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.
Decomposes financial networks to reveal cause-effect hierarchies during crises.
The study quantifies the information needed for causal queries at different levels of Pearl's hierarchy.
New causal distances improve evaluation of causal discovery algorithms.
The causal compatibility question asks whether a given causal structure graph -- possibly involving latent variables -- constitutes a genuinely plausible causal explanation for a given probability distribution over the graph's observed variables. Algorithms predicated on merely necessary constraints for causal compatib…
The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications of the recently solved ``folk questions on smoothability'', and alternative prop…
Visual objects are composed of a recursive hierarchy of perceptual wholes and parts, whose properties, such as shape, reflectance, and color, constitute a hierarchy of intrinsic causal factors of object appearance. However, object appearance is the compositional consequence of both an object's intrinsic and extrinsic c…
TRAM-DAG models bridge interpretability and flexibility in causal modeling.
POSCMs extend SCMs for causal modeling with latent contexts.
Unified multilinear model for causal factor disentanglement.
Learning transferable knowledge across similar but different settings is a fundamental component of generalized intelligence. In this paper, we approach the transfer learning challenge from a causal theory perspective. Our agent is endowed with two basic yet general theories for transfer learning: (i) a task shares a c…
Recent interest in the external validity of prediction models (i.e., the problem of different train and test distributions, known as dataset shift) has produced many methods for finding predictive distributions that are invariant to dataset shifts and can be used for prediction in new, unseen environments. However, the…
Paper simplifies complex causal identifiability problems with exogenous isomorphism.
Unified approach to causal representation learning using invariance principles.
Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em causal mapping} between spacetimes --essentially equivalent in this context to the {\em chronological map} one in abstract chronological spaces--, and the related notion of {\em causal structure}, have been introduced as new tools to study causal…
Causal deep learning tackles causal inference using tensor factor analysis.
Study evaluates large language models' ability to understand probabilistic real-world distributions.
Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped surfaces have positivity of a certain curvature, related to surface gravity. Increas…
Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal distribution or other distribution encouraging sparsity. However, this prior is agnostic to…
Generates counterfactuals in target domain from source domain observations.
Study reveals which startup valuation factors are most critical.
Constructs integrable hierarchies for generalized Frobenius manifolds with non-flat unity.
Study identifies pitfalls in assessing hierarchies for multi-class classification.
Super tau-covers extend bihamiltonian hierarchies' symmetries.
Hydrodynamic hierarchy deformed using conservation laws.
Legendre transformations link related integrable hierarchies.
Twisted - and twisted -hierarchies are soliton hierarchies introduced by Terng to find higher flows of the generalized sine-Gordon equation. Twisted -hierarchies are among the most important classes of twisted hierarchies. In this paper, interesting first and higher flows of twi…
Derive bihamiltonian structure for rational reduction of 2D-Toda hierarchy
We propose a formally completely integrable extension of heat hierarchy based on the space of symmetries isomorphic to the Weyl algebra . The extended heat hierarchy will be the basic model for the analysis of the extension of KP hierarchy, and other integrable equations.
Wise's Quasiconvex Hierarchy Theorem classifying hyperbolic virtually compact special groups in terms of quasiconvex hierarchies played an essential role in Agol's proof of the Virtual Haken Conjecture. Answering a question of Wise, we construct a new virtual quasiconvex hierarchy for relatively hyperbolic virtually co…
New hierarchies derived from KP hierarchy using non-formal operators and Yang-Mills action.
Symmetry reduction of Painlevé IV to Flaschka-Newell Painlevé II
Scroll structures on solutions of 4D integrable equations are involutive and governed by a dispersionless hierarchy.
A relation between the Goldstein-Petrich hierarchy for plane curves and the Toda lattice hierarchy is investigated. A representation formula for plane curves is given in terms of a special class of -functions of the Toda lattice hierarchy. A representation formula for discretized plane curves is also discussed.
Constructs tri-Hamiltonian structure and Frobenius manifold for asymmetric gAL hierarchy
New integrable deformations for topological hierarchies from Frobenius manifolds.
We introduce two families of soliton hierarchies: the twisted hierarchies associated to symmetric spaces. The Lax pairs of these two hierarchies are Laurent polynomials in the spectral variable. Our constructions gives a hierarchy of commuting flows for the generalized sine-Gordon equation (GSGE), which is the Gauss-Co…
Paper investigates methods to improve classification by inducing a hierarchy from flat labels.
We compute the central invariants of the bihamiltonian structures of the constrained KP hierarchies, and show that these integrable hierarchies are topological deformations of their hydrodynamic limits.
We prove that the extended Toda hierarchy of \cite{CDZ} admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators , of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau fu…
Paper addresses limitations of traditional hierarchical clustering methods.
We present the Lax pair formalism for certain extension of the continuous limit of the classical Toda lattice hierarchy, provide a well defined notion of tau function for its solutions, and give an explicit formulation of the relationship between the topological sigma model and the extended Toda hierarchy. We al…
New diffiety theory leads to a well-posed KP hierarchy.
We propose an extension of the differential system for constant mean curvature (CMC) surfaces in a three dimensional space form to an associated hierarchy of evolution equations by the higher-order commuting symmetries. The infinite sequence of higher-order conservation laws of CMC surfaces admit the corresponding exte…
This is the third in a series of papers attempting to describe a uniform geometric framework in which many integrable systems can be placed. A soliton hierarchy can be constructed from a splitting of an infinite dimensional group as positive and negative subgroups L_+, L_- and a commuting sequence in the Lie algebr…
Study bihamiltonian structures and Frobenius manifolds for specific Toda hierarchies.
Investigate the evolving structure of cryptocurrency interactions using high-frequency returns.
We observe that the modular class of a Poisson-Nijhenhuis manifold has a canonical representative and that, under a cohomological assumption, this vector field is bi-hamiltonian. In many examples the associated hierarchy of flows reproduces classical integrable hierarchies.
ProHOC detects OOD samples in class hierarchies, predicting them to correct internal nodes.