Two approximate lifted variational methods for hybrid domains improve inference scalability and accuracy.
problem Efficient inference in hybrid probabilistic relational models with multi-modality and continuous evidence.
method Two approximate lifted variational approaches applicable to hybrid domains, exploiting model symmetries.
result The proposed variational methods are scalable and can leverage approximate model symmetries, outperforming existing message-passing approaches.
We analyze variational inference for highly symmetric graphical models such as those arising from first-order probabilistic models. We first show that for these graphical models, the tree-reweighted variational objective lends itself to a compact lifted formulation which can be solved much more efficiently than the sta…
Paper shows domain recursion is more powerful than previously thought, enabling faster inference.
problem Intractable probabilistic inference in relational models.
method Study of domain recursion rule and its impact on lifted inference.
result Domain recursion extends the range of models for which lifted inference is polynomial-time.
Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group provides a precise mathematical framework for lifted inference in the general expone…
Hybrid continuous-discrete models naturally represent many real-world applications in robotics, finance, and environmental engineering. Inference with large-scale models is challenging because relational structures deteriorate rapidly during inference with observations. The main contribution of this paper is an efficie…
Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is…
NIFTy.re accelerates imaging models and expands Gaussian processes and variational inference.
problem Slow performance and limited inference strategies in NIFTy.
method Rewritten NIFTy with new modeling principles, inference strategies, and JAX integration.
result Dramatic acceleration of models and new inference capabilities.
Existence and rigidity results for lifts in Carnot groups.
problem Existence and properties of lifts for maps between Carnot groups.
method Use central extensions to define lifts and prove existence and rigidity results for Lipschitz, Sobolev, and quasiconformal maps.
result Quasiconformal maps admit contact lifts that are bi-Lipschitz.
Study lift metrics and connections on tangent bundles of Riemannian manifolds.
problem Investigate geometric properties of tangent bundles and their lifts.
method Analyze lift metrics and connections on TM of (M,g), and study statistical and Codazzi couples. result Prove a result on 1-Stein and Osserman structures on TM. We tackle the problem of inferring node labels in a partially labeled graph where each node in the graph has multiple label types and each label type has a large number of possible labels. Our primary example, and the focus of this paper, is the joint inference of label types such as hometown, current city, and employe…
Deep neural nets predict vortex-induced vibrations from limited flow data.
problem Predicting lift and drag forces on structures from scattered velocity field data.
method Extended deep neural networks solving coupled Navier-Stokes and structural dynamics equations.
result Deep neural networks can accurately infer structural parameters, pressure field, and velocity field from limited flow data.
New sampling methods for constrained and composite distributions.
problem Sampling from log-concave distributions with constraints and composite structures.
method Proximal sampler applied to lifted convex sets with separation and subgradient oracles.
result Practical and unbiased samplers for constrained and composite distributions.
In this paper, we define a complete lift for semisprays. If S is a semispray on a manifold M, its complete lift is a new semispray Sc on TM. The motivation for this lift is two-fold: First, geodesics for Sc correspond to the Jacobi fields for S, and second, this complete lift generalizes and unifies previ…
Unified approach to constructing integrable systems using Stäckel lifts.
problem Constructing new integrable Hamiltonian systems.
method Generalized Stäckel geometry and Haantjes structure.
result Hamiltonian systems with momentum-dependent Stäckel matrices exhibit symplectic-Haantjes structures.
Smooth Schrödinger Bridges improve trajectory inference by smoothing Gaussian processes.
problem Improving trajectory inference in applications like particle tracking.
method Generalizes Schrödinger Bridge problem to smooth Gaussian processes, solving the problem on phase space.
result The method outperforms existing methods on real datasets.
Geometric structures are lifted to higher tangent bundles preserving statistical properties.
problem Lifting statistical structures to higher tangent bundles while maintaining their properties.
method Natural lifts of geometric objects and potentials to higher tangent bundles, preserving statistical manifold structures.
result Lifted statistical structures on higher tangent bundles maintain pseudo-Riemannian metrics and are again statistical manifolds.
