LDLE embeds manifolds in lower dimensions with low distortion.
problem Embedding manifolds in lower dimensions with low distortion.
method Constructs local views using global eigenvectors of the graph Laplacian, registers them using Procrustes analysis, and tears manifolds apart for intrinsic dimension embedding.
result LDLE preserves distances up to a constant scale with low distortion.
New study shows tradeoffs between compression quality, distortion, and perception.
problem Optimizing compression for low distortion often sacrifices perceptual quality.
method Adopted Blau & Michaeli's perceptual quality definition and studied the rate-distortion-perception tradeoff.
result Restricting perceptual quality to high generally requires a trade-off between rate and distortion.
DeepTwist compresses models by occasionally distorting weights, improving accuracy and efficiency.
problem Challenges in model compression due to high design complexity and additional overhead.
method DeepTwist uses occasional weight distortion without changing training algorithms.
result Significantly improved compression rates for various techniques with reduced effort.
Proposes new terms for neural image compression to improve quality and efficiency.
problem Improving the quality and efficiency of neural image compression.
method Introduces a compression objective and a cycle loss term, applied to autoencoder encoder outputs, combined with reconstruction losses.
result Different autoencoders trained with varying losses produce images with distinct perceptual qualities and image-domain distortions.
The paper tackles matrix completion under nonlinear distortions.
problem Matrix completion with nonlinear distortions.
method Alternates between low-rank matrix estimation and monotonic function estimation.
result Empirical results show the method's competitiveness.
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.
We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. The codebook is defined by a design matrix and codewords are structured linear combinations of columns of this matrix. The proposed encoding algorithm sequentially chooses columns of the design matrix to suc…
Paper studies fundamental limits of communication in distributed learning.
problem Communication efficiency in model aggregation for distributed learning.
method Rate-Distortion approach to model aggregation as a vector Gaussian CEO problem.
result Derives rate region bound and sum-rate-distortion function for model aggregation.
New method finds knots without low treewidth diagrams.
problem Finding knots without low treewidth diagrams.
method Structural graph theory and knot theory.
result Optimal obstruction for high representativity knots.
New methods correct spectral distortions using known analyte concentrations.
problem Distorted spectral shapes from absorbing and scattering contributions.
method Modified penalized baseline correction methods that incorporate known analyte concentrations.
result Improved prediction performance on near infra-red data sets.
The paper proposes a method to improve data analysis by considering multiple subsets of attributes (views) to enhance geometric information.
problem Distortion of distance metrics in high-dimensional data analysis.
method Partitioning attributes into multiple subsets (views) and using consensus between views to extract geometric information.
result Enhanced geometric information from multiple views improves data analysis.
We study a new class of codes for lossy compression with the squared-error distortion criterion, designed using the statistical framework of high-dimensional linear regression. Codewords are linear combinations of subsets of columns of a design matrix. Called a Sparse Superposition or Sparse Regression codebook, this s…
New method estimates rate-distortion function using optimal transport.
problem Estimating the fundamental performance limit of data compression.
method Wasserstein gradient descent to learn optimal reproduction distribution.
result Local convergence and sample complexity analysis of R-D estimator.
The paper embeds manifolds into finite Euclidean spaces using eigenvector fields of the connection Laplacian.
problem Embedding manifolds into finite-dimensional Euclidean spaces using eigenvector fields of the connection Laplacian.
method Constructing local coordinate charts with low distortion using eigenvector fields and proving estimates for eigenvector fields and the heat kernel.
result The distortion constants depend only on geometric properties of manifolds in the little Hölder space c2,α, allowing for embedding into a finite-dimensional Euclidean space. Stability of knots at low regularity, and symmetric critical knots for Möbius energy.
problem Stability of knot equivalence at low regularity.
method Localized Gromov distortion and Hausdorff-distance criteria.
result Compactness theorem for knot equivalence classes and existence of symmetric critical knots for Möbius energy.
Diffusion models improve image compression at low bit-rates.
problem Efficiently compressing images at very low bit-rates.
method Encoding into an embedding, using diffusion models to refine the embedding iteratively.
result Realistic reconstructions can be generated at extremely low bit-rates.
Low frequency perturbations improve model robustness, contrary to high frequency attacks.
problem Improving model robustness against adversarial attacks.
method Systematic control of frequency components in perturbations.
result Low frequency perturbations improve model robustness, especially in white-box and black-box settings.
In this paper, the `Approximate Message Passing' (AMP) algorithm, initially developed for compressed sensing of signals under i.i.d. Gaussian measurement matrices, has been extended to a multi-terminal setting (MAMP algorithm). It has been shown that similar to its single terminal counterpart, the behavior of MAMP algo…
Paper introduces SCP to measure classifier distortion and optimized coding strategies.
problem Noise impacts binary classifier performance; goal is to minimize distortion.
method Developed a low-complexity estimate of SCP using quantization and polynomial multiplication. Also studied replication error-correcting codes for maximizing SCP.
result Introduced optimized coding strategies that specifically aim to maximize classification probability (minimizing distortion) for the same redundancy overhead.
