329 papers
This paper establishes explicit upper bounds on the quadratic Wasserstein distance between trained single-layer neural networks and their Gaussian process limits, demonstrating that the approximation error decays polynomially with network width while accounting for the influence of architectural parameters and training dynamics.
This paper establishes non-asymptotic bounds on the efficiency of conformalized regression trained via SGD, revealing how prediction set length depends on training and calibration set sizes as well as the miscoverage level, and identifying phase transitions that guide optimal data allocation.
This paper theoretically demonstrates that in overparameterized two-layer ReLU networks trained below the edge of stability, data geometry dictates generalization by determining whether gradient descent learns shared patterns (for data hard to shatter) or favors memorization (for data easily shattered).
This paper introduces a principled framework for testing excessive influence in linear least-squares models by deriving exact influence formulas and their corresponding extreme value distributions, thereby enabling rigorous hypothesis tests to distinguish between natural sampling variation and problematic data subsets across various scientific domains.
The paper introduces SACP, a novel method that aggregates nonconformity scores from multiple predictive models into e-values using symmetric functions to generate valid and more efficient uncertainty sets within the conformal prediction framework.
This paper proposes a Bayesian nonparametric framework for finite mixture models with nonparametric components, establishing theoretical guarantees for component identifiability and near-polynomial posterior contraction rates while providing an efficient MCMC algorithm for inference.
This paper establishes a minimax theory for operator learning in Hilbert spaces, proving that even with higher regularity assumptions, learning generic Lipschitz operators from noisy samples inevitably suffers from a curse of sample complexity where the risk cannot decay at any algebraic rate.
This paper introduces Latent-IMH, an efficient Bayesian sampling method for inverse problems with expensive operators that leverages cost-effective approximations to shift computational costs to an offline phase, achieving significantly faster performance than state-of-the-art methods like NUTS.
This paper proposes a variational framework that interprets transformer layers as optimization iterations, enabling the design of a Nesterov-accelerated transformer architecture that outperforms standard baselines on language modeling tasks.
This paper proposes minimax-optimal online conformal prediction algorithms for non-stationary data streams with distribution drift, utilizing drift detection to adaptively update calibration sets and leveraging model stability to achieve optimal training-conditional cumulative regret.
This paper proposes a regularized online RLHF framework using Generalized Bilinear Preference Models to identify Nash Equilibria, establishing the first statistically efficient, dimension-free regret bounds for high-dimensional settings through two simple algorithms that leverage strong convexity and low-rank structures.
This paper proposes a conformal prediction framework for graph-valued outputs that ensures distribution-free coverage guarantees by utilizing Z-Gromov-Wasserstein distances for nonconformity scoring and introducing Score Conformalized Quantile Regression (SCQR) to generate adaptive prediction sets.
This paper proposes FreST Loss, a model-agnostic training objective that leverages the Joint Fourier Transform to align predictions with ground truth in the joint spatio-temporal frequency domain, thereby effectively decorrelating complex dependencies and outperforming state-of-the-art baselines on real-world datasets.
This study introduces Equilibrium-Informed Neural Networks (EINNs), a novel deep learning approach that reverses the traditional parameter-search process by inferring system parameters from candidate equilibrium states to efficiently detect critical bifurcation thresholds and tipping points in complex nonlinear dynamical systems.
This paper introduces Dictionary Based Pattern Entropy (DPE), a novel framework that combines Algorithmic and Shannon Information Theories to infer causal directions and identify driving subpatterns in symbolic sequences by quantifying how compact, rule-based patterns in a cause systematically reduce uncertainty in an effect, demonstrating robust performance across diverse synthetic and real-world datasets.
This paper applies a probabilistic machine learning framework to analyze Collatz stopping times up to $10^7$, demonstrating that a Bayesian hierarchical Negative Binomial regression outperforms a mechanistic odd-block generator in predictive likelihood while revealing that low-order modular structure significantly drives the observed heterogeneity.
This paper introduces the Volterra signature, a principled and interpretable feature representation for non-Markovian time series that combines universal approximation guarantees, time-reparameterization invariance, and efficient computation via linear state-space ODEs and kernel tricks to outperform existing path signature baselines in dynamic learning tasks.
This paper introduces an oracle-efficient learning algorithm for the Hybrid Online Learning setting with constrained adversaries that achieves statistical optimality by leveraging the Rademacher complexity of the learner's and adversary's function classes, while also providing a novel tool for computing equilibria in structured stochastic zero-sum games.
This paper establishes a rigorous variational and gradient-based equivalence between K-Means and differentiable Radial Basis Function networks, proving that the latter converges to the former as temperature vanishes and proposing Entmax-1.5 to ensure stable training for end-to-end differentiable clustering.
This paper introduces optimal prediction-augmented algorithms for testing the independence of distributions that maintain worst-case validity while significantly improving sample efficiency in high-dimensional settings when provided with accurate, albeit untrustworthy, auxiliary predictions.