We consider the problem of distortion minimal morphing of -dimensional compact connected oriented smooth manifolds without boundary embedded in . Distortion involves bending and stretching. In this paper, minimal distortion (with respect to stretching) is defined as the infinitesimal relative change in vol…
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48 results for “minimally distorted”
Algorithm finds optimal affine transformation to minimize overall distortion.
problem Minimizing distortion in affine transformations.
method Riemannian geometry approach to define and minimize distortion.
result Mean distorting transformation found for minimizing overall distortion.
The study finds minimal distortion embeddings of surfaces into small domains.
problem Finding the minimal distortion of embeddings between two-dimensional manifolds.
method Proving a lower bound on distortion in terms of areas' discrepancy, characterizing minimizers, and proving stability.
result Homotheties are the unique minimizers for , and non-homothetic minimizers exist for .
Vertex distortion measures how far lattice knots deviate from straight lines.
problem Measuring how much lattice knots deviate from straight paths.
method Analogous to smooth knots, study vertex distortion in lattice knots.
result Vertex distortion is 1 only for the unknot and can be arbitrarily high.
We study the statistical meaning of the minimization of distortion measure and the relation between the equilibrium points of the SOM algorithm and the minima of distortion measure. If we assume that the observations and the map lie in an compact Euclidean space, we prove the strong consistency of the map which almost …
Let and be compact smooth oriented Riemannian -manifolds without boundary embedded in . Several problems about minimal distortion bending and morphing of to are posed. Cost functionals that measure distortion due to stretching or bending produced by a diffeomorphism are …
New stretch maps minimize distortion in geometric group theory.
problem Finding optimal maps in geometric group theory.
method Proving minimizers using modulus of curve families and MSP.
result Stretch maps are minimizers of mean quasiconformal distortion.
Paper proposes a new black-box attack approach to minimize visual distortion.
problem Constructing adversarial examples that minimize visual distortion in a black-box threat model.
method Learning the noise distribution of adversarial examples to approximate the gradient of a non-differentiable loss function.
result The proposed attack results in much lower visual distortion compared to state-of-the-art black-box attacks.
New metric defines surface shapes, minimizing area and angle distortions.
problem Defining and measuring the shape of high genus surfaces.
method Defined a metric space, introduced energies for area and angle distortions, showed minimizers by lower semicontinuity.
result Energy minimizers in surface shape space correspond to quasiconformal homeomorphisms.
A morph between two Riemannian -manifolds is an isotopy between them together with the set of all intermediate manifolds equipped with Riemannian metrics. We propose measures of the distortion produced by some classes of morphs and diffeomorphisms between two isotopic Riemannian -manifolds and, with respect to th…
This paper addresses the challenges in classifying textual data obtained from open online platforms, which are vulnerable to distortion. Most existing classification methods minimize the overall classification error and may yield an undesirably large type I error (relevant textual messages are classified as irrelevant)…
New bounds on knot distortion and Seifert surface properties.
problem Understanding the distortion of knots and properties of Seifert surfaces.
method Analyzing embeddings of Seifert surfaces and using properties of monodromy maps.
result Bounds on the distortion of certain knots and properties of Seifert surfaces.
The Madry Lab recently hosted a competition designed to test the robustness of their adversarially trained MNIST model. Attacks were constrained to perturb each pixel of the input image by a scaled maximal distortion = 0.3. This discourages the use of attacks which are not optimized on the dis…
Hierarchical clustering is a popular method for analyzing data which associates a tree to a dataset. Hartigan consistency has been used extensively as a framework to analyze such clustering algorithms from a statistical point of view. Still, as we show in the paper, a tree which is Hartigan consistent with a given dens…
New adversarial examples with structured distortion sets improve robustness and perceptibility.
problem Improving adversarial robustness and perceptibility of images.
method Exploring and constraining adversarial search with trace-norms and other norms.
result Structured adversarial perturbations allow larger distortions and control over generation.
We solve the vector embedding problem by minimizing total distortion under constraints.
problem Assigning representative vectors to items with similarity and dissimilarity constraints.
method Projected quasi-Newton method for MDE problems, scalable to large data sets.
result Our method provides principled ways to validate embeddings and scales to millions of items.
