We obtain variational formulas for holomorphic objects on Riemann surfaces with respect to arbitrary local coordinates on the moduli space of complex structures. These formulas are written in terms of a canonical object on the moduli space which corresponds to the pairing between the space of quadratic differentials an…
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48 results for “object hierarchy”
A new method learns object hierarchies from images to reason about physical interactions.
problem Learning about the interactions of complex objects and their dynamics.
method Unsupervised learning of object hierarchies from raw visual images.
result Improves over a strong baseline at modeling synthetic and real-world videos.
New integrable deformations for topological hierarchies from Frobenius manifolds.
problem Integrable deformations of topological hierarchies from Frobenius manifolds.
method Construction of integrable deformations with polynomial tau-structures.
result Conjecture of universal object for Riemann--Hopf hierarchy.
Compositional structures between parts and objects are inherent in natural scenes. Modeling such compositional hierarchies via unsupervised learning can bring various benefits such as interpretability and transferability, which are important in many downstream tasks. In this paper, we propose the first deep latent vari…
This paper proposes to learn hierarchical compositional AND-OR model for interpretable image synthesis by sparsifying the generator network. The proposed method adopts the scene-objects-parts-subparts-primitives hierarchy in image representation. A scene has different types (i.e., OR) each of which consists of a number…
BoTier optimizes experiments by balancing multiple objectives hierarchically.
problem Balancing multiple competing objectives in scientific experiments.
method Composite objective that flexibly represents a hierarchy of preferences over outcomes and parameters.
result Demonstrates robust applicability across various use cases and seamless integration.
Concept Hierarchies and Formal Concept Analysis are theoretically well grounded and largely experimented methods. They rely on line diagrams called Galois lattices for visualizing and analysing object-attribute sets. Galois lattices are visually seducing and conceptually rich for experts. However they present important…
When related learning tasks are naturally arranged in a hierarchy, an appealing approach for coping with scarcity of instances is that of transfer learning using a hierarchical Bayes framework. As fully Bayesian computations can be difficult and computationally demanding, it is often desirable to use posterior point es…
New method optimizes hierarchical multi-label classification results.
problem Optimizing classification results respecting class hierarchy and classifier scores.
method Introducing CATCH objective function and mLPR metric to rank multi-label classification results.
result HierRank algorithm optimizes CATCH, improving decision accuracy.
This study shows the moment-SOS hierarchy converges in polynomial optimization over product of spheres.
problem Minimizing multihomogeneous polynomials over product of spheres.
method Moment-SOS hierarchy, local optimality conditions, differential geometry, Morse theory.
result The moment-SOS hierarchy has finite convergence for generic multihomogeneous objective functions.
Unified tensor model disentangles object appearance factors.
problem Representing hierarchical intrinsic and extrinsic causal factors of object appearance.
method Compositional hierarchical tensor factorization.
result Interpretable object representation robust to occlusion and reduced training data requirements.
Multigrid modeling algorithms are a technique used to accelerate relaxation models running on a hierarchy of similar graphlike structures. We introduce and demonstrate a new method for training neural networks which uses multilevel methods. Using an objective function derived from a graph-distance metric, we perform or…
Novel approximation hierarchy for sparse quadratic programs.
problem Sparse Quadratic Programs with Cardinality Constraints.
method Exploits rank-dominating eigenvectors for min-max optimization over binary variables.
result Efficient screening of nonzero elements with scalable optimization algorithms.
Generates infinite-depth hierarchical clusters from few examples.
problem Inadequate finite-sample clustering methods for fine-scale hierarchical structures.
method Classification fields generated by a local refinement rule, approximated by predictors.
result Learned predictors can approximate infinite-depth hierarchical structures.
Unified multilinear model for causal factor disentanglement.
problem Disentangling causal factors from complex data without direct manipulation.
method Hierarchical block multilinear factorization (M-mode Block SVD) and incremental approach.
result Interpretable object representation robust to occlusion and reduced training data.
This paper develops a cohomological hierarchy for bistable visual paradoxes.
problem Understanding the hierarchy of visual paradoxes built from bistable elements.
method Develops a cohomological hierarchy using coefficients and a discrete Stokes theorem.
result Reveals a hierarchy of paradox classes from through , refined at each degree by the relative/absolute distinction.
Constructs integrable hierarchies for generalized Frobenius manifolds with non-flat unity.
problem Integrable hierarchies for generalized Frobenius manifolds with non-flat unity.
method Constructs a bihamiltonian integrable hierarchy of hydrodynamic type.
result Integrable hierarchy possesses Virasoro symmetries and a tau structure.
Kernels for structured data are commonly obtained by decomposing objects into their parts and adding up the similarities between all pairs of parts measured by a base kernel. Assignment kernels are based on an optimal bijection between the parts and have proven to be an effective alternative to the established convolut…
Study identifies pitfalls in assessing hierarchies for multi-class classification.
problem Lack of understanding in selecting hierarchies for multi-class classification.
method Analyzed and compared popular approaches to extracting hierarchies.
result Hierarchy quality becomes irrelevant when using powerful classifiers.
Super tau-covers extend bihamiltonian hierarchies' symmetries.
problem Extending symmetries of bihamiltonian hierarchies.
method Constructing super tau-covers for bihamiltonian integrable hierarchies.
result Symmetries of bihamiltonian hierarchies extended to super tau-covers.
