New methods using natural gradient for structured optimization.
problem Structured optimization problems.
method Structured second-order methods via natural gradient descent.
result Efficiency demonstrated on non-convex and deep learning problems.
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48 results for “natural structure”
A reductive structure is associated here with Lagrangian canonically defined conserved quantities on gauge-natural bundles. Parametrized transformations defined by the gauge-natural lift of infinitesimal principal automorphisms induce a variational sequence such that the generalized Jacobi morphism is naturally self-ad…
Character varieties get a natural Poisson structure.
problem Character varieties of surfaces.
method Natural Poisson structure.
result Character varieties have a Poisson structure.
Classifies 7- and 8-dimensional naturally reductive spaces.
problem Classifying naturally reductive spaces in 7 and 8 dimensions.
method Combines structure theory and new construction methods.
result Complete classification of 7- and 8-dimensional naturally reductive spaces.
Classifies R-spaces with a specific symmetric structure.
problem Classifying R-spaces with a natural Γ-symmetric structure.
method Classification and determination of maximal antipodal sets.
result Classification of R-spaces with a natural Γ-symmetric structure.
SparseMAP selects sparse structures efficiently for structured prediction.
problem Efficiently searching over combinatorial structures in structured prediction.
method SparseMAP: a new method for sparse structured inference with a differentiable loss function.
result SparseMAP selects only a few global structures efficiently.
We continue the study of the anti-Hermitian structures of general natural lift type on the tangent bundles. We get the conditions under which these structures are in the eight classes obtained by Ganchev and Borisov. We complete the characterization of the general natural anti-Kahlerian structures on the tangent bundle…
Generates natural product-like compounds using GPT models.
problem Challenges in generating and evaluating natural product-like compounds.
method Trained GPT-based chemical language models on natural product dataset.
result Generated compounds have similar distribution to natural products.
We develop a more efficient NGD method for structured parameters.
problem Computational challenges in NGD for structured parameter spaces.
method Local-parameter coordinates to simplify Fisher-matrix computations.
result New structured second-order algorithms and learning methods.
Proves natural operations on holomorphic forms are limited.
problem Identifying natural differential operations on holomorphic forms.
method Developed theory of natural holomorphic bundles, proving a categorical equivalence.
result Only linear combinations, exterior product, and exterior differential are natural operations.
Submanifolds of Frobenius manifolds are studied. In particular, so-called natural submanifolds are defined and, for semi-simple Frobenius manifolds, classified. These carry the structure of a Frobenius algebra on each tangent space, but will, in general, be curved. The induced curvature is studied, a main result being …
We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. We prove the characterization theorem…
Unique birational structure proven on Inoue surfaces.
problem Proving uniqueness of birational structures on Inoue surfaces.
method Generalizing a result by Bruno Klingler, proving uniqueness of structures.
result The natural -structure on an Inoue surface is the unique -structure.
Tree-Transformer improves grammar correction in code and natural language.
problem Grammar correction in tree-structured data.
method Tree-Transformer neural network architecture for tree-structured data.
result Significant improvement in grammar correction accuracy.
The natural topological, differentiable and geometrical structures on the space of light rays of a given spacetime are discussed. The relation between the causality properties of the original spacetime and the natural structures on the space of light rays are stressed. Finally, a symplectic geometrical approach to the …
The paper defines conditions for learning causal graphs from data with unobserved variables.
problem Learning causal graphs from data with unobserved variables.
method Formalizes constraint-based structure learning algorithms under conditions and assumptions.
result Natural family of algorithms output Markov equivalent graphs to the causal graph under faithfulness assumption.
We describe a model for capturing the statistical structure of local amplitude and local spatial phase in natural images. The model is based on a recently developed, factorized third-order Boltzmann machine that was shown to be effective at capturing higher-order structure in images by modeling dependencies among squar…
The paper constructs new structures for manifolds using connections and combinations.
problem Understanding smooth manifolds with precise infinitesimal affine structures.
method Constructing new infinitesimal structures for higher-order neighbourhoods of the diagonal.
result Any symmetric affine connection on a manifold extends to a second-order infinitesimally affine structure.
