By a result of John Ball (1981), a locally orientation preserving Sobolev map is almost everywhere globally invertible whenever its boundary values admit a homeomorphic extension. As shown here for any dimension, the conclusions of Ball's theorem and related results can be reached while completely avoiding the problem …
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
Trend · papers per month
48 results for “invertible maps”
The paper studies global invertibility of maps on Finsler manifolds.
problem Global invertibility of locally Lipschitz maps on Finsler manifolds.
method Introduces pseudo-Jacobian and studies its relations with local metric properties of the map.
result Conditions for a map to be globally invertible and covering.
ISR creates analytical relationships from data via invertible maps.
problem Creating analytical relationships from datasets.
method Combines INNs and EQL, using invertible maps and sparsity promoting regularization.
result ISR can serve as a normalizing flow for density estimation and solve inverse problems.
New model for simulating and inferring from inverse problems.
problem Bayesian inverse problems in conditional sampling.
method Invertible generative model using triangular normalizing flows.
result Training loss for invertible map proposed.
JacNet learns Jacobians to enforce structure on derivatives for invertibility and Lipschitz functions.
problem Enforcing structure on derivatives of neural network mappings.
method Proposes using a neural network to directly learn the Jacobian of the input-output function, allowing control over derivative structure.
result Demonstrates learning invertible approximations to simple and 1-Lipschitz functions.
Maps from metrics to Ricci curvature are locally invertible near Einstein manifolds.
problem Understanding the invertibility of maps from metrics to Ricci curvature near Einstein manifolds.
method Analyzing the invertibility of maps involving Ricci curvature, conformal classes, and mean curvature.
result The map is locally invertible near an Einstein manifold with boundary.
We establish a link between Fourier optics and a recent construction from the machine learning community termed the kernel mean map. Using the Fraunhofer approximation, it identifies the kernel with the squared Fourier transform of the aperture. This allows us to use results about the invertibility of the kernel mean m…
We study invertible generating pairs of fundamental groups of graph manifolds, that is, pairs of elements (g,h) for which the map g --> g^{-1}, h --> h^{-1} extends to an automorphism. We show in particular that a graph manifold is of Heegaard genus 2 if and only if its fundamental group has an invertible generating pa…
The paper explores how invertibility affects the complexity of encoder models in VAEs.
problem The complexity of the encoder model in VAEs when the generative map is invertible.
method Formalizes the concept of strong invertibility and analyzes the complexity of the encoder model.
result Strongly invertible generative maps allow for simpler encoder models, while non-invertible maps require exponentially larger encoders.
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…
Develops equivariant grid homology for strongly invertible knots.
problem Invariants of strongly invertible knots.
method Equivariant grid diagrams and mapping cones.
result Equivariant unknotting numbers and genus bounds.
Augmented KRnet improves flow-based generative modeling by maintaining exact invertibility.
problem Maintaining exact invertibility in flow-based generative models.
method Integrates augmented dimensions into KRnet to achieve full nonlinear updates in two iterations, keeping exact invertibility.
result Augmented KRnet achieves full nonlinear updates in two iterations, maintaining exact invertibility.
iGNN tackles inverse graph prediction using invertible neural networks.
problem Inverse graph prediction problem in data analysis and machine learning.
method Developed invertible graph neural network (iGNN) to solve inverse prediction problem on graphs.
result iGNN model allows efficient generation from output labels and forward prediction.
Study on equivariant Q-sliceness for strongly invertible knots.
problem Understanding Q-sliceness for strongly invertible knots.
method Constructive and obstructive approaches using Fox-Milnor condition and equivariant concordance.
result Klein amphichiral knots are equivariant Q-slice in a single Q-homology 4-ball.
ButterflyFlow uses butterfly matrices for efficient invertible layers in normalizing flows.
problem Building efficient invertible layers for complex probability distributions.
method Proposes butterfly layers for invertible linear layers, leveraging their ability to capture complex structures.
result ButterflyFlow achieves strong density estimation and significantly better log-likelihoods on various datasets.
