arXiv research

Unified framework for lifted training and inversion of neural networks.

Despite the recent successes of deep neural networks, the corresponding training problem remains highly non-convex and difficult to optimize. Classes of models have been proposed that introduce greater structure to the objective function at the cost of lifting the dimension of the problem. However, these lifted methods…

A new method to rescale ReLU neural networks based on path-lifting.

Reinforcement learning approaches have long appealed to the data management community due to their ability to learn to control dynamic behavior from raw system performance. Recent successes in combining deep neural networks with reinforcement learning have sparked significant new interest in this domain. However, pract…

Develops a new bidding system to maximize advertiser profit.

A new method lifts training of input-convex neural networks to avoid dead weights and plateaued loss.

Proposes neural dynamic mode decomposition for end-to-end modeling of nonlinear dynamics.

Existence and rigidity results for lifts in Carnot groups.

Study lift metrics and connections on tangent bundles of Riemannian manifolds.

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 $S^c$ on $TM$. The motivation for this lift is two-fold: First, geodesics for $S^c$ 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.

Geometric structures are lifted to higher tangent bundles preserving statistical properties.

The article classifies liftings of connections on differential manifolds for geodesic modeling.

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 $T^A M$ defined by a Frobenius Weil algebra $A$. For a Poisson manifold $(M,w)$, we show that the complete lift $w^C$ and the vertical lift $w^V$ of the Poisson tensor $w$ are Poisson tensors on $T^…

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,…

The adaptability of the convolutional neural network (CNN) technique for aerodynamic meta-modeling tasks is probed in this work. The primary objective is to develop suitable CNN architecture for variable flow conditions and object geometry, in addition to identifying a sufficient data preparation process. Multiple CNN …

Study covers of sphere with homeomorphisms lifting 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.

New quantum code lacks sparse lift.

Criteria for lifting manifold diffeomorphisms to vector bundle automorphisms.

Simple lifts of non-simple curves on surfaces.

This paper extends braid lifting to coloured braid groupoids for all simple disc 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 …

Proves harmonicity equivalence on manifold metrics.

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…

The Eisenhart lift connects Hamiltonian systems to geodesics in pp-wave spacetimes.

New methods lift weak supervision to structured prediction, providing robustness guarantees.

Survey of twistor lifts of surfaces in 4-dimensional spaces.

Study of lifting maps in branched covers of 3-manifolds, showing non-injectivity.

In studies of smooth maps with good differential topological conditions such as immersions, embeddings, Morse functions and their higher dimensional versions including fold maps and application to geometry, especially algebraic and differential topology of manifolds, liftings or desingulizations of maps of appropriate …

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…

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.

Develops a new algebraic framework for differential geometry of infinite dimensional spaces.

Researchers lift knot coloring polynomial to Habiro ring.

We show the total space of the canonical line bundle $\mathbb{L}$ of a Kahler-Einstein manifold $X^n$ supports integrable $SU(n+1)$ structures, or Calabi-Yau structures. The canonical real line bundle $L \subset \mathbb{L}$ over a minimal Lagrangian submanifold $M \subset X$ is calibrated in this setting and hence can …

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…

Study proves Hecke lifting conjecture for torus knots and verifies it for any framed knots.

Lie groupoids and their orbit spaces are linked through equivalence classes.

Develops a lifting theory for exponential maps in semi-Riemannian geometry.

We construct counterexamples to lifting properties of Hamiltonian and contact isotopies.

We show that any pseudo-Anosov map that is a lift of pseudo-Anosov homeomorphism of a nonorientable surface has vanishing SAF invariant. We also provide a criterion to certify that a pseudo-Anosov map is not such a lift.

Introduces new construction for Courant algebroids and curved structures.

We study natural lifting operations from a bundle E over R to the dual bundle of its first-jet bundle. The main purpose is to define a complete lift of a type (1,1) tensor field on E and to understand all features of its construction. Various other lifting operations of tensorial objects on E are needed for that purpos…

Let M be an n-dimensional Riemannian manifold and TM its tangent bundle. The conformal and fiber preserving vector fields on TM have well-known physical interpretations and have been studied by physicists and geometricians. Here we define a Riemannian or pseudo-Riemannian lift metric on TM, which is in some senses more…

The present research work proposes a new fast fixed-point averaging algorithm on the compact Stiefel manifold based on a mixed retraction/lifting pair. Numerical comparisons between fixed-point algorithms based on the proposed non-associated retraction/lifting map pair and two associated retraction/lifting pairs confir…

Deep learning predicts back-pain risk during manual lifting.