Novel approach to universal online learning for bounded losses, closing open problems.
problem Characterizing processes for universal online learning under non-i.i.d. conditions.
method Characterization of processes admitting strong and weak universal learning, introduction of optimistically universal learning rule.
result Introduction of a novel 1NN algorithm that is optimistically universal for bounded losses.
Solves open problem on universally consistent online learning with unbounded losses.
problem Open problem on universally consistent online learning with unbounded losses.
method Constructs random measurable partitions of the instance space.
result Simple memorization rule is optimistically universal for any unbounded loss.
This paper studies universal rates of ERM for binary classification under agnostic learning.
problem The challenge of achieving universal rates of ERM for binary classification under agnostic learning.
method The paper explores the agnostic universal rates of ERM for binary classification, revealing three possible rates: e−n, o(n−1/2), or arbitrarily slow. result The paper provides a complete characterization of which concept classes fall into each of the three categories of agnostic universal rates.
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.
Market sectors play a key role in the efficient flow of capital through the modern Global economy. We analyze existing sectorization heuristics, and observe that the most popular - the GICS (which informs the S&P 500), and the NAICS (published by the U.S. Government) - are not entirely quantitatively driven, but rather…
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.
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.
This research finds three meta-indicators for university rankings.
problem Complexity in university ranking systems.
method Interpretable machine learning approach.
result Identified three meta-indicators: time, space, and relationships.
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.
Reduces bounded loss learning to binary classification.
problem Universal consistency of non-i.i.d. processes with bounded loss.
method Constructive reduction to binary classification.
result Any bounded loss output setting can be reduced to binary classification.
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.
A universal learner achieves best rates for all distributions.
problem Improving learning algorithm rates under various settings.
method Simple extension of Levin's universal search.
result Achieves best-possible rates for all distributions.
New rule universally consistent for online learning with non-ergodic data.
problem Online learning with non-ergodic data processes.
method Developed an online learning rule for processes on (X,Y) pairs.
result Generalizes past results to non-ergodic processes on (X,Y).
New algorithm achieves consistent learning from context in bandit problems.
problem Learning from context in bandit problems with non-i.i.d. contexts.
method Optimistically universal learning rule balancing generalization and personalization.
result Achieves universal consistency for large classes of non-i.i.d. contexts.
Transformers enable in-context learning with guarantees for a wide range of tasks.
problem How to enable in-context learning with transformers for various tasks.
method Developed a universal approximation theory integrating Barron's function approximation with transformer capabilities.
result Transformers can approximate any target function with vanishingly small risk using a few in-context examples.
This work initiates a general study of learning and generalization without the i.i.d. assumption, starting from first principles. While the traditional approach to statistical learning theory typically relies on standard assumptions from probability theory (e.g., i.i.d. or stationary ergodic), in this work we are inter…
MPE framework proves universal approximation for quantum data distribution.
problem Challenges in generating quantum data from underlying distributions.
method Many-body Projected Ensemble (MPE) framework for quantum state design.
result MPE can approximate any quantum distribution within 1-Wasserstein distance error.
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.
We extend a recently proposed 1-nearest-neighbor based multiclass learning algorithm and prove that our modification is universally strongly Bayes-consistent in all metric spaces admitting any such learner, making it an "optimistically universal" Bayes-consistent learner. This is the first learning algorithm known to e…
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.
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.
Develops hierarchical reinforcement learning value function approximators.
problem Estimating long-term returns in reinforcement learning with multiple goals.
method Introduces hierarchical universal value function approximators (H-UVFAs) using the options framework.
result Demonstrates generalization and improved performance of H-UVFAs over UVFAs.
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.
Theory extends optimal learning rates without realizability assumption.
problem Agnostic binary classification without realizability assumption.
method Identifies tetrachotomy of optimal rates and combinatorial structures.
result Optimal universal rates for binary classification in agnostic setting.
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.
Unified theorem for deep and shallow joint-equivariant machines.
problem Universal approximation of joint-equivariant machines.
method Constructive universal approximation theorem based on ridgelet transform.
result Unified approximation of deep and shallow networks.
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.
