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.
Mutation graph of support τ-tilting modules over skew-gentle algebras is connected.
Classifies objects in graded skew-gentle algebras using geometric models.
We describe some of the algebra underlying the decomposition of planar grid diagrams. This provides a useful toy model for an extension of Heegaard Floer homology to 3-manifolds with parametrized boundary. This paper is meant to serve as a gentle introduction to the subject, and does not itself have immediate topologic…
New model for Calabi-Yau- categories using decorated marked surfaces.
Quantum states can be learned efficiently using gentle measurements.
Introduces non-abelian Hodge correspondence linking algebraic structures to geometry.
We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include interpreting dimensions of as intersection numbers of ta…
Study braid group actions on exceptional sequences using branched coverings.
Teaches matrix calculus for machine learning and optimization.
This paper is a gentle introduction to some recent results involving the theory of gerbes over orbifolds for topologists, geometers and physicists. We introduce gerbes on manifolds, orbifolds, the Dixmier-Douady class, Beilinson-Deligne orbifold cohomology, Cheeger-Simons orbifold cohomology and string connections.
The aim of this paper is to provide a gentle introduction to Chabauty topology, while very little background knowledge is assumed. As an example, we provide pictures for the Chabauty space of C*. Note that the description of this space is not new; however the pictures are novel.
Introduces new gradient-based methods for machine learning problems.
This post introduces model calibration and evaluation measures, highlighting issues with a common measure.
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory. We target at a broad audience, not necessarily machine learning researchers. Thi…
Active learning reduces SP calculations by 90%.
Blockchain is a distributed database that keeps a chronologically-growing list (chain) of records (blocks) secure from tampering and revision. While computerisation has changed the nature of a ledger from clay tables in the old days to digital records in modern days, blockchain technology is the first true innovation i…
In this tutorial we explain the inference procedures developed for the sparse Gaussian process (GP) regression and Gaussian process latent variable model (GPLVM). Due to page limit the derivation given in Titsias (2009) and Titsias & Lawrence (2010) is brief, hence getting a full picture of it requires collecting resul…
Nonnegative Matrix Factorization (NMF) was first introduced as a low-rank matrix approximation technique, and has enjoyed a wide area of applications. Although NMF does not seem related to the clustering problem at first, it was shown that they are closely linked. In this report, we provide a gentle introduction to clu…
Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to non-parametric Bayesian modeling of complex networks: Using an infinite mixture model …
This guide introduces machine learning for medical data analysis.
This survey explores various optimality concepts in importance sampling.
Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and hard to approximate in the presence of negative correlations, DPPs offer efficie…
Geometric formulation of 4D supergravity for mathematicians.
This paper has two-fold goal: it provides gentle introduction to Knot Theory starting from 3-coloring, the concept introduced by R. Fox to allow undergraduate students to see that the trefoil knot is non-trivial, and ending with statistical mechanics. On the way we prove various (old and new) facts about knots. We rela…
This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We employ a step-by-step approach to develop an implementation of the PMH algorithm …
State-of-the-art solutions in the areas of "Language Modelling & Generating Text", "Speech Recognition", "Generating Image Descriptions" or "Video Tagging" have been using Recurrent Neural Networks as the foundation for their approaches. Understanding the underlying concepts is therefore of tremendous importance if we …
The Ma-Trudinger-Wang curvature --- or cross-curvature --- is an object arising in the regularity theory of optimal transportation. If the transportation cost is derived from a Hamiltonian action, we show its cross-curvature can be expressed in terms of the associated Jacobi fields. Using this expression, we show the l…
New neural network criterion connects RH to minimization problem.
Parameter pruning is a promising approach for CNN compression and acceleration by eliminating redundant model parameters with tolerable performance degrade. Despite its effectiveness, existing regularization-based parameter pruning methods usually drive weights towards zero with large and constant regularization factor…
The first part of this text is a gentle exposition of some basic constructions and results in the extended prequantum theory of Chern-Simons-type gauge field theories. We explain in some detail how the action functional of ordinary 3d Chern-Simons theory is naturally localized ("extended", "multi-tiered") to a map on t…
Federated learning improves bioinformatics by sharing data legally.
Method learns conditional distributions using neural entropic optimal transport.
This book provides a gentle introduction to the study of arithmetic subgroups of semisimple Lie groups. This means that the goal is to understand the group SL(n,Z) and certain of its subgroups. Among the major results discussed in the later chapters are the Mostow Rigidity Theorem, the Margulis Superrigidity Theorem, R…
A tutorial on dynamic Laplacian for time-evolving data clusters.
The adaptive processing of graph data is a long-standing research topic which has been lately consolidated as a theme of major interest in the deep learning community. The snap increase in the amount and breadth of related research has come at the price of little systematization of knowledge and attention to earlier li…
Spurred by the enthusiasm surrounding the "Big Data" paradigm, the mathematical and algorithmic tools of online optimization have found widespread use in problems where the trade-off between data exploration and exploitation plays a predominant role. This trade-off is of particular importance to several branches and ap…
This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural optimization and stochastic optimization. Our presentation of black-box optimizati…
A novel approach models rating transitions using Lie groups and Deep Learning.
The paper explains the richness scale of wide neural networks.
New bounds show robust models can generalize well, contrary to prior theories.
Quality-Diversity algorithms explore multiple high-performing solutions in a search space.
New approach to deeper graph neural networks to avoid performance degradation.
This paper introduces compositional data analysis for financial ratios, improving industry-level analysis.
Conformal prediction provides distribution-free uncertainty quantification for black-box models.
New algebraic structure derived from Hopf algebra and Drinfel'd twist.
Study of cluster and skein algebras for surfaces, showing their connection.
We consider distributed optimization under communication constraints for training deep learning models. We propose a new algorithm, whose parameter updates rely on two forces: a regular gradient step, and a corrective direction dictated by the currently best-performing worker (leader). Our method differs from the param…
New statistical guarantee improves conformal predictors for small datasets.