Hydrodynamic hierarchy deformed using conservation laws.
problem Deforming a hydrodynamic hierarchy with non-vanishing Nijenhuis torsion.
method Using a chain of conservation laws to deform the hierarchy.
result The resulting hierarchy has non-vanishing Nijenhuis torsion but vanishing Haantjes tensor.
The development of algorithms for hierarchical clustering has been hampered by a shortage of precise objective functions. To help address this situation, we introduce a simple cost function on hierarchies over a set of points, given pairwise similarities between those points. We show that this criterion behaves sensibl…
DiffEnc improves diffusion models by adding flexibility and achieving better likelihood on CIFAR-10.
problem Improving the likelihood of diffusion models on image datasets.
method Introducing a data- and depth-dependent mean function and a free weight parameter for noise variance.
result Achieved statistically significant improvement in likelihood on CIFAR-10.
Building models, or maps, of robot environments is a highly active research area; however, most existing techniques construct unstructured maps and assume static environments. In this paper, we present an algorithm for learning object models of non-stationary objects found in office-type environments. Our algorithm exp…
A new method for optimizing hierarchical multi-objective problems.
problem Symmetry and neglect of objective hierarchy in existing multi-objective methods.
method Priority-Constrained Descent (PCD) framework exploiting hierarchical objective structures.
result Pareto dominance and better per-objective performance with secondary progress guarantees.
Legendre transformations link related integrable hierarchies.
problem Understanding relationships between integrable hierarchies.
method Legendre-type transformations of generalized Frobenius manifolds.
result Linear reciprocal transformations link related 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…
Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes then depends only on their cluster assignment. Currently available models can b…
Derive bihamiltonian structure for rational reduction of 2D-Toda hierarchy
problem Derive bihamiltonian structure for rational reduction of 2D-Toda hierarchy
method Direct computations
result Derive local bihamiltonian structure
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.
In clustering we normally output one cluster variable for each datapoint. However it is not necessarily the case that there is only one way to partition a given dataset into cluster components. For example, one could cluster objects by their colour, or by their type. Different attributes form a hierarchy, and we could …
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.
problem Formal solutions of KP hierarchy and their non-formal counterparts.
method Developed new hierarchies of non-linear equations on non-formal pseudo-differential operators.
result Expressed one hierarchy as Yang-Mills action minimization.
A symmetry reduction of the Painlevé IV hierarchy to the Flaschka-Newell Painlevé II hierarchymath-ph
Symmetry reduction of Painlevé IV to Flaschka-Newell Painlevé II
problem Isomonodromic deformation problem associated with rank-two meromorphic connections
method Symmetry
result Induced isomonodromic dynamics coincides with Flaschka-Newell Painlevé II hierarchy
Scroll structures on solutions of 4D integrable equations are involutive and governed by a dispersionless hierarchy.
problem Characterizing the geometry of solutions to 4D integrable equations.
method Defining rational normal scrolls and showing their involutivity.
result Involutive scroll structures are governed by a dispersionless integrable hierarchy.
Constructs tri-Hamiltonian structure and Frobenius manifold for asymmetric gAL hierarchy
problem Tri-Hamiltonian structure and Frobenius manifold for asymmetric gAL hierarchy
method Local tri-Hamiltonian structure construction and Frobenius manifold construction
result Dispersionless limits of flows belong to Principal 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.
HAKE embeds entities in polar coordinates to model semantic hierarchies in knowledge graphs.
problem Lack of modeling semantic hierarchies in knowledge graph embeddings.
method HAKE embeds entities in a polar coordinate system, where the radial coordinate represents hierarchy levels and the angular coordinate distinguishes entities at the same level.
result HAKE significantly outperforms existing methods on link prediction tasks in knowledge graphs.
Paper studies ResNet dynamics using NTH, reducing width requirement.
problem Understanding ResNet dynamics and improving training efficiency.
method Uses Neural Tangent Hierarchy (NTH) to analyze ResNet dynamics.
result Reduces width requirement from quartic to cubic for ResNet.
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.
problem Improving classification performance on datasets lacking a natural hierarchy.
method The approach involves clustering conditional distributions and using a hierarchical classifier with the induced hierarchy.
result The methods can discover latent hierarchies and improve accuracy in various applications.
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.
problem Traditional hierarchical clustering methods face limitations in binary trees and ultrametrics.
method Introduces the notion of a valid hierarchy and a two-step algorithm to construct a binary tree and prune it to enforce validity.
result Proposes a method to recover the finest valid hierarchy, which is not constrained to binary structures.
The Extended Toda Hierarchynlin.SI
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…
In this paper we study a new reinforcement learning setting where the environment is non-rewarding, contains several possibly related objects of various controllability, and where an apt agent Bob acts independently, with non-observable intentions. We argue that this setting defines a realistic scenario and we present …
New diffiety theory leads to a well-posed KP hierarchy.
problem Formalizing diffieties for better hierarchy analysis.
method Definition of diffiety based on Frolicher structures.
result Formation of a well-posed Kadomtsev-Petviashvili hierarchy.
CMC hierarchymath.DG
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…