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.
Proposes a neural network method to correct residual distortions in coordinate transformations.
problem Nonlinear and spatially dependent distortions in coordinate transformation models.
method Residual-based neural network approach focusing on systematic distortions.
result The method improves accuracy and stability in challenging conditions.
This paper explores the problem of learning transforms for image compression via autoencoders. Usually, the rate-distortion performances of image compression are tuned by varying the quantization step size. In the case of autoen-coders, this in principle would require learning one transform per rate-distortion point at…
The study examines distortion in specific homeomorphisms of Cantor sets.
problem Distortion in homeomorphisms of Cantor sets.
method Analyzes equivalence of conditions related to discontinuities and conjugacy.
result Elements are distorted if they satisfy certain conditions.
Small neural networks embed arbitrary metric spaces into Gaussian mixtures.
problem Embedding arbitrary metric spaces into a fixed space with low distortion.
method Probabilistic transformers of small depth and width.
result Embeddings with low metric distortion for various metric spaces.
We discuss boundedness and distortion in transformation groups. We show that the groups Diff0r(Rn) and Diffr(Rn) have the strong distortion property, whenever 0≤r≤∞,r=n+1. This implies in particular that every abstract length function on these groups i…
We exhibit rigid rotations of spheres as distortion elements in groups of diffeomorphisms, thereby answering a question of J Franks and M Handel. We also show that every homeomorphism of a sphere is, in a suitable sense, as distorted as possible in the group Homeo(S^n), thought of as a discrete group. An appendix by Y …
MLDL preserves manifold geometry in vector transformations.
problem Geometric deterioration in neural network transformations.
method Locally isometric smoothness (LIS) and Markov random field (MRF) encoding.
result Enhanced vector transformations into well-behaved metric homeomorphisms.
We study the recently introduced stability training as a general-purpose method to increase the robustness of deep neural networks against input perturbations. In particular, we explore its use as an alternative to data augmentation and validate its performance against a number of distortion types and transformations i…
A robust method for decomposing spectral peaks robust to distortion and interference.
problem Decomposing spectral peaks in the presence of distortion and interference.
method Optimizing a nonparametric approach using pseudo-symmetric functions with nonincreasing behavior.
result Decomposed spectral peaks show pseudo-orthogonal behavior and power preserving equality.
Develops a power-calibrated framework for LLM watermarking, optimizing tradeoffs between detectability and distortion.
problem The trade-off between detectability and semantic distortion in logit-based watermarking.
method Power-calibrated statistical framework for watermark hyperparameters, establishing explicit relationships.
result Derives practical parameter selection procedures achieving optimal tradeoffs under constraints.
This paper clarifies VAE's property through geometric and information-theoretic interpretations.
problem The transparency of VAE model is an underlying issue.
method Quantitative understanding of VAE through differential geometry and information theory.
result VAE can be mapped to an implicit isometric embedding with a scale factor derived from the posterior parameter.
We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that are mapped to circles. We apply this result to analyze the dilatation of the circ…
Efficient point cloud compression is fundamental to enable the deployment of virtual and mixed reality applications, since the number of points to code can range in the order of millions. In this paper, we present a novel data-driven geometry compression method for static point clouds based on learned convolutional tra…
In this paper, we continue our previous work on the Dirichlet mixture model (DMM)-based VQ to derive the performance bound of the LSF VQ. The LSF parameters are transformed into the ΔLSF domain and the underlying distribution of the ΔLSF parameters are modelled by a DMM with finite number of mixture components. The…
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.
DiffC compresses images by diffusing Gaussian noise, outperforming state-of-the-art methods.
problem Efficient lossy image compression without transform coding.
method Unconditional diffusion generative models to encode and denoise corrupted pixels.
result DiffC outperforms HiFiC on ImageNet 64x64, achieving a 3 dB gain at high bitrates.
SISR improves feature attribution in complex payoff schemes.
problem Distorted feature attributions due to non-additive payoff functions and high-dimensional feature spaces.
method Sparse Isotonic Shapley Regression (SISR) learns a monotonic transformation to restore additivity and enforces L0 sparsity.
result SISR achieves strong support recovery and stable attributions across various payoff schemes.
Autoencoder optimizes data embedding for accurate PDF reproduction.
problem Inaccurate PDF reproduction in latent space of VAEs.
method Rate-Distortion Optimization guided autoencoder with isometric property.
result Our method achieves isometric data embedding and tractable PDF relations.