Paper improves model compression techniques without significant loss in performance.
problem Challenges in deploying large deep neural networks due to their size.
method Proposes principled approaches to improve model compression via rate distortion theory and novel objective functions.
result Proves the optimality of the proposed scheme for compressing one-hidden-layer ReLU neural networks.
Foundation models fail to preserve continuous geometry, identified as the Geometric Alignment Tax.
problem Continuous geometry is lost in foundation models due to discrete categorical bottlenecks.
method Controlled ablations on synthetic systems and evaluation of 14 biological models using rate-distortion theory and MINE.
result Replacing cross-entropy with a continuous head reduces geometric distortion by up to 8.5x.
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.
C3 compresses images and videos with low complexity and high performance.
problem High complexity and low performance in neural compression models.
method Overfits a small model to each image or video separately, improving RD performance with low complexity.
result Matches the RD performance of state-of-the-art neural and video codecs with significantly lower decoding complexity.
A new approach for efficient data compression in split DNN computing.
problem Optimizing data compression for DNN models split between mobile devices and edge servers.
method Systematic design and training of bottleneck units that can be inserted at the split point.
result Achieves excellent rate-distortion performance with minimal compute and storage overhead.
A new method compresses point clouds efficiently, outperforming existing techniques.
problem Efficiently compressing large point cloud datasets for VR applications.
method Learned convolutional transforms and uniform quantization for joint rate and distortion optimization.
result Significant rate-distortion improvement (51.5% BDBR savings) on Microsoft Voxelized Upper Bodies dataset.
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.
We present two statistical causes for the distortion of correlations on high-frequency financial data. We demonstrate that the asynchrony of trades as well as the decimalization of stock prices has a large impact on the decline of the correlation coefficients towards smaller return intervals (Epps effect). These distor…
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.
Distorted surfaces in graph manifolds have specific distortion properties.
problem Distortion of surfaces in graph manifolds.
method Analysis of immersed horizontal surfaces in 3D graph manifolds.
result Fundamental group of surfaces is quadratically distorted if virtually embedded, exponentially distorted otherwise.
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.
Hyperbolic embeddings reduce dimensions for hierarchical data with high precision.
problem Embedding hierarchical data structures like synonym or type hierarchies efficiently.
method Combinatorial construction and hyperbolic multidimensional scaling (h-MDS) for metric spaces.
result Hyperbolic embeddings achieve high precision with few dimensions, e.g., 0.989 MAP with only 2 dimensions on WordNet.
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.
The net-premium principle is considered to be the most genuine and fair premium principle in actuarial applications. However, an insurance company, applying the net-premium principle, goes bankrupt with probability one in the long run, even if the company covers its entire costs by collecting the respective fees from i…
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.
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear…
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…
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.
Finite distortion maps cannot have compact branch sets under growth conditions.
problem Understanding the structure of branch sets in mappings of finite distortion.
method Analyzing the asymptotic growth of distortion and constructing specific examples.
result The bound on the size of branch sets is strict and achievable.
This paper proposes a new method for efficient data compression using Bayesian neural networks.
problem Efficient compression of data represented as functions mapping coordinates to signal values.
method Overfitting variational Bayesian neural networks to the data and compressing an approximate posterior weight sample using relative entropy coding.
result Our method achieves strong performance on image and audio compression while retaining simplicity.
A new method embeds high-dimensional data in a low-dimensional space while preserving its geometry.
problem Difficulty in exploring high-dimensional data due to 'curse of dimensionality'.
method Dictionary-based framework for geometrically driven data analysis including dimensionality reduction, out-of-sample extension, and anomaly detection.
result Preserves the original high-dimensional geometry of the data up to a user-defined distortion rate.
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…
Paper proposes efficient algorithms to certify robustness of ReLU networks.
problem NP-complete problem of verifying robustness for ReLU networks.
method Two computationally efficient algorithms Fast-Lin and Fast-Lip.
result Delivers bounds close to exact minimum distortion with significant speedup.
The paper calculates subgroup distortions in 3-manifold groups.
problem Understanding subgroup distortions in 3-manifold groups.
method Computed all finitely generated subgroups of finitely generated 3-manifold groups and analyzed their distortions.
result Subgroup distortions in 3-manifold groups are linear, quadratic, exponential, or double exponential.
Proposes EOT eigenmaps for aligning and embedding multiple datasets.
problem Aligning and embedding multiple datasets with shared structures but individual distortions.
method Entropic Optimal Transport (EOT) eigenmaps, leveraging leading singular vectors of EOT plan matrix.
result Proves theoretical guarantees and favorable properties for aligning and embedding datasets.
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.