The article classifies liftings of connections on differential manifolds for geodesic modeling.
problem Classifying liftings of connections on differential manifolds.
method Liftings of connections on frame bundles, induced and adjust liftings.
result Developed a method for geodesic modeling of differential equations.
Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.
problem Embedding maps in higher dimensions without self-intersections.
method Lifting maps to embeddings in product spaces.
result Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.
In the present paper, we study complete and vertical lifts of tensor fields from a smooth manifold M to its Weil bundle TAM defined by a Frobenius Weil algebra A. For a Poisson manifold (M,w), we show that the complete lift wC and the vertical lift wV of the Poisson tensor w are Poisson tensors on $T^…
Study lifts plane mappings to Heisenberg group.
problem Contact quasiconformal mappings in hyperbolic Heisenberg group.
method Lifting Theorem for symplectic mappings.
result Symplectic mappings lifted to Heisenberg group.
The paper lifts spherical Morse functions to immersions and embeddings.
problem Lifting spherical Morse functions to other maps.
method New methods to lift to special generic maps with non-positive codimensions.
result Constructs most lifts to special generic maps.
In this paper we continue to study equivariant pencil liftings and differential operators on the algebra of densities. We emphasize the role that the geometry of the extended manifold plays. Firstly we consider basic examples. We give a projective line of diff(M)-equivariant pencil liftings for first order operators,…
Study covers of sphere with homeomorphisms lifting property.
problem Finite abelian covers of sphere with lifting homeomorphisms.
method Completely determined covers with specific lifting property.
result Properties of finite abelian covers with lifting homeomorphisms.
This paper studies surfaces with a special lift property.
problem Geometry of surfaces with a specific lift property.
method Generalizes previous results by Bernstein and Tinaglia.
result Leaves of minimal laminations satisfy the generalised simple lift property.
The canonical trace and the Wodzicki residue on classical pseudodifferential operators on a closed manifold are characterised by their locality and shown to be preserved under lifting to the universal covering as a result of their local feature. As a consequence, we lift a class of spectral ζ-invariants using lifted …
The paper constructs Sasakian lifts from Kähler manifolds and studies their properties.
problem Constructing Sasakian structures from Kähler manifolds and analyzing their geometric properties.
method Local construction of Sasakian manifolds from Kähler base using vector field operations.
result Existence and properties of α-Sasakian Ricci solitons in Sasakian lifts. The paper discusses symplectic lifts for actions on Lagrangian fibrations.
problem Understanding symplectic lifts for actions on Lagrangian fibrations.
method Describes symplectic cotangent lifts in terms of 1-cocycles and generalizes to complete Lagrangian fibrations.
result Symplectic lifts of actions for complete Lagrangian fibrations are understood in terms of cohomology.
New quantum code lacks sparse lift.
problem Existence of sparse lifts for quantum codes.
method Constructed a sparse Z2 chain complex without a sparse lift. result Found a quantum code without a sparse lift.
Criteria for lifting manifold diffeomorphisms to vector bundle automorphisms.
problem Lifting diffeomorphisms to vector bundles.
method Criteria for lifting diffeomorphisms to linear automorphisms of vector bundles.
result Criteria for lifting diffeomorphisms to linear automorphisms of vector bundles.
This paper extends braid lifting to coloured braid groupoids for all simple disc covers.
problem Lifting braids to homeomorphisms on branched covers of the disc.
method Defines a map from a coloured braid groupoid to a mapping class groupoid for all simple covers of the disc.
result Characterizes the lift of every coloured braid, recovering classical lifting on liftable braids.
Simple lifts of non-simple curves on surfaces.
problem Finding simple lifts of non-simple closed curves on surfaces.
method Constructing finite covers and curves on surfaces.
result Explicit non-simple closed curves with simple lifts on degree n covers.
We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This generalizes the complete lift defined by I.Sato and the horizontal lift introduced by K.Yano and S.Ishihara. We study some geometric properties of this lift and its compatibility with symplectic …
Curious examples of lifting spaces not as inverse limits of covering spaces.
problem Understanding inverse limits of covering spaces and their properties.
method Analyzing inverse limits of sequences of covering spaces over a given space.
result Presented examples of lifting spaces that cannot be obtained as inverse limits of covering spaces.
