A threshold κ=Θ(1/√α) (α=m/n) separates easy collision finding from OGP-based exponential lower bounds against online algorithms in single-layer binary NNs.
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Comput.54, 2 (2025), 193–232
31 Pith papers cite this work. Polarity classification is still indexing.
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No universal constant exists allowing convex-hull bounds with controlled L_log norms for the difference set of arbitrary finite T under symmetric Weibull(r) processes when 0<r<1.
Derives ODE deterministic equivalents and an adversarial homogenized SDE for SGD iterates in high-dim ℓ2-adversarial training, showing no constant learning rate ensures monotone descent for single-class adversarial least squares and equivalence to adaptive regularized standard SGD.
Minimax sample complexity for uniform L_infty estimation is Theta(n^{d+1}) for degree-d polynomials and Theta(ns^2) for s-sparse Fourier-Walsh polynomials under noise, exceeding noiseless rates by factors of n and s.
Establishes statistical and computational optimality thresholds for common subspace estimation and inference under varying SNR regimes, including an impossibility result for adaptive confidence intervals below strong inference SNR.
SASA replaces single-vector decoders in SAEs with learned subspaces plus block sparsity and nuclear-norm regularization, proving that a single group becomes the global minimizer once block size meets intrinsic dimension and yielding polynomial rather than exponential sample complexity.
A Gaussian mean width bound in weighted geometry yields a single-letter strong converse for the classical identification capacity of quantum channels, improving known results for depolarizing, Pauli, erasure, and amplitude damping channels.
Introduces a TAP-motivated framework and constructs explicit parameter-free spectral algorithms that achieve strong detection and weak recovery thresholds in three canonical correlated two-view models with matching lower bounds.
Random fields destroy phase transitions in low-dimensional Widom-Rowlinson models but preserve them in high dimensions for large densities.
The test error of random-feature ridge regression with arbitrary data augmentation admits a closed-form asymptotic characterization in the proportional regime that depends only on population covariances and augmentation statistics.
The Sinkhorn treatment effect is a new entropic optimal transport measure of divergence between counterfactual distributions that admits first- and second-order pathwise differentiability, debiased estimators, and asymptotically valid tests for distributional treatment effects.
PUICL is a transformer pretrained on synthetic PU data from structural causal models that solves positive-unlabeled classification via in-context learning without gradient updates or fitting.
Decomposes excess risk in nonstationary weighted ERM into learning and drift terms, then proves oracle inequalities under mixing that recover minimax rates in stationary cases.
Generalized entanglement entropies are constructed via left-, right-, and bi-invariant unit-invariant singular value decompositions to ensure scale invariance for non-Hermitian and rectangular operators in quantum mechanics, random matrices, and Chern-Simons theory.
Proposes ERHT-CC test based on spatial median and spatial-sign covariance with Cauchy aggregation over ridge parameters, deriving asymptotic normality and local power under elliptical symmetry.
Defines saturation index S(K) = erank(Σ̂_W^(K))/K that identifies when linear discriminant stabilizes in binary few-shot classification, with empirical phase diagram and stopping-rule AUC of 0.752 on 17 tasks.
Characterizes duals of white-noise-driven continuous stochastic flows by explicit SDEs and introduces a self-dual polynomially self-repelling flow model.
Wasserstein least squares extends Euclidean least squares to distribution-valued responses via convex analysis, yielding n^{-1/2} rates under template deformation and faster barycenter rates than prior work.
Establishes n^{1-ε}-hardness of approximation for dichromatic number and acyclic number on tournaments, plus polynomial-time approximations for ℓ-dicolorable digraphs and special dense cases.
Perturb-and-Correct generates epistemically diverse predictors from a single pretrained network via hidden-layer perturbations followed by affine least-squares corrections that enforce agreement on calibration data.
Resolvents of the sample covariances in the separable mixture model approximate deterministic matrices defined via solutions to a dual system of equations, without simultaneous diagonalizability assumptions.
Dynamic directed spectral co-clustering on degree-corrected stochastic co-blockmodels embedded in VAR-type models uncovers latent community paths, with non-asymptotic misclassification bounds and applications to U.S. payrolls and global stock volatilities.
A new framework combines AI-derived concept embeddings with high-dimensional selective inference to enable statistically principled, interpretable discovery from unstructured data in empirical economics.
Gaussian randomized rounding on two-qubit marginals of depth-D circuits with local depolarizing noise p yields samples whose expected Max-Cut cost matches the noisy quantum device up to an approximation ratio of 1-O[(1-p)^D].
citing papers explorer
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Characterizing the Generalization Error of Random Feature Regression with Arbitrary Data-Augmentation
The test error of random-feature ridge regression with arbitrary data augmentation admits a closed-form asymptotic characterization in the proportional regime that depends only on population covariances and augmentation statistics.
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Latent community paths in VAR-type models via dynamic directed spectral co-clustering
Dynamic directed spectral co-clustering on degree-corrected stochastic co-blockmodels embedded in VAR-type models uncovers latent community paths, with non-asymptotic misclassification bounds and applications to U.S. payrolls and global stock volatilities.
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Generalization of Zeroth-Order Method for Quotients of Quadratic Functions
A generalized zeroth-order method samples random directions on the sphere to optimize quotients of quadratics, estimates Riemannian derivatives with surrogates, and yields an accelerated algorithm outperforming prior work.