arXiv research

Global invertibility proven for orientation-preserving maps without homeomorphic extension.

The paper studies global invertibility of maps on Finsler manifolds.

The paper proves global invertibility for certain local diffeomorphisms and biholomorphisms in higher dimensions.

Study shows global invertibility in nonlinear elasticity with vanishing self-repulsion term.

Paper shows X-ray transform invertible on certain curved spaces.

Local invertibility of higher order tensor transforms on compact manifolds.

GONs improve predictions of maximizers from noisy black-box functions.

Local invertibility of ray transforms on convex manifolds.

A new model decouples global and local image representations without supervision.

This work tackles exploding inverses in INNs, revealing and mitigating their numerical non-invertibility.

Consider a Riemannian manifold in dimension $n\geq 3$ with strictly convex boundary. We prove the local invertibility, up to potential fields, of the geodesic ray transform on tensor fields of rank four near a boundary point. This problem is closely related with elastic \textit{qP}-wave tomography. Under the condition …

In this paper we study the local magnetic ray transform of symmetric tensor fields up to rank two on a Riemannian manifold of dimension $\geq 3$ with boundary. In particular, we consider the magnetic ray transform of the combinations of tensors of different orders due to the nature of magnetic flows. We show that such …

Electronic power inverters are capable of quickly delivering reactive power to maintain customer voltages within operating tolerances and to reduce system losses in distribution grids. This paper proposes a systematic and data-driven approach to determine reactive power inverter output as a function of local measuremen…

We consider the problem of finding sufficient conditions for a locally Lipschitz mapping between Finsler manifolds to be a global homeomorphism. For this purpose, we develop the notion of Clarke generalized differential in this context and, using this, we obtain a version of the Hadamard integral condition for invertib…

INVERT connects neural representations to human-understandable concepts.

We introduce a special class of knots, called global knots, in F^2 x R and we construct new isotopy invariants, called T-invariants, for global knots. Some T-invariants are of finite type but they cannot be extracted from the generalized Kontsevitch integral (which is consequently not the universal invariant of finite …

We prove the local invertibility, up to potential fields, and stability of the geodesic X-ray transform on tensor fields of order 1 and 2 near a strictly convex boundary point, on manifolds with boundary of dimension n>=3. We also present an inversion formula. Under the condition that the manifold can be foliated with …

Under a convexity assumption on the boundary we solve a local inverse problem, namely we show that the geodesic X-ray transform can be inverted locally in a stable manner; one even has a reconstruction formula. We also show that under an assumption on the existence of a global foliation by strictly convex hypersurfaces…

In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential geometry tools such as moving frame and parallel transportation are successfully…

We consider the problem of developing a method to reconstruct a potential $q$ from the partial data Dirichlet-to-Neumann map for the Schrödinger equation $(-Δ_g+q)u=0$ on a fixed admissible manifold $(M,g)$. If the part of the boundary that is inaccessible for measurements satisfies a flatness condition in one directio…

We develop and analyze efficient "coordinate-wise" methods for finding the leading eigenvector, where each step involves only a vector-vector product. We establish global convergence with overall runtime guarantees that are at least as good as Lanczos's method and dominate it for slowly decaying spectrum. Our methods a…

We consider topological conditions under which a locally invertible map admits a global inverse. Our main theorem states that a local diffeomorphism $f: M \to\mathbb{R}^n$ is bijective if and only if $H_{n-1}(M)=0$ and the pre-image of every affine hyperplane is non-empty and acyclic. The proof is based on some geometr…

We consider Calderon's inverse problem with partial data in dimensions $n \geq 3$. If the inaccessible part of the boundary satisfies a (conformal) flatness condition in one direction, we show that this problem reduces to the invertibility of a broken geodesic ray transform. In Euclidean space, sets satisfying the flat…

Improved sampling quality with RBM-Flow and D-Flow models.

BayesFlow learns complex models using neural networks.

In this paper we consider the local X-ray transform for general flows. We extend the results on the local and global invertibility of the geodesic ray transform proved by Uhlmann and Vasy \cite{UV} to the X-ray transform for a general flow. The key improvement is that our argument for the ellipticity of the conjugated …

Study on estimating invertible functions with minimax analysis.

An intrinsic definition in terms of conformal capacity is proposed for the conformal type of a Carnot--Carathéodory space (parabolic or hyperbolic). Geometric criteria of conformal type are presented. They are closely related to the asymptotic geometry of the space at infinity and expressed in terms of the isoperimetri…

Study of strongly invertible Legendrian links in contact 3-space.

A multi-neck spacetime wormhole is constructed with a simple metric tensor.

GAAVI offers anytime-valid tests for CMF global null and contrasts.

Study on invariant Seifert surfaces for strongly invertible knots, showing large gaps in genus.

Dirac operator invertibility proven for specific manifolds.

Table of symmetric diagrams for knots up to 10 crossings.

ISR creates analytical relationships from data via invertible maps.

CF-INNs can approximate any invertible function, resolving a long-standing problem.

This work presents a novel approach to train invertible linear layers by adding rank-one perturbations.

Develops equivariant grid homology for strongly invertible knots.

New findings on knot genera using advanced techniques.

In this work, we develop a new approach to generative density estimation for exchangeable, non-i.i.d. data. The proposed framework, FlowScan, combines invertible flow transformations with a sorted scan to flexibly model the data while preserving exchangeability. Unlike most existing methods, FlowScan exploits the intra…

By developing a generalized cobordism theory, we explore the higher global symmetries and higher anomalies of quantum field theories and interacting fermionic/bosonic systems in condensed matter. Our essential math input is a generalization of Thom-Madsen-Tillmann spectra, Adams spectral sequence, and Freed-Hopkins's t…

Defines knot signature invariant using G-signature theorem.

A new method integrates autoencoders with geometry regularization for manifold learning.

Paper shows invertibility of tensor X-ray transform on certain manifolds.

Deep neural networks are vulnerable to adversarial attacks and hard to interpret because of their black-box nature. The recently proposed invertible network is able to accurately reconstruct the inputs to a layer from its outputs, thus has the potential to unravel the black-box model. An invertible network classifier c…

For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae. Such Darboux transformations are not invertible in the sense that the corresponding mappings of the operator kernels are not invertible. The only known invertible ones wer…

Framework for designing nonlinearities in neural networks with slope constraints.

New invertible transformations improve flow-based generative models.