Defines lift of partial cohomological field theories and finds new bi-Hamiltonian structures.
problem Non-semisimple homogeneous partial cohomological field theories and their integrable systems.
method Lift procedure for Frobenius algebras and local polyvector fields.
result Examples of non-semisimple homogeneous partial cohomological field theories with second Hamiltonian structure.
Fenchel lifted networks improve neural network training without performance loss.
problem The difficulty and non-convexity of training deep neural networks.
method Introduces Fenchel lifted networks that represent activation functions as biconvex constraints and uses Lagrange Multipliers to create a lower bound of the training problem.
result Fenchel lifted networks match or outperform traditional neural networks in performance.
In Finsler geometry the complete lift vector fields have distinguished geometric significance. For example a vector field on a Finsler manifold is said to be conformal if its complete lift is conformal in usual sense. In this work we define a new Riemannian or Pseudo-Riemannian metric on TM derived from a Finsler metri…
Proves harmonicity equivalence on manifold metrics.
problem Harmonicity of metrics on pseudo-Riemannian manifolds.
method Equivalence of harmonicity on manifold metrics and their lifts.
result Harmonicity of a metric is equivalent to its lifts' harmonicity.
The Eisenhart lift connects Hamiltonian systems to geodesics in pp-wave spacetimes.
problem Studying the stability and dynamics of Hamiltonian systems.
method Eisenhart lift to pp-wave spacetimes and conformal classes of ODEs.
result Existence of a constant of the motion generalizing conservation of energy.
Survey of twistor lifts of surfaces in 4-dimensional spaces.
problem Understanding the properties of surfaces in 4-dimensional Euclidean space.
method Definitions of Gauss maps and twistor lifts using orthogonal complex structures.
result Holomorphicity and isotropicity of minimal surfaces in E4. New method tightens convex relaxations for permutation matrix problems without lifting.
problem Optimizing quadratic problems over permutation matrices.
method Lifting-free convex relaxation approach.
result Proves at least as tight as existing methods and performs better experimentally.
Study of lifting maps in branched covers of 3-manifolds, showing non-injectivity.
problem Injectivity of lifting maps in branched covers of 3-manifolds.
method Analysis of branched covers and mapping class groups.
result Lifting map is generally not injective for most regular branched covers of 3-manifolds.
Investigates fundamental groups and path lifting for algebraic varieties.
problem Understand fundamental groups and path lifting properties of algebraic varieties.
method Analyzes three fundamental questions about fundamental groups of algebraic varieties.
result Identifies conditions for surjectivity on fundamental groups and path lifting properties.
Develops a new bidding system to maximize advertiser profit.
problem Inaccurate prediction of ad lift-effect due to biased log data.
method Unbiased Lift-based Bidding System that predicts lift-effect from biased log data.
result Demonstrates superior and practical high-performing lift-based bidding strategy.
We construct a connection and a curving on a bundle gerbe associated with lifting a structure group of a principal bundle to a central extension. The construction is based on certain structures on the bundle, i.e. connections and splittings. The Deligne cohomology class of the lifting bundle gerbe with the connection a…
Develops a new algebraic framework for differential geometry of infinite dimensional spaces.
problem Creating a differential geometry for infinite dimensional spaces without topology or local coordinates.
method Introduces a general algebraic framework for lifted geometry applicable to various infinite dimensional spaces.
result Stokes' Theorem appears as a form of differentiability in the lifted geometry of spaces of submanifolds.
We show that one can lift locally real analytic curves from the orbit space of a compact Lie group representation, and that one can lift smooth curves even globally, but under an assumption.
Researchers lift knot coloring polynomial to Habiro ring.
problem Lifting colored Jones polynomial of knots to Habiro ring.
method Introduced new Habiro ring and map, used Alexander polynomial.
result Existence of loop expansion at roots of unity confirmed.
We show the total space of the canonical line bundle L of a Kahler-Einstein manifold Xn supports integrable SU(n+1) structures, or Calabi-Yau structures. The canonical real line bundle L⊂L over a minimal Lagrangian submanifold M⊂X is calibrated in this setting and hence can …