arXiv research

Self-organized action hierarchy and compositionality learned by RNNs.

Symmetry reduction of Painlevé IV to Flaschka-Newell Painlevé II

Proposes DHEB model for predicting online ad performance.

We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure. We identify the dominating variable and extract its explicit stochastic model. …

Definition of frustration is expressed by transitivity of binary entanglement relation in considered complex system. Extending this definition into n-ary relation a hierarchy of frustrations is derived. As a complex system the U.S. Intermarket is chosen where the correlation coefficient of intermarket sectors plays the…

Decomposes financial networks to reveal cause-effect hierarchies during crises.

Proves efficient learning of hierarchical structure in meta-reinforcement learning.

Study of deep neural networks' NTK evolution during training.

The Davey Stewartson hierarchy will be developed based on a set of three matrix differential operators. These equations will act as evolution equations for different types of surface deformation in Euclidean four space. The Weierstrass representation for surfaces will be developed and its uniqueness up to gauge transfo…

We propose dynamical systems trees (DSTs) as a flexible class of models for describing multiple processes that interact via a hierarchy of aggregating parent chains. DSTs extend Kalman filters, hidden Markov models and nonlinear dynamical systems to an interactive group scenario. Various individual processes interact a…

A new method learns object hierarchies from images to reason about physical interactions.

Extensions of the generalized Weierstrass representation to generic surfaces in 4D Euclidean and pseudo-Euclidean spaces are given. Geometric characteristics of surfaces are calculated. It is shown that integrable deformations of such induced surfaces are generated by the Davey -Stewartson hierarchy. Geometrically thes…

Symmetry unifies AI learning dynamics, complexity, and representation.

We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of statistical independence between the microscopical variables of the system. Moreover, we e…

Novel Lie-superalgebraic description of superstring dynamics.

Paper studies ResNet dynamics using NTH, reducing width requirement.

Constructs integrable hierarchies for generalized Frobenius manifolds with non-flat unity.

UrbanRhythm reveals urban dynamics from mobility data.

Study identifies pitfalls in assessing hierarchies for multi-class classification.

Super tau-covers extend bihamiltonian hierarchies' symmetries.

Deep learning approximates system moments from data.

Hydrodynamic hierarchy deformed using conservation laws.

New hierarchy for a special group type.

We propose a new anytime hierarchical clustering method that iteratively transforms an arbitrary initial hierarchy on the configuration of measurements along a sequence of trees we prove for a fixed data set must terminate in a chain of nested partitions that satisfies a natural homogeneity requirement. Each recursive …

Legendre transformations link related integrable hierarchies.

Twisted $U$- and twisted $U/K$-hierarchies are soliton hierarchies introduced by Terng to find higher flows of the generalized sine-Gordon equation. Twisted $\frac {O(J,J)}{O(J)\times O(J)}$-hierarchies are among the most important classes of twisted hierarchies. In this paper, interesting first and higher flows of twi…

ManifoldMind uses adaptive-curvature probabilistic spheres for trustworthy recommendations in semantic hierarchies.

In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid. Active traders are characterised by the decision to buy, (+1), or sell, (-1), a …

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 $\mathcal{A}_1$. The extended heat hierarchy will be the basic model for the analysis of the extension of KP hierarchy, and other integrable equations.

New hierarchies derived from KP hierarchy using non-formal operators and Yang-Mills action.

Scroll structures on solutions of 4D integrable equations are involutive and governed by a dispersionless hierarchy.

Constructs tri-Hamiltonian structure and Frobenius manifold for asymmetric gAL 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 $τ$-functions of the Toda lattice hierarchy. A representation formula for discretized plane curves is also discussed.

HAKE embeds entities in polar coordinates to model semantic hierarchies in knowledge graphs.

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.

Paper develops a new framework for analyzing certainty equivalents and dynamic risk premia using Malliavin calculus and Wiener chaos analysis.

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 $L_m$, $m\geq -1$ 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.

A new hierarchy quantifies agency in systems based on information processing.

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 $CP^1$ topological sigma model and the extended Toda hierarchy. We al…

New diffiety theory leads to a well-posed KP hierarchy.

A framework combining HSMM and survival analysis for lifecycle-oriented mobility analysis.

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 $L$ as positive and negative subgroups L_+, L_- and a commuting sequence in the Lie algebr…