New framework uses cohomology to analyze probabilistic distortions and arbitrage.
problem Analyzing probabilistic distortions and arbitrage in categorical filtrations.
method Transport cohomological framework, simplicial structure, loop effects, holonomy.
result Nontrivial probabilistic distortions and obstructions generated by loops.
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.
New insights into risk aversion for complex decision models.
problem Understanding risk aversion in non-monotone decision models.
method Characterization of probabilistic risk aversion for generalized rank-dependent functions.
result Probabilistic risk aversion is determined by the distortion function, which is convex or scaled quantile-spread mixtures.
Bandit algorithms handle human-like decision-making distortions.
problem Emulating human decision-making with probabilistic distortions.
method Stochastic multi-armed bandit problems with distorted probabilities, incorporating reward distortions.
result Sublinear regret for proposed algorithms in both K-armed and linear bandit settings. Proposes DILATE and STRIPE++ for precise time series forecasting.
problem Non-stationary signals with sudden changes.
method Incorporates shape and temporal criteria in deep learning models.
result Improves precision in deterministic and probabilistic forecasting.
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…
Study optimal risk sharing in decentralized peer-to-peer markets with robust risk measures.
problem Optimizing risk sharing in decentralized markets with non-convex risk measures.
method Characterization of Pareto-optimal allocations using robust distortion risk measures and probabilistic risk aversion.
result Shape of allocations depends on agents' tail risk assessments.
Hierarchical spiking networks resist physical distortions for neuromorphic computing.
problem Distortions in physical neuromorphic implementations of spiking networks.
method Used hierarchical leaky integrate-and-fire neurons to create robust spiking networks.
result Hierarchical spiking networks are robust to physical distortions.
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.
This paper improves probabilistic latent models on hyperbolic spaces.
problem Uncertainty in predictions due to geodesics crossing low-data regions.
method Augmenting hyperbolic manifold with a pullback metric for probabilistic pullback metrics.
result Geodesics on pullback metric respect both geometry and data distribution, reducing uncertainty.
New insights into optimizing latent representations in hierarchical VAEs.
problem Optimizing latent representations in hierarchical VAEs for various applications.
method Identifying a general class of inference models and deriving theoretical bounds on performance.
result Guidance for practitioners on optimal regions in rate-space for different applications.
Memory affects how we perceive time and make decisions about the future.
problem Temporal distortions and intertemporal choice preferences in humans and non-human subjects.
method Combining information theory and artificial intelligence, the study explains these phenomena through sensorimotor representation coding efficiency.
result Memory constraints lead to a renormalization of perceived timescales, resulting in different discount functions.
PROVEN extends neural network robustness verification to probabilistic settings.
problem Quantifying robustness of neural networks under probabilistic noise distributions.
method PROVEN: Probabilistic Verification of Neural Networks (PROVEN) with statistical guarantees.
result PROVEN achieves up to 75% improvement in robustness certification compared to worst-case methods.
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.
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 robust image classification models using probabilistic graphical models.
problem Robust image classification under acquisition noise and insufficient training data.
method Discriminative learning framework exploiting multiple projections and conditional correlations.
result Robust graphical model classifier minimizes classification error.
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.
Efficiently samples conformal boundaries in high dimensions using flows.
problem Difficulty in interpreting and using prediction sets in high-dimensional or structured output spaces.
method Flow-based approach using differentiable nonconformity scores to induce deterministic flows on the output space.
result Sampling conformal boundaries in arbitrary dimensions becomes computationally efficient and training-free.
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.
Paper introduces Prob-SSI for robust OMA in noisy data.
problem Challenges in estimating modal parameters from noisy data.
method Probabilistic formulation of SSI, robust Prob-SSI algorithm.
result Robust Prob-SSI outperforms conventional SSI in corrupted data.
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.
New k-means method handles random data better than traditional techniques.
problem Limitations of traditional clustering methods in random data.
method Probabilistic metric space with random normed k-means (RNKM).
result RNKM outperforms traditional methods in complex clustering scenarios.
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…
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.
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.
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.
A new method reduces preference distortion in LLM alignment.
problem Vulnerability of traditional LLM alignment methods to human preference heterogeneity.
method Sign Estimator: A simple, provably consistent, and efficient estimator using binary classification loss.
result Substantially reduces preference distortion over a panel of simulated personas.
Paper tackles noisy label distributions in machine learning.
problem Learning from noisy label distributions where true labels are distorted by unknown noise.
method Proposes a probabilistic model with hidden noise parameters and learns it using variational Bayesian methods.
result The proposed model outperforms existing methods in true label estimation.
Sharp bounds on distortion of surfaces in 3D space.
problem Finding the minimum distortion of surfaces in 3D space.
method Analyzing convex embedded 2-spheres and surfaces of positive genus.
result π/2 is a sharp lower bound on the distortion of surfaces of positive genus.
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.
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.
Introduces new performance criteria for investment under distorted probabilities.
problem Reconciling time-consistent performance with probability distortions.
method Two definitions of forward rank-dependent criteria, equivalence established; characterization of viable probability distortion processes.
result Characterization of optimal wealth process and new distorted measure.
Computes distortion of surfaces in non-geometric 3-manifolds.
problem Distortion of surfaces in non-geometric 3-manifolds.
method Computes distortion of π1(S) in π1(N) and relates it to separability.
result Distortion is linear, quadratic, exponential, or double exponential.
Introduces a new conditional expectation under distorted probabilities, addressing time-inconsistency.
problem Time-inconsistency in nonlinear expectations under probability distortion.
method Localizes probability distortion and constructs a time-consistent conditional expectation.
result Constructs a conditional expectation that is time-consistent and corresponds to a parabolic differential equation.
Study stabilizers in handlebody group; meridians are undistorted, others are exponentially distorted.
problem Geometric properties of stabilizers in handlebody group.
method Analysis of stabilizers of meridians and primitive curves/annuli.
result Stabilizers of meridians are undistorted, others are exponentially distorted.
New method tackles complex systems with hidden confounders and feedback loops.
problem Understanding complex systems with hidden confounders and feedback loops.
method Robust Causal Analysis of Linear Cyclic Systems with Hidden Confounders (LLC)
result LLC method can robustly analyze cyclic systems with hidden confounders.
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.
Sharp bounds for distortion risk metrics under uncertain distributions.
problem Modeling risk metrics under distributional uncertainty.
method Established bounds for distortion risk metrics using specific features of underlying distributions.
result Identified worst- and best-case values of distortion risk metrics.
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.
We construct 2-dimensional CAT(-1) groups which contain free subgroups with arbitrary iterated exponential distortion, and with distortion higher than any iterated exponential.
Study dynamic risk measures and performance indices using distortion functions.
problem Investigate time consistency of dynamic risk measures and performance indices generated by distortion functions.
method Analyze dynamic coherent risk measures (DCRMs) and dynamic weighted value at risk measures, proving their equivalence. Establish properties of families of DCRMs generated by distortion functions and define corresponding dynamic coherent acceptability indices (DCAIs). Examine time consistency of DCRMs and DCAIs.
result DCRM generated by distortion functions are sub-martingale time consistent but not super-martingale time consistent and not weakly acceptance time consistent.