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 e^{-n} e − n , o ( n − 1 / 2 ) o(n^{-1/2}) 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.
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.
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.
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.
Prototype rules simplify multiclass classification in metric spaces, achieving consistency and reduced complexity.
problem Multiclass classification in metric spaces, focusing on universal consistency and convergence rates.
method Novel Proto-NN and hybrid rules for multiclass classification in metric spaces, analyzing convergence rates.
result Proto-NN is universally consistent and simpler to implement, with similar computational advantages.
Paper establishes universal lower bounds and optimal rates for clustering sub-exponential mixture models.
problem Achieving optimal error rates in clustering sub-exponential mixture models.
method Establishes universal lower bounds and demonstrates iterative algorithms' optimality in sub-exponential mixture models.
result Iterative algorithms achieve the universal lower bound in sub-exponential mixture models.
Paper establishes a universal growth rate for smooth surrogate losses in classification.
problem Analyzing growth rates of consistency bounds for various surrogate losses.
method Proves square-root growth rate for smooth margin-based losses; extends to multi-class classification.
result Demonstrates a universal square-root growth rate for smooth comp-sum and constrained losses.
We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal an interesting phase transition behavior universal to this class of high dimensional problems. In the {\it sparse regime} when the components are sufficientl…
New theorem for generalized group sparsity improves consistency and convergence rates.
problem Improving statistical inference in high-dimensional data with element-wise and group-wise sparsity.
method Developed a generalized version of Sparse-Group Lasso and proved a universal theorem for consistency and convergence rates.
result Obtained results on consistency and convergence rates for different forms of double sparsity regularization.
We study the problem of minimizing a strongly convex, smooth function when we have noisy estimates of its gradient. We propose a novel multistage accelerated algorithm that is universally optimal in the sense that it achieves the optimal rate both in the deterministic and stochastic case and operates without knowledge …
In this paper we study the growth rates of Artin monoids and we show that 4 is a universal upper bound. We also show that the generating functions of the associated right-angled Artin monoids are given by families of Chebyshev polynomials. Applications to Artin groups and positive braids are given.
Unified framework for comparing classification metrics across different imbalance rates.
problem Differences in scale and sensitivity to class imbalance rates in classification metrics.
method Introduces outperformance standardization (OPS) function to map metrics to a common scale.
result Unified o-value metric provides clear comparison across different imbalance rates.
A new neural network model identifies hysteresis universally.
problem Inability of existing models to simulate hysteresis universally.
method Inspired by the Preisach model, an Extended Preisach Neural Network (EPNN) is introduced with two hidden layers and a hybrid training algorithm.
result EPNN successfully identifies various hysteresis phenomena from different fields.
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.
AI improves credit rating predictions over traditional methods.
problem Improving credit rating predictions for global corporate entities.
method Applying deep learning techniques, specifically neural networks with categorical embeddings, to a large dataset of corporate obligations.
result Deep learning models achieve adequate accuracy in predicting different credit rating classes.
OptiNet achieves near-minimax error rates with compression in Euclidean space.
problem Error and compression rates in non-parametric multiclass classification.
method Compression-based learning rule OptiNet and a novel general compression scheme.
result OptiNet achieves non-trivial compression rates with near-minimax error rates in Euclidean space.
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.
The paper proves neural networks' consistency and optimal convergence rates for various function classes.
problem Proving neural networks' consistency and optimal convergence rates for diverse function classes.
method Analyzes wide and deep ReLU neural networks trained on logistic loss and Kolmogorov-Donoho optimal function classes.
result Proves universal consistency and minimax optimal convergence rates for neural networks.
Transfer learning improves chaotic dynamics predictions with less data.
problem Efficiently predicting chaotic dynamics with limited data.
method Transfer learning for nonlinear dynamics, optimizing transfer rate and leveraging small-scale turbulence universality.
result Significantly more accurate inference of chaotic dynamics achieved.
Study expands multiclass classification models with new rates and partial concept classes.
problem Multiclass classification with a bounded number of labels under various conditions.
method Extends traditional PAC model to distribution-dependent and data-dependent learning rates, characterizes optimal rates for universal and partial concept classes.
result Characterizes three types of learning rates (exponential, linear, arbitrarily slow) for fixed distributions and complexity measures for partial concept classes.
To estimate a sparse linear model from data with Gaussian noise, consilience from lasso and compressed sensing literatures is that thresholding estimators like lasso and the Dantzig selector have the ability in some situations to identify with high probability part of the significant covariates asymptotically, and are …
Paper establishes rates of universal approximation for neural tangent kernels using transport mappings.
problem Universal approximation for neural tangent kernels with microscopic weight changes.
method Generic scheme to approximate functions with NTK using transport mappings, constructed via Fourier transforms.
result Approximation of continuous functions with roughly 1 / δ^(10d) nodes, where δ depends on function continuity.
New proof shows incremental flow models are essential for universal generation.
problem Understanding the universality of flow-based models in generating natural maps.
method Topological-dynamical argument and algebraic properties of flows.
result Incremental generation is necessary and sufficient for universal flow-based generation.
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.
DAmageNet generates universal adversarial samples with high transferability.
problem Vulnerability of deep neural networks to adversarial attacks.
method Generated 96,000 transferable adversarial samples from ImageNet.
result Adversarial samples misclassify various models with up to 90% error rate.
This note provides a neat and enjoyable expansion and application of the magnificent Ordentlich-Cover theory of "universal portfolios." I generalize Cover's benchmark of the best constant-rebalanced portfolio (or 1-linear trading strategy) in hindsight by considering the best bilinear trading strategy determined in hin…
FibQuant improves KV-cache compression for long-context inference.
problem Memory traffic bottleneck in long-context inference due to KV cache growth.
method Introduces FibQuant, a universal vector quantizer that combines Beta-quantile radii, Fibonacci/Roberts-Kronecker directions, and Lloyd-Max refinement.
result FibQuant achieves high compression rates with minimal loss in attention cosine similarity.