ETC improves Transformer models for long and structured inputs.
problem Scaling input length and encoding structured inputs in Transformers.
method Introduces global-local attention, relative position encodings, and CPC pre-training.
result Achieves state-of-the-art results on four natural language datasets.
A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.
The Holomorphic Sectional Curvature of General Natural KÄhler Structures on Cotangent Bundlesmath.DG
We study the conditions under which a Kählerian structure of general natural lift type on the cotangent bundle of a Riemannian manifold has constant holomorphic sectional curvature. We obtain that a certain parameter involved in the condition for to be a Kählerian manifold, is expres…
Naturality of the Contact Invariant in Monopole Floer Homology Under Strong Symplectic Cobordismsmath.GT
The contact invariant in monopole Floer homology behaves naturally under strong symplectic cobordisms.
problem Understanding the behavior of the contact invariant under symplectic cobordisms.
method Extending the gluing argument to handle cylindrical ends, showing naturality.
result The contact invariant is natural under strong symplectic cobordisms.
Natural volume forms defined for pseudo-Finslerian manifolds with specific metrics.
problem Defining natural volume forms on pseudo-Finslerian manifolds with -th root metrics.
method Definitions depend on the parity of , expressed in terms of Cayley hyperdeterminants.
result Volume forms computation simplified by avoiding integration over the indicatrix.
We study the conditions under which the cotangent bundle of a Riemaannian manifold , endowed with a Kählerian structure of general natural lift type (see \cite{Druta1}), is Einstein. We first obtain a general natural Kähler-Einstein structure on the cotangent bundle . In this case, a certain…
This note aims to demonstrate that every parabolic geometry has a naturally defined per-Courant algebroïd structure. This structure is a Courant algebroïd if and only if the the curvature of the Cartan connection vanishes. In all other cases, if the parabolic geometry is regular, there does not exist a natural univ…
Proposes a new algorithm for efficient probabilistic inference.
problem Efficient probabilistic inference in deep models with graphical structures.
method Structured inference networks and variational message-passing algorithm.
result Enables fast and efficient natural-gradient inference for deep structured models.
Classifies 7D manifolds with specific geometric properties.
problem Classifying 7D manifolds with parallel skew-symmetric torsion and holonomy.
method Extending Friedrich's work, using classification techniques for naturally reductive spaces and nearly parallel -structures.
result Complete classification of 7D manifolds with the specified properties.
Almost para-Hermitian and almost paracontact metric structures induced by natural Riemann extensionsmath.DG
The paper explores new structures on cotangent bundles induced by natural Riemann extensions.
problem Investigating new geometric structures on cotangent bundles.
method Constructing and analyzing almost para-Hermitian and paracontact metric structures.
result Conditions for paracontact metric, K-paracontact metric, and para-Sasakian structures.
New kernel model for natural language processing improves expressibility and scalability.
problem Limited expressibility and scalability of traditional convolution kernels in natural language processing.
method Proposes a nonstationary kernel model and a stochastic sampling algorithm for scalable learning.
result Demonstrates improved performance on extracting biological models from scientific text.
NES optimizes discrete structured VAEs effectively without gradient propagation.
problem Learning high-dimensional discrete latent spaces in generative models.
method Natural Evolution Strategies (NES) for gradient-free optimization of discrete structures.
result NES effectively optimizes discrete structured VAEs, comparable to gradient-based methods.
A family of naturally reductive pseudo-Riemannian spaces is constructed out of the representations of Lie algebras with ad-invariant metrics. We exhibit peculiar examples, study their geometry and characterize the corresponding naturally reductive homogeneous structure.
The study classifies natural almost Hermitian structures on specific Lie groups.
problem Classifying natural almost Hermitian structures on conformally foliated Lie groups.
method Examining 4-dimensional Riemannian Lie groups with a 2-dimensional conformal foliation and minimal leaves, constructing new examples of multi-dimensional structures.
result Constructing several new multi-dimensional examples of almost Kähler, integrable, and Kähler structures.
