Researchers found specific conformal groups for Einstein static universe models.
problem Understanding conformal groups of Einstein static universe models.
method Constructed explicit models for restricted conformal groups and universal covering groups.
result Determined all conformal Lorentz manifolds with maximal restricted conformal group dimension.
Develops a new approach to establish universality for any-dimensional machine learning models.
problem Understanding universality for models with inputs of varying sizes.
method Identifies any-dimensional functions with a unique function in an infinite-dimensional limit space, using symmetries and relations between inputs of different sizes.
result Establishes universality for several existing architectures and proposes modifications to restore it.
GCNNs gain rotation invariance with more training augmentation, making SVD-Universal more effective.
problem Improving robustness of GCNNs to adversarial attacks.
method SVD-Universal technique applied to GCNNs trained with larger rotations.
result SVD-Universal becomes more effective as GCNNs gain rotation invariance.
Simple technique turns any adversarial attack into a universal one using few test examples.
problem Creating universal adversarial attacks with minimal data.
method Universalization technique using few adversarial test examples and spectral properties.
result Simple universalization technique achieves comparable fooling rates to state-of-the-art methods.
New model closes gap in understanding equivariant set functions.
problem Understanding universality of equivariant set functions.
method Proves PointNet not equivariant universal and introduces PointNetST.
result PointNetST is the simplest permutation equivariant universal model.
A universal LSTM model outperforms asset-specific models in forecasting stock volatilities.
problem Forecasting stock volatilities across different assets.
method Trained an LSTM network on a pooled dataset of liquid stocks to forecast daily realized volatilities.
result The LSTM model consistently outperforms other asset-specific parametric models in volatility forecasting.
MAT combines meta-learning and adversarial training to defend against universal patches.
problem Defending against universal patches that fool models in various contexts.
method Meta adversarial training (MAT) integrates meta-learning with adversarial training.
result MAT increases robustness against universal patch attacks on image classification and traffic-light detection.
MLPs can approximate any function in context, challenging the importance of in-context universality.
problem Understanding why transformers are more effective than classical models.
method Proved MLPs with trainable activation functions are universal in context.
result Transformer success is likely due to factors other than in-context universality.
Paper finds universal speech command perturbations that fool models.
problem Existence of universal adversarial examples in speech command classification.
method Proposed a novel analytical framework for evaluating universal perturbations and a detailed distortion measurement method.
result Universal perturbations can fool speech command classification models across different models.
Simple proof shows graph neural networks are versatile.
problem Proving the universality of graph neural networks.
method Introduced a Graph Homomorphism Model to prove universality.
result Simple proofs of graph neural network universality.
Computational model uncovers linguistic universals.
problem Manual processing of linguistic typology by linguists is time-consuming and leaves key universals unexplored.
method Presented a computational model to identify known and new linguistic universals.
result The model successfully identifies known universals and uncovers new ones.
Sig-Splines model uses signatures and splines for time series data, achieving universality and convexity.
problem Creating a generative model for multivariate time series data.
method Combines linear transformations and signature transforms into a neural spline flow.
result Achieves universality and introduces convexity in model parameters.
Universal approximation for rough paths and Lévy processes.
problem Approximating continuous functionals of càdlàg paths.
method Linear functionals of time-extended signatures.
result Universal approximation theorem for continuous functionals of càdlàg paths.
Deep networks have recently been shown to be vulnerable to universal perturbations: there exist very small image-agnostic perturbations that cause most natural images to be misclassified by such classifiers. In this paper, we propose the first quantitative analysis of the robustness of classifiers to universal perturba…
CF-INNs can approximate any invertible function, resolving a long-standing problem.
problem Whether CF-INNs can approximate any invertible function.
method Demonstrated CF-INNs are universal approximators for invertible functions by showing a convenient criterion.
result CF-INNs are universal approximators for invertible functions.
Diffusion models generate data with Gaussian Universality, matching linear model test errors.
problem Analyzing the performance of models trained on synthetic data generated by diffusion models.
method Investigates Gaussian Universality for data distributions generated via diffusion models, matching test errors of linear models trained on synthetic data to Gaussian Mixture models.
result The test error of a linear model trained on diffusion-generated data matches the test error of a linear model trained on Gaussian Mixture data with matching means and covariances per class.
Killing vector fields of a closed homogeneous and isotropic universe are studied. It is shown that in general case there is no time-like Killing vector fields in such a universe. Two exceptional cases are revealed.