This appendix proves CORN's universal consistency. One of Bin's PhD thesis examiner (Special thanks to Vladimir Vovk from Royal Holloway, University of London) suggested that CORN is universal and provided sketch proof of Lemma 1.6, which is the key of this proof. Based on the proof in Gyprfi et al. [2006], we thus pro…
Deep Sets approximates functions on sets with high-dimensional latent space.
problem Modeling functions of sets (permutation-invariant functions).
method Deep Sets, a method known to be a universal approximator for continuous set functions.
result Deep Sets' universal approximation property is only guaranteed with a sufficiently high-dimensional latent space.
The goal of this paper is to characterize function distributions that deep learning can or cannot learn in poly-time. A universality result is proved for SGD-based deep learning and a non-universality result is proved for GD-based deep learning; this also gives a separation between SGD-based deep learning and statistic…
Universal supervised learning is considered from an information theoretic point of view following the universal prediction approach, see Merhav and Feder (1998). We consider the standard supervised "batch" learning where prediction is done on a test sample once the entire training data is observed, and the individual s…
Characterizes concept classes for optimistic online learning.
problem Understanding minimal assumptions for online learnability.
method Investigates two questions about concept classes' learnability.
result Characterizes all concept classes for optimistically universal online learnability.
The study extends kernel universality to Riemannian symmetric spaces.
problem Understanding kernel universality in non-Euclidean domains.
method Harmonic analysis on Riemannian symmetric spaces.
result Proves universality of recent kernels on Riemannian symmetric spaces.
Universal approximation for ODENet and ResNet with a single activation function.
problem Approximating complex dynamical systems with limited vector fields.
method Examined ODENet and ResNet with vector fields composed of a single activation function and affine mapping.
result ODENet and ResNet with restricted vector fields can uniformly approximate those with general vector fields.
A new machine learning model uses matrix exponentials for universal approximation.
problem Developing a robust and efficient machine learning model.
method Introduces a novel architecture using matrix exponentials as the only nonlinearity.
result The model achieves universal approximation properties and outperforms other models on benchmark tasks.
Group invariant and equivariant Multilayer Perceptrons (MLP), also known as Equivariant Networks, have achieved remarkable success in learning on a variety of data structures, such as sequences, images, sets, and graphs. Using tools from group theory, this paper proves the universality of a broad class of equivariant M…
The study proves Gaussian universality of deep random features learning.
problem Understanding the test error in deep random features learning.
method Proving Gaussian universality of test error in ridge regression and arbitrary convex losses.
result Sharp asymptotic formula for test error in ridge regression setting.
Kernel methods have been widely applied to machine learning and other questions of approximating an unknown function from its finite sample data. To ensure arbitrary accuracy of such approximation, various denseness conditions are imposed on the selected kernel. This note contributes to the study of universal, characte…
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.
Using deep neural networks that are either invariant or equivariant to permutations in order to learn functions on unordered sets has become prevalent. The most popular, basic models are DeepSets [Zaheer et al. 2017] and PointNet [Qi et al. 2017]. While known to be universal for approximating invariant functions, DeepS…
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.
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.
OptFormer learns universal HPO from diverse datasets.
problem Learning HPO from experiments with different hyperparameters.
method Text-based Transformer framework for joint policy and function prediction.
result OptFormer can imitate multiple HPO algorithms and improve predictions.
Framework for universal graph function approximators outperforms existing methods.
problem Graph classification and separation of graph classes.
method Inspired by persistent homology, dependency parsing, and multivalued functions, the framework constructs universal approximators on graph isomorphism classes.
result Achieves state-of-the-art performance on four graph datasets.
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…
Convolutional neural networks (CNN) have become one of the most popular machine learning tools and are being applied in various tasks, however, CNN models are vulnerable to universal perturbations, which are usually human-imperceptible but can cause natural images to be misclassified with high probability. One of the s…
Adversarial examples are inputs intentionally perturbed with the aim of forcing a machine learning model to produce a wrong prediction, while the changes are not easily detectable by a human. Although this topic has been intensively studied in the image domain, classification tasks in the audio domain have received les…
The paper proves universality in optimization problems with i.i.d. random vectors.
problem Optimization problems with i.i.d. random vectors and their projections.
method Proves universality of empirical risk minimization under specific conditions.
result The minimum value of the optimization problem is universal and depends only on the mean and covariance of the random vectors.