Deep neural networks (DNNs) are known vulnerable to adversarial attacks. That is, adversarial examples, obtained by adding delicately crafted distortions onto original legal inputs, can mislead a DNN to classify them as any target labels. In a successful adversarial attack, the targeted mis-classification should be ach…
Discover equations of motion from distorted video frames.
problem Learning equations of motion from unlabeled, distorted video.
method Train an autoencoder to map frames into latent space, then use symbolic regression to find differential equations.
result The method can discover motion equations even when video is distorted.
Study optimal reinsurance contracts to prevent moral hazard under non-concave premium principles.
problem Preventing moral hazard in reinsurance contracts under non-concave premium principles.
method Develops optimal reinsurance contracts under a diffusion risk model with incentive compatibility constraints and extended distortion premium principles.
result An optimal reinsurance contract exists and is characterized by solving a double obstacle problem.
Equitable Mirrorsastro-ph.IM
In this article we explore some finer properties of equi-areal mirrors and introduce techniques for developing new mirror surfaces that simultaneously minimize angular and areal distortion.
A new fast adversarial attack finds minimal perturbations to change class.
problem Evaluating robustness of neural networks against adversarial attacks.
method White-box adversarial attack minimizing perturbation size.
result Outperforms or matches state-of-the-art attacks.
High-dimensional VAEs inevitably collapse to prior, requiring large datasets for good performance.
problem Posterior collapse in VAEs leads to poor representation learning quality.
method Analyzed a minimal VAE in a high-dimensional limit, evaluating conditions for posterior collapse with respect to beta and dataset size.
result VAEs face 'inevitable posterior collapse' beyond a certain beta threshold, regardless of dataset size.
Motivated by models of human decision making proposed to explain commonly observed deviations from conventional expected value preferences, we formulate two stochastic multi-armed bandit problems with distorted probabilities on the reward distributions: the classic -armed bandit and the linearly parameterized bandit…
Registration, which aims to find an optimal 1-1 correspondence between shapes, is an important process in different research areas. Conformal mappings have been widely used to obtain a diffeomorphism between shapes that minimizes angular distortion. Conformal registrations are beneficial since it preserves the local ge…
Proposes ITISC for clustering with minimized worst-case expected distortions.
problem Real-world clustering data distribution mismatch.
method Information theoretical importance sampling, constrained minimax optimization, Lagrange method.
result Validation of ITISC on synthetic and real-world datasets.
Modified BA algorithm computes RD and DR functions efficiently.
problem Computing rate-distortion and distortion-rate functions.
method A novel modification of the BA algorithm using Newton's method for root-finding.
result The modified algorithm converges to RD and DR function solutions with rate and provides -approximations.
We propose a data-driven framework for optimizing privacy-preserving data release mechanisms to attain the information-theoretically optimal tradeoff between minimizing distortion of useful data and concealing specific sensitive information. Our approach employs adversarially-trained neural networks to implement random…
The problem of minimal distortion bending of smooth compact embedded connected Riemannian -manifolds and without boundary is made precise by defining a deformation energy functional on the set of diffeomorphisms $\diff(M,N)$. We derive the Euler-Lagrange equation for and determine smooth minimizers o…
Study on costs of manipulating AMM-based price oracles.
problem Cost of manipulation in AMM-based on-chain price oracles.
method Analyzes the robustness of AMM-based oracles to strategic manipulation, considering different aggregation methods and market conditions.
result Manipulation costs depend on the total quote depth and can be minimized by optimal liquidity weights.
Vertex distortion detects if a knot is unknot.
problem Determining if a knot is the unknot.
method Using Denne-Sullivan's bound on Gromov distortion, the vertex distortion of nontrivial lattice knots is bounded. Then, it is shown that trivial vertex distortion implies the unknot.
result The conjecture that trivial vertex distortion implies the unknot is proven.
UVeQFed tackles FL model compression over limited channels.
problem Efficiently transmitting trained models over rate-constrained channels.
method Universal vector quantization for FL (UVeQFed).
result UVeQFed minimizes distortion and converges to optimal model.
New method corrects complex distortions in single view images.
problem Complex distortions in images, especially those caused by refractive surfaces.
method Differentiable image sampling and semantic information augmentation.
result Model can estimate and correct highly complex distortions.