Softmax attention approximates complex functions and subsumes many known universal approximators.
problem Universal approximation of continuous sequence-to-sequence functions.
method Interpolation-based analysis of attention's internal mechanism, showing its ability to approximate ReLU functions.
result Softmax attention is a universal approximator for continuous sequence-to-sequence functions.
The closed homogeneous and isotropic universe is considered. The bundles of Weyl and Dirac spinors for this universe are explicitly described. Some explicit formulas for the basic fields and for the connection components in stereographic and in spherical coordinates are presented.
This research formalizes uncertainty quantification for Universal Differential Equations models.
problem Quantifying uncertainties in Universal Differential Equations models.
method Formalized uncertainty quantification methods for UDEs, including frequentist and Bayesian approaches.
result Evaluation of ensemble, variational inference, and MCMC sampling methods for UDEs.
Universal audio perturbations fool ASR systems.
problem Speech recognition systems are vulnerable to adversarial attacks.
method Developed an algorithm to create universal perturbations that fool ASR models.
result Universal perturbations can fool ASR systems across different models.
New findings on universal learning in contextual bandits with adversarial rewards.
problem Learning in contextual bandits with time-varying, adversarial rewards.
method Characterization of learnable processes and necessary/sufficient conditions for universal learning.
result Optimistic universal learning for contextual bandits with adversarial rewards is impossible in general.
Survey on computational models in dynamical systems, including new universality concepts.
problem Understanding the relationship between computational models and dynamical systems.
method Review of recent works on Turing universality, Topological Kleene Field Theories, and dynamical bordisms.
result Introduction of new perspectives on computability through dynamical systems.
Improved algorithm speeds up generation of universal adversarial perturbations.
problem Slow generation of universal adversarial perturbations.
method Optimized algorithm based on orientation of perturbation vectors.
result Significantly faster generation of universal perturbations with higher fooling rates.
New findings show Gaussian universality breaks down in high-dimensional linear factor mixtures.
problem The limitations of Gaussian universality in high-dimensional classification.
method Characterization of empirical risk minimization for classification under linear factor mixture models.
result Gaussian universality breaks down under high-dimensional linear factor mixtures.
PanRep learns universal node embeddings for heterogeneous graphs.
problem Learning universal node embeddings for heterogeneous graphs.
method Graph Neural Network (GNN) model with four decoders capturing different properties.
result PanRep outperforms unsupervised and supervised methods in node classification and link prediction.
We obtain universal models for several types of locally conformal symplectic manifolds via pullback or reduction. The relation with recent embedding results for locally conformal Kähler manifolds is discussed.
The study examines the universality of Gaussian data in high-dimensional generalized linear estimation.
problem Understanding when Gaussian data suffices for high-dimensional generalized linear estimation.
method Sharp asymptotic expressions for test and training errors in high-dimensional Gaussian mixture data with labels from a single-index model.
result The universality of Gaussian data in error estimation depends on the alignment between target weights and mixture cluster means and covariances.
New method evaluates LLMs fairness in universal prediction.
problem Evaluating fairness of large language models in universal prediction.
method Introducing batch regret as a modification of average regret for LLMs.
result Asymptotical value of batch regret for add-constant predictors on memoryless and first-order Markov sources.
This work establishes universality for deep equivariant networks, overcoming limitations of previous approaches.
problem Rarity of universality results for equivariant neural networks, especially in high-dimensional settings.
method Develops a more general account of universality for equivariant networks, introducing entry-wise separability and readout layers.
result Deep equivariant networks achieve universality under entry-wise separability, with or without readout layers.
Modified relative universality for unbiasedness and consistency in dimension reduction.
problem Gap in proof of unbiasedness and Fisher consistency in relative universality.
method Modified definition of relative universality using ǫ-measurability.
result Established unbiasedness and Fisher consistency rigorously.
Study models of Gödel Universe using Lie groups and Iwasawa decomposition.
problem Modeling the Gödel Universe as a Lie group with specific metrics.
method Iwasawa decomposition for semisimple Lie groups, left-invariant Lorentz metric on SL(2,R).
result Isometry between sub-Riemannian Lie groups induced by Iwasawa decomposition.