Regression-based Inverter Control for Decentralized Optimal Power Flow and Voltage Regulationeess.SY
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…
Statistical generative models for molecular graphs attract attention from many researchers from the fields of bio- and chemo-informatics. Among these models, invertible flow-based approaches are not fully explored yet. In this paper, we propose a powerful invertible flow for molecular graphs, called graph residual flow…
Normalizing flows attempt to model an arbitrary probability distribution through a set of invertible mappings. These transformations are required to achieve a tractable Jacobian determinant that can be used in high-dimensional scenarios. The first normalizing flow designs used coupling layer mappings built upon affine …
Incorporates matrix exponential into generative flows for improved performance.
problem Improving generative flow models for better density estimation.
method Integrates matrix exponential into generative flows, proposing new layers and modifying network architecture.
result The proposed model achieves great performance on density estimation.
Strongly invertible knots, equivariant slice genera, and an equivariant algebraic concordance groupmath.GT
Study on knots, genera, and algebraic concordance groups.
problem Understanding the equivariant slice genus of strongly invertible knots.
method Using the Blanchfield form to establish lower bounds and formulate an equivariant algebraic concordance group.
result The equivariant slice genus of an equivariant connected sum of a genus one strongly invertible slice knot is at least n/4.
The LG Fibrationmath.DG
Paper presents a nearly invertible mapping between high-dimensional and lower-dimensional spheres.
problem Lack of rigorous mathematical foundation in deep learning algorithms.
method Utilizes Multicomplex rotation groups and polyspherical coordinates to define two maps and a composite LG Fibration.
result Derives a distance difference function to determine invariant inner products under the transformation.
While conformal transformations of the plane preserve Laplace's equation, Lorentz-conformal mappings preserve the wave equation. We discover how simple geometric objects, such as quadrilaterals and pairs of crossing curves, are transformed under nonlinear Lorentz-conformal mappings. Squares are transformed into curvili…
Featurization improves density ratio estimation for complex data.
problem Difficulty in estimating density ratios for high-dimensional, different distributions.
method Invertible generative model to map distributions into a common feature space.
result Improved accuracy in density ratio estimation through feature space.
Generative Adversarial Networks (GANs) play an increasingly important role in machine learning. However, there is one fundamental issue hindering their practical applications: the absence of capability for encoding real-world samples. The conventional way of addressing this issue is to learn an encoder for GAN via Vari…
SGNs use Hamiltonian mechanics for invertible deep generative modeling.
problem Efficient and exact likelihood evaluation for deep generative models.
method Symplectic structure in latent space, Hamiltonian dynamics for data generation.
result Exact likelihood evaluation without Jacobian calculations.
Method generates time-series attribution maps with identifiability guarantees.
problem Lack of identifiability guarantees in gradient-based attribution methods.
method Regularized contrastive learning algorithm trained on time-series data.
result Empirically shows robust approximation of zero vs. non-zero entries in the ground-truth attribution map.
Index map, -connections, and Connes-Chern character in the setting of twisted spectral triplesmath.OA
Twisted spectral triples are a twisting of the notion of spectral triple aiming at dealing with some type III geometric situations. In the first part of the paper, we give a geometric construction of the index map of a twisted spectral triple in terms of -connections on finitely generated projective modules. This ma…
Supersymmetry contains initially noninvertible objects, but it is common to deal with the invertible ones only, factorizing former in some extent. We propose to reconsider this ansatz and try to redefine such fundamental notions as supermanifolds, fiber bundles and homotopies using some weakening invertibility conditio…
We present and discuss several old and new methods for mapping a circular disc to a square. In particular, we present analytical expressions for mapping each point (u,v) inside the circular disc to a point (x,y) inside a square region. Ideally, we want the mapping to be smooth and invertible. In addition, we put emphas…
On existence, uniqueness and scalability of adversarial robustness measures for AI classifiersstat.ML
Mathematical conditions and practical computations for adversarial robustness measures are established.
problem Existence, uniqueness, and scalability of adversarial robustness measures for AI classifiers.
method Formulated and proven mathematical conditions for existence, uniqueness, and explicit analytical computation of minimal adversarial paths and distances. Practical computation demonstrated on various AI tools and synthetic benchmarks.
result Explicit mathematical conditions and practical computations for adversarial robustness measures are established.
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…
OT-Flow uses optimal transport to improve CNFs for faster and more accurate density estimation.
problem Computational challenges in continuous normalizing flows.
method OT-Flow leverages optimal transport to regularize CNFs and uses exact trace computation.
result OT-Flow achieves competitive performance with one-fourth the number of weights and significant speedups.
