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.
Overview of fiber bundles in gauge theories with visual emphasis.
Pedagogical approaches help interpret embedding models in knowledge bases.
A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is gi…
Conformal prediction offers distribution-free inference for complex models.
Kernelized PCovR reveals structure-property relations in chemistry and materials.
Overview of high-dimensional dynamical systems and their applications to machine learning.
Neural pedagogical agent updates user models in real-time for mobile education apps.
Geometric GNNs model 3D atomic systems with rotations and translations.
A self-contained introduction is presented of the notion of the (abstract) differentiable manifold and its tangent vector fields. The way in which elementary topological ideas stimulated the passage from Euclidean (vector) spaces and linear maps to abstract spaces (manifolds) and diffeomorphisms is emphasized. Necessar…
The paper contains a review on the general connection theory on differentiable fibre bundles. Particular attention is paid to (linear) connections on vector bundles. The (local) representations of connections in frames adapted to holonomic and arbitrary frames is considered.
DeepXDE uses neural networks to solve complex differential equations.
Overview of latent variable models in probabilistic frameworks.
Explains three neural network types: feedforward, convolutional, and recurrent.
By proving graph theoretical versions of Green-Stokes, Gauss-Bonnet and Poincare-Hopf, core ideas of undergraduate mathematics can be illustrated in a simple graph theoretical setting. In this pedagogical exposition we present the main proofs on a single page and add illustrations. While discrete Stokes is is old, the …
Bayesian optimization with Gaussian processes speeds up searches for stationary points.
Introduces Kundt spaces using geometric language.
A quick overview is provided on the current development of the WP metric geometry.
In this short paper, we re-derive the Bochner formula for the Laplacian by considering local variations of volume. The derivation is rooted in the fact that the Laplacian of a function measures the volume variation along the flow of the gradient vector of the function. Possible extensions of this approach/technique are…
Overview of affine surface area and its history.
Overview of infinite surface mapping class groups.
Overview of multi-task learning in deep neural networks.
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables based on the indirect information contained in the measurements. For such problem…
Overview of AI and ML uncertainty quantification methods.
This paper provides an overview of CCA-based multi-view learning approaches.
We give a quite detailed overview on the proof of the Cheeger-Colding-Gromoll splitting theorem in the abstract framework of spaces with Riemannian Ricci curvature bounded from below.
The paper simplifies complex jump-diffusion markets to complete models.
This a free translation with additional explanations of {\em Processus à Accroissement Independants Chapitre I: La Décomposition de Paul Lévy}, by J.L. Bretagnolle, in {\em Ecole d'Eté de Probabilités}, Lecture Notes in Mathematics 307, Springer 1973. The Lévy-Khintchine representation of infinitely divisible distribut…
This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary differential equations, these algebras, or infinitesimal groups, are a recurring theme in 20th-century research on Lie algebras. I will…
This is the first monograph on the geometry of anisotropic spinor spaces and its applications in modern physics. The main subjects are the theory of gravity and matter fields in spaces provided with off--diagonal metrics and associated anholonomic frames and nonlinear connection structures, the algebra and geometry of …
We give a pragmatic/pedagogical discussion of using Euclidean path integral in asset pricing. We then illustrate the path integral approach on short-rate models. By understanding the change of path integral measure in the Vasicek/Hull-White model, we can apply the same techniques to "less-tractable" models such as the …
Explains ABC methods with examples.
Simplified explanation of ML for mixtures and OT.
Overview of Higgs bundles and related conjectures.
The purpose of these notes is to provide a systematic quantitative framework - in what is intended to be a "pedagogical" fashion - for discussing mean-reversion and optimization. We start with pair trading and add complexity by following the sequence "mean-reversion via demeaning -> regression -> weighted regression ->…
Surveying nonparametric inference with shape constraints, past and future.
This paper provides an overview of activation functions in neural networks.
Overview of Teichmüller theory theorems and conjectures.
This paper offers an overview of neural network compression techniques.
Overview of Thurston's work in math.
Abstract: Overview of scalar curvature constraints in Riemannian spaces.
We present a brief overview of the Korányi-Reimann theory of quasiconformal mappings on the Heisenberg group stressing on the analogies as well as on the differences between the Heisenberg group case and the classical two-dimensional case. We examine the extensions of the theory to more general spaces and we state some…
Introduces non-abelian Hodge correspondence linking algebraic structures to geometry.
Provides an overview of Bartnik's quasi-local mass.
Survey of methods to verify deep neural networks.
In this note we discuss - in what is intended to be a pedagogical fashion - FX option pricing in target zones with attainable boundaries. The boundaries must be reflecting. The no-arbitrage requirement implies that the differential (foreign minus domestic) short-rate is not deterministic. When the band is narrow, we ca…
Overview of methods for rotating 2D and 3D data.
Develops algorithms for constructing statistical risk models.
Overview of risk-sensitive Markov decision processes with Optimized Certainty Equivalent.