A fast method computes class-specific adversarial perturbations for deep networks.
problem Computing robust adversarial perturbations for deep networks.
method Linear function of weights, no training data, no hyper-parameters.
result Obtains 34% to 51% fooling rate on ImageNet, transfers across models.
Transformers can approximate any sequence-to-sequence function, surprising given their complexity.
problem Understanding the expressive power of Transformer models for sequence-to-sequence functions.
method Established that Transformers are universal approximators of continuous permutation equivariant sequence-to-sequence functions with compact support, and extended this to arbitrary functions using positional encodings.
result Transformers are universal approximators of arbitrary continuous sequence-to-sequence functions on a compact domain.
Paper explores universal rates of ERM in machine learning.
problem Understanding universal learning rates for ERM.
method Analyzes realizable concept classes and ERM principles.
result Four possible universal learning rates by ERM.
A new model uses Toeplitz matrices to analyze time-series data transitions.
problem Analyzing transitions in time-series data from nonautonomous systems.
method Deep Koopman-layered models with learnable Toeplitz matrices, leveraging Toeplitz matrices' universal property.
result The model demonstrates universality and generalization, outperforming existing methods.
Study free energy in spherical spin glasses, proving universality dichotomy.
problem Analyzing free energy in spherical spin glass models with different tail exponents.
method Introduced a tail-adapted normalization and used universality dichotomy.
result Sharp universality dichotomy for free energy across different tail exponents.
A new approach to continuous-time universal portfolios using pathwise Itô calculus.
problem Continuous-time version of Cover's universal portfolio strategies.
method Pathwise Itô calculus approach to establish existence and properties of universal portfolio strategies.
result The universal portfolio strategy's portfolio value process is the average of all values of constant rebalanced strategies.
Adversarial training helps classifiers resist universal perturbations.
problem Vulnerability of classifiers to universal perturbations.
method Adversarial training with shared adversarial examples.
result Adversarial training reduces sensitivity to universal perturbations.
Paper characterizes and constructs universal approximators for neural networks.
problem Limited understanding of universal approximation in neural networks.
method Characterization, representation, construction method, existence result for any universal approximator.
result Improved capabilities of feed-forward architecture to approximate continuous functions.
This paper finds universal perturbations to fool black-box ML classifiers.
problem Breaking security through obscurity in black-box ML settings.
method Zeroth-order optimization for finding universal adversarial perturbations in a black-box setting.
result State-of-the-art ML classifiers can be fooled with a single imperceptible image perturbation.
In the framework of Lorentzian warped products, we study the Friedmann-Robertson-Walker cosmological model to investigate non-smooth curvatures associated with multiple discontinuities involved in the evolution of the universe. In particular we analyze non-smooth features of the spatially flat Friedmann-Robertson-Walke…
New method generates universal adversarial perturbations across different image sources.
problem Certifying robustness of deep learning models with universal adversarial perturbations across various image sources.
method Few-shot learning approach using bilevel optimization and learning-to-optimize techniques.
result Improved attack success rate and faster performance compared to existing methods.
Enhanced synthetic dataset improves asset allocation analysis.
problem Lack of realistic synthetic data for fixed income portfolio construction.
method Improved CorrGAN model for synthetic correlation matrices and Encoder-Decoder model for additional data conditioning.
result Synthetic dataset enhances portfolio construction and asset allocation analysis.
Neural networks are known to be vulnerable to adversarial examples, inputs that have been intentionally perturbed to remain visually similar to the source input, but cause a misclassification. It was recently shown that given a dataset and classifier, there exists so called universal adversarial perturbations, a single…
Paper proves GDL models can approximate any continuous function on non-Euclidean data.
problem Processing non-Euclidean data with universal feedforward models.
method Introduces geometric deep learning framework for differentiable manifold geometries.
result GDL models can uniformly approximate any continuous function on compact sets.
A new risk budgeting scheme derived from universal portfolio theory.
problem Risk allocation in portfolio management.
method Integrates Cover's universal portfolio selection with modern risk allocation models.
result Proves mathematical equivalence to a novel universal portfolio scheme.
Universal AI seeks high-optionality states through empowerment and curiosity.
problem Understanding and optimizing AI behavior in uncertain environments.
method Unified framework combining AIXI and variational empowerment, showing how universal AI agents balance goal-directed behavior with uncertainty reduction curiosity.
result Self-AIXI asymptotically converges to AIXI performance and exhibits power-seeking behavior due to intrinsic motivations.