be described as geometrico-functional data, that is a da…
We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm. We use the mathematical concept of fiber bundle to characterize the multivalued …
Study Gram determinants in knot theory, focusing on a Möbius band determinant.
The so-called great divergence in the income per capita is described in the Unified Growth Theory as the mind-boggling and unresolved mystery about the growth process. This mystery has now been solved: the great divergence never happened. It was created by the manipulation of data. Economic growth in various regions is…
This paper studies how knots combine using Alexander Polynomials.
Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus, approximation theory, optimization and linear algebra. This article provides a very…
Euler derived elastica equation using modern mathematical concepts.
The main purpose of this paper is to formalize the modelling process, analysis and mathematical definition of corruption when entering into a contract between principal agent and producers. The formulation of the problem and the definition of concepts for the general case are considered. For definiteness, all calculati…
Defines tensor eigenvalues and singular values without basis, simplifying analysis.
New concept of illiquidity linked to credit risk, using Jarrow & Turnbull's analogy.
This paper explores historical and philosophical aspects of angles and solid angles, inspired by Euler's work.
This monograph aims at providing an introduction to key concepts, algorithms, and theoretical results in machine learning. The treatment concentrates on probabilistic models for supervised and unsupervised learning problems. It introduces fundamental concepts and algorithms by building on first principles, while also e…
Study clarifies Bayesian generalization error in CBM for 3-layered linear neural networks.
Extends V-IP framework to use LLMs for generating task-relevant concepts, improving interpretability and performance.
Paper defines XAI concepts using category theory.
In this pedagogical study, carried out by adopting standard mathematical methods of nonlinear dynamics, we have presented some simple analytical models to understand terminal behaviour in industrial growth. This issue has also been addressed from a dynamical systems perspective, with especial emphasis on the concept of…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of the fibre bundle in question] in a more natural way. It starts off with a review o…
LLMs will inevitably hallucinate due to their mathematical structure.
LLMs can be tricked into recalling facts based on context clues.
Discretization of curves is an ancient topic. Even discretization of curves with an eye toward differential geometry is over a century old. However there is no general theory or methodology in the literature, despite the ubiquitous use of discrete curves in mathematics and science. There are conflicting definitions of …
Strict partial order is a mathematical structure commonly seen in relational data. One obstacle to extracting such type of relations at scale is the lack of large-scale labels for building effective data-driven solutions. We develop an active learning framework for mining such relations subject to a strict order. Our a…