Recent work has shown that additive threat models, which only permit the addition of bounded noise to the pixels of an image, are insufficient for fully capturing the space of imperceivable adversarial examples. For example, small rotations and spatial transformations can fool classifiers, remain imperceivable to human…
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.
Investigates portfolio optimisation in rough Heston models with two approaches.
problem Optimizing portfolios under rough Heston models with non-Markovian structure.
method Two approaches: auxiliary random process and finite dimensional approximation.
result Derives optimal strategies in semi-closed form and compares results.
A new method for automatically aligning and clustering time series data.
problem Challenges in aligning and clustering time series data, especially without a template signal.
method TROUT (Temporal Registration using Optimal Unitary Transformations) method based on a novel dissimilarity measure.
result TROUT outperforms competitors in clustering time series data.
We develop embeddings for nonlinear subspaces preserving vector norms.
problem Preserving vector norms in nonlinear subspaces.
method Low-distortion embeddings for subspaces under nonlinear transformations.
result First low-distortion embeddings for a wide class of nonlinear functions.
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.
New method calculates super-hedging prices with transaction costs.
problem Super-hedging European contingent claims under proportional transaction costs.
method Explicit recursive scheme based on convex duality and Legendre-Fenchel transform.
result Computes super-hedging price and optimal strategy without martingale arguments.
Bregman divergences play a central role in the design and analysis of a range of machine learning algorithms. This paper explores the use of Bregman divergences to establish reductions between such algorithms and their analyses. We present a new scaled isodistortion theorem involving Bregman divergences (scaled Bregman…
This study proposes a trainable adaptive window switching (AWS) method and apply it to a deep-neural-network (DNN) for speech enhancement in the modified discrete cosine transform domain. Time-frequency (T-F) mask processing in the short-time Fourier transform (STFT)-domain is a typical speech enhancement method. To re…
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 consider the problem of distortion minimal morphing of n-dimensional compact connected oriented smooth manifolds without boundary embedded in Rn+1. Distortion involves bending and stretching. In this paper, minimal distortion (with respect to stretching) is defined as the infinitesimal relative change in vol…
Compression is at the heart of effective representation learning. However, lossy compression is typically achieved through simple parametric models like Gaussian noise to preserve analytic tractability, and the limitations this imposes on learning are largely unexplored. Further, the Gaussian prior assumptions in model…
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.
This paper solves a financial portfolio selection problem in incomplete markets.
problem Portfolio selection in incomplete financial markets with ambiguity.
method Constructing an efficient frontier, simplifying the problem, introducing a new distorted Legendre transformation, and proving the bipolar relation and distorted duality theorem.
result The existence and uniqueness of optimal strategies are shown for different utility functions under specific conditions.
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…
Optimizes maps with controlled distortion for geometric tasks.
problem Free-boundary diffeomorphism optimization in geometric modeling.
method Least-squares quasiconformal (LSQC) operator and Spectral Beltrami Network (SBN).
result LSQC minimizer well-posed under mild conditions, stable under mesh refinement.
The input data features set for many data driven tasks is high-dimensional while the intrinsic dimension of the data is low. Data analysis methods aim to uncover the underlying low dimensional structure imposed by the low dimensional hidden parameters by utilizing distance metrics that consider the set of attributes as…
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…
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.
Estimates rate-distortion function for large datasets using neural networks.
problem Designing lossy data compression schemes and comparing them with theoretical limits.
method Re-formulate rate-distortion objective and solve using neural networks.
result NERD accurately estimates the rate-distortion function for real-world datasets.
Generative models improve image restoration from unknown transformations.
problem Restoring images distorted by unknown transformations.
method Combining maximum a-posteriori probability with maximum likelihood estimation.
result Restores images without requiring exact knowledge of transformations.
A new method flips class values to address class and treatment imbalance in uplift modeling and HTE.
problem Class and treatment imbalance in imbalanced RCT data.
method Class flipping approach to address imbalance without distorting predictions.
result The method does not distort predicted effects and does not require calibration.
New coding theorem shows achievable rate matches theoretical limit.
problem Unknown existence of encoders and decoders for RDPF.
method Used stochastic, variable-length codes to prove RDPF achievable.
result Achievable rate matches theoretical rate-distortion-perception function.
We construct 2-dimensional CAT(-1) groups which contain free subgroups with arbitrary iterated exponential distortion, and with distortion higher than any iterated exponential.