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We analyze various Lipschitz bounds of the nonlinear analysis map and we establish theoretical performance bo…
Sobolev maps on product spaces are split or approximately split.
problem Characterizing Sobolev maps on product spaces.
method Analyzing weak differentials and using properties of Sobolev spaces.
result Sobolev maps on product spaces are split or approximately split.
We address representational challenges in normalizing flows, particularly depth and conditioning issues.
problem Challenges in training normalizing flows, including vanishing/exploding gradients and poor conditioning.
method Analyzes representational aspects of depth and conditioning in normalizing flows, proving theoretical bounds and investigating phenomena.
result Proves that shallow affine coupling networks are universal approximators in Wasserstein distance if ill-conditioning is allowed.
Index difference on surfaces of genus at least 3 is non-trivial.
problem Index difference on surfaces of genus at least 3
method Show that the index difference is non-trivial
result Index difference is non-trivial
Flip symmetry on knot diagrams affects Khovanov homology.
problem Understanding the flip map on Khovanov homology.
method Analyzing the behavior of the flip map on unlinks and using it to determine the involution.
result The flip map is the identity map over \(\mathbb{F}_2\), confirming a conjecture.
Momentum ResNets improve ResNets' memory efficiency.
problem Memory inefficiency in deep residual neural networks (ResNets).
method Adding a momentum term to the forward rule of ResNets to make them invertible.
result Momentum ResNets can learn any linear mapping up to a multiplicative factor, improving memory efficiency.
A C*algebra A generated by a class of zero-order classical pseudodifferential operator on a cylinder RxB, where B is a compact riemannian manifold, containing operators with periodic symbols, is considered. A description of the K-theory index map associated to the continuous extension to A of the principal-symbol map i…
Survival MDN uses invertible functions to speed up survival analysis models.
problem Training neural ODEs for survival analysis is computationally expensive.
method Survival MDN applies an invertible positive function to MDN outputs.
result Survival MDN outperforms or matches other models on concordance, Brier score, and log-likelihood.
Study on estimating invertible functions with minimax analysis.
problem Minimizing risk of estimating invertible functions on a plane.
method Introduce two types of -risks, derive lower and upper rates for minimax values, develop an asymptotically almost everywhere invertible estimator.
result Invertibility does not reduce the complexity of the estimation problem in terms of the rate.
Paper aims to find joint representation between vocal tract geometry and speech sound acoustics.
problem Finding a joint latent representation between articulatory and acoustic domains for vowel sounds.
method Invertible neural network models, convolutional autoencoder, normalizing flows, semi-supervised learning.
result Satisfactory performance in articulatory-to-acoustic and acoustic-to-articulatory mapping.
A new framework solves complex optimization problems with continuous worst-case distributions.
problem Optimizing under uncertain distributions with continuous worst-case scenarios.
method Flow-based distributionally robust optimization (DRO) with Wasserstein uncertainty sets and invertible transport maps.
result The framework finds continuous worst-case distributions and samples efficiently.
A new method for aligning multiple distributions efficiently.
problem Aligning multiple distributions in a shared latent space.
method Iterative alignment of variational approximations of distribution divergences using invertible alignment maps.
result Our method achieves competitive distribution alignment at low computational cost.
It is widely believed that the success of deep convolutional networks is based on progressively discarding uninformative variability about the input with respect to the problem at hand. This is supported empirically by the difficulty of recovering images from their hidden representations, in most commonly used network …
A promising class of generative models maps points from a simple distribution to a complex distribution through an invertible neural network. Likelihood-based training of these models requires restricting their architectures to allow cheap computation of Jacobian determinants. Alternatively, the Jacobian trace can be u…
Local invertibility of higher order tensor transforms on compact manifolds.
problem Invertibility of higher order tensor transforms on compact manifolds.
method Local invertibility of transverse and mixed ray transforms of tensors on compact Riemannian manifolds.
result Local invertibility of transverse and mixed ray transforms of tensors for specific dimensions.
Study of strongly invertible Legendrian links in contact 3-space.
problem Characterizing and understanding strongly invertible Legendrian links.
method Equivariant analogs of basic results for strongly invertible and Legendrian links.
result Existence of maximal equivariant Thurston-Bennequin number for strongly invertible links.