Paper constructs naturally reductive spaces with a general formula.
problem Understanding naturally reductive spaces.
method Explicit construction from \cite{Storm2018} and general formula derivation.
result Proves reducibility and isomorphism criteria.
Study Godbillon-Vey class for regular Jacobi foliations.
problem Characterizing foliations in Jacobi manifolds.
method Explicitly defined and computed Godbillon-Vey class for regular foliations.
result Expressed Godbillon-Vey class in terms of Jacobi structures.
New naturally reductive spaces constructed with group isometries.
problem Creating new naturally reductive spaces.
method Constructing infinitesimal models, specifying transitive groups of isometries, and explicitly defining the naturally reductive structure.
result A large number of new naturally reductive spaces constructed.
Weil algebra morphism induce natural transformations between Weil bundles. In some well known cases, a natural transformation is endowed with a canonical structure of affine bundle. We show that this structure arises only when the Weil algebra morphism is surjective and its kernel has null square. Moreover, in some cas…
Stochastic prediction tackles natural language processing with bandit feedback.
problem Natural language processing with partial task loss feedback.
method Stochastic first-order methods for convex and non-convex objectives.
result Non-convex objective yields best performance under both practical and optimization criteria.
Generative adversarial networks improve spectral image visualization.
problem Displaying spectral images in natural colors for better interpretation.
method Proposes a GAN with adversarial and structure losses.
result Generative adversarial networks generate structure-preserved and natural-looking visualizations.
Two projective structures on Riemann surfaces are described and shown not to be identical.
problem Characterizing and distinguishing projective structures on Riemann surfaces.
method Construction and analysis of projective structures and using the period map and moduli space.
result The Hodge projective structure is not the same as the uniformization projective structure .
In this paper we systematically describe relations between various structure sets which arise naturally for pairs of compact topological manifolds with boundary. Our consideration is based on a deep analogy between the case of a compact manifold with boundary and the case of a closed manifold pair. This approach also g…
We construct a natural generalized complex structure on the total space of any bundle endowed with a Chern connection and whose typical fibre is a homogeneous symplectic manifold. This extends known constructions of generalized complex structures on Lie groups and leads to natural examples of holomorphic maps between g…
We slightly extend the notion of a natural fibre bundle by requiring diffeomorphisms of the base to lift to automorphisms of the bundle only infinitesimally, i.e. at the level of the Lie algebra of vector fields. Spin structures are natural only in this extended sense. We classify fibre bundles with this property, assu…
Superintegrable systems on curved manifolds found to have Hessian structures.
problem Characterizing superintegrable systems on curved manifolds.
method Identifying and computing Hessian coordinates for superintegrable systems.
result Examples of superintegrable systems in 2D and 3D have natural Hessian coordinates.
Let S be a closed oriented surface of genus at least two. Labourie and the author have independently used the theory of hyperbolic affine spheres to find a natural correspondence between convex RP^2 structures on S and pairs (Σ,U) consisting of a conformal structure Σon S and a holomorphic cubic differential U over Σ. …
Structured Optimal Transportstat.ML
Develops a new optimal transport model capturing complex structures.
problem Limited ability of optimal transport to capture complex structures.
method Develops a nonlinear generalization of optimal transport.
result Demonstrates improved performance in tasks like domain adaptation and natural language processing.
Quantum spin networks' tails are -series linked to colored Jones polynomials.
problem Understanding the -series of quantum spin networks.
method Analyzing the -series of quantum spin networks and their relation to the colored Jones polynomial.
result Quantum spin networks' tails are related to the tail of the colored Jones polynomial.
PixL2R maps natural language to pixel-based rewards for RL, improving sample efficiency.
problem Sparse reward settings in RL limit applicability to complex problems.
method Directly maps natural language descriptions to pixel-based rewards for guiding RL.
result Language-based rewards significantly improve sample efficiency in policy learning.
New structures help create harmonic maps.
problem Creating harmonic maps.
method Introducing Riemannian twistorial structures.
result New constructions of harmonic maps.