Deep neural networks without regularization can achieve consistent estimates with good convergence rates.
problem The necessity of regularization in deep neural networks for consistent estimates.
method Gradient descent on an over-parametrized neural network without regularization, with specific initialization, step size, and number of steps.
result An estimate without regularization is universally consistent and achieves good convergence rates.
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.
PLN-Nets with two linear layers and parallel LN achieve universal approximation.
problem Limitations of standard neural network architectures in universal approximation.
method Introduced PLN-Nets combining two linear layers with parallel LN.
result PLN-Nets achieve universal approximation, while standard LN has limited power.
The paper introduces a new learning model that explains practical aspects of machine learning.
problem Understanding how quickly a concept class can be learned from examples in practical scenarios.
method Introducing a new learning model that considers fixed data sources and varying number of training examples.
result There are only three possible rates of universal learning: exponential, linear, or arbitrarily slow.
Study optimal rates for multiclass classification, resolving open questions.
problem Optimal rates for multiclass classification with any label space.
method Establishes optimal rates for all hypothesis classes, defining new tree structures.
result Optimal rates for multiclass classification with no infinite DSL trees.
Consider a family of portfolio strategies with the aim of achieving the asymptotic growth rate of the best one. The idea behind Cover's universal portfolio is to build a wealth-weighted average which can be viewed as a buy-and-hold portfolio of portfolios. When an optimal portfolio exists, the wealth-weighted average c…
New analysis shows halting time is predictable for large models, improving optimization efficiency.
problem Understanding the average-case complexity of optimization algorithms for large-scale models.
method Average-case analysis of first-order methods on random least squares and neural networks.
result Halting time is independent of input distribution, leading to tighter convergence rates.
Improved rates for continual learning using SGD and last-iterate analysis.
problem Forgetting in overparameterized models after fitting multiple tasks.
method Developed novel SGD upper bounds for continual linear models and analyzed their performance.
result Established universal forgetting rates for continual learning.
Develops a new model-free approach to portfolio theory using rough paths.
problem Handles more general portfolios without probabilistic assumptions.
method Rough path theory for stochastic portfolio theory (SPT).
result Asymptotic growth rates of various portfolios match.
The paper shows neural networks can approximate functions over non-compact domains with non-polynomial activation.
problem Approximating functions over non-compact domains using neural networks.
method Using single-hidden-layer feedforward neural networks with non-polynomial activation functions over non-compact subsets of Euclidean spaces.
result Neural networks can approximate functions in weighted C k C^k C k -spaces and weighted Sobolev spaces over unbounded domains. The study shows how nonnegative Ricci curvature and metric cones imply the existence of abelian subgroups in the fundamental group of open manifolds.
problem Understanding the structure of fundamental groups of open manifolds with specific curvature properties.
method Analyzing the properties of the Riemannian universal cover and its asymptotic cones.
result The fundamental group of an open manifold with nonnegative Ricci curvature and certain geometric properties contains an abelian subgroup of finite index.
In this paper, we study adaptive online convex optimization, and aim to design a universal algorithm that achieves optimal regret bounds for multiple common types of loss functions. Existing universal methods are limited in the sense that they are optimal for only a subclass of loss functions. To address this limitatio…
Unified framework proves neural networks' ability to mimic complex tasks.
problem Lack of a single constructive framework for neural network universality.
method Introduces neural network approximate identity (nAI) and proves it leads to universality.
result Any nAI activation function is universal.
Universal adversarial patches prevent face detection in various frameworks.
problem Preventing face detection in state-of-the-art face detection systems.
method Investigated the phenomenon of patches that suppress face detection and proposed optimization-based approaches for automatic design.
result Universal adversarial patches can prevent face detection without introducing false positives.
The paper addresses the gap between theoretical and practical confidence set widths in universal inference.
problem Inference procedures can be overly conservative, leading to wider confidence sets than expected.
method The authors identify the source of asymptotic conservativeness and propose a remedy based on studentization and bias correction.
result The proposed method achieves exact asymptotic coverage at the nominal 1 − α 1-α 1 − α level, even under model misspecification. Random feature models approximate functions in Banach spaces efficiently.
problem Approximating functions in Banach spaces efficiently.
method Randomly initialized feature maps and linear readout training.
result Universal approximation in Bochner spaces for Banach space-valued models.
New bounds for optimal transport using Gaussian processes and rate-distortion functions.
problem Finding bounds for entropic optimal transport with mutual information constraints.
method Lifting technique to construct a Gaussian process and applying the majorizing measure theorem.
result Maximum expected inner product is equivalent to a truncated integral involving the rate-distortion function.
New methods for inferring, predicting, and estimating continuous-time, discrete-event processes.
problem Inferring, predicting, and estimating entropy rate of continuous-time, discrete-event processes.
method Bayesian structural inference extended with neural networks.
result Methods are competitive for prediction and entropy-rate estimation with state-of-the-art.
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.
A new method for faster optimization of noisy functions.
problem Optimizing noisy functions efficiently.
method A universal and adaptive second-order method for convex functions.
result Achieves O ( σ / T ) O(σ/ \sqrt{T}) O ( σ / T ) convergence for stochastic oracles and O ( 1 / T 3 ) O( 1 / T^3) O ( 1/ T 3 ) for deterministic oracles. Empirical study on UEEs reveals liquidity's role and universal recovery patterns.
problem Understanding and stabilizing financial markets affected by UEEs.
method Comparative analysis of UEEs over different years in US stock market.
result Liquidity is dominant in UEEs emergence and recovery patterns are universal.