Study models weather index insurance pricing by insurers and farmers, finding flexible pricing kernels boost profits.
problem Monopoly pricing of weather index insurance with risk and flexibility considerations.
method Bowley-type sequential game with insurer and farmer, using neural networks for farmer's payoff.
result Flexible pricing kernels increase insurer profits closer to indemnity insurance levels.
New approach avoids excess empirical risk in domain generalization.
problem Learning models that generalize to unseen distributions from diverse data sets.
method Minimizes penalty under constraint of optimal empirical risk, leveraging rate-distortion theory.
result Significant improvements in domain generalization performance across multiple methods.
Single training run learns optimal VAE parameters for various β values.
problem Training VAEs with varying β values for optimal trade-off between distortion and rate.
method Introduced Multi-Rate VAE (MR-VAE) using hypernetworks to map β to optimal parameters.
result MR-VAEs can construct the full rate-distortion curve without additional training.
Study homeomorphism groups of ordinals, proving strong distortion and normal generators.
problem Understanding algebraic and geometric properties of homeomorphism groups of ordinals.
method Analyzing successor ordinals with connections to permutation groups and manifolds.
result Proves strong distortion and normal generators for homeomorphism groups of ordinals.
This paper shows how to calculate risk measures for sums of two counter-monotonic risks.
problem Calculating risk measures for sums of two counter-monotonic risks.
method Using a fixed distortion function and expressing the risk measure of a sum as the sum of two related measures of the marginals.
result The risk measure of a sum of two counter-monotonic risks can be expressed as the sum of two related distortion risk measures of the marginals.
A new family of stochastic dominance orders based on distortion functions.
problem Determining a continuum of dominance relations for risk assessment.
method Introducing H-distorted stochastic dominance, a generalized family of stochastic orders.
result Power-distorted stochastic dominance is particularly appealing due to its simplicity and statistical interpretations.
Study distortion risk measures for step-weighted distributions.
problem Analyzing risk measures for specific distribution types.
method Investigate distortion risk measures of step-weighted distributions.
result Developed methods for calculating risk measures.
The distortion of a curve measures the maximum arc/chord length ratio. Gromov showed any closed curve has distortion at least pi/2 and asked about the distortion of knots. Here, we prove that any nontrivial tame knot has distortion at least 5pi/3; examples show that distortion under 7.16 suffices to build a trefoil kno…
We present a new method to compare the shapes of genus-zero surfaces. We introduce a measure of mutual stretching, the symmetric distortion energy, and establish the existence of a conformal diffeomorphism between any two genus-zero surfaces that minimizes this energy. We then prove that the energies of the minimizing …
Computed distortion coefficients for the α-Grushin plane.
problem Analyzing the distortion coefficients of the α-Grushin plane.
method Using generalised trigonometric functions and synthetic curvature conditions.
result Estimates for distortion coefficients and a curvature condition conjecture.
Study on risk measures using distorted Choquet integrals with random distortions.
problem Developing risk measures under random distortions of capacities.
method Introducing and analyzing randomly distorted Choquet integrals with respect to a distorted capacity, establishing properties and providing representations.
result Representation of comonotonic additive conditional risk measures using G-randomly distorted Choquet integrals.
We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire, continuous, open and discrete mapping of finite distortion which is piecewise smooth, ha…
After being trained, classifiers must often operate on data that has been corrupted by noise. In this paper, we consider the impact of such noise on the features of binary classifiers. Inspired by tools for classifier robustness, we introduce the same classification probability (SCP) to measure the resulting distortion…
Develops a unified framework for computing n-dimensional quasi-conformal mappings.
problem Effective mapping methods for higher-dimensional objects with geometric constraints.
method Variational model integrating quasi-conformal distortion, volumetric distortion, and other factors.
result Existence and efficient numerical methods for solving the optimization problem.
The distortion of a curve is the supremum, taken over distinct pairs of points of the curve, of the ratio of arclength to spatial distance between the points. Gromov asked in 1981 whether a curve in every knot type can be constructed with distortion less than a universal constant C. Answering Gromov's question seems to…
The study shows exponential distortion in virtually special groups containing free subgroups.
problem Understanding distortion in virtually special groups containing free subgroups.
method Constructing examples of virtually special groups with finite rank free subgroups.
result Distortion functions grow like exp^k(x^m) and can be superexponential.