{"total":31,"items":[{"citing_arxiv_id":"2607.00647","ref_index":59,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Not All Prediction Targets Keep Training-Free Diffusion Guidance on the Manifold","primary_cat":"cs.CV","submitted_at":"2026-07-01T09:01:13+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"x-prediction maintains manifold adherence during training-free diffusion guidance better than ε- or v-prediction, per theoretical analysis and experiments on bird classification and style transfer.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2607.00538","ref_index":13,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Failure of Convex-Hull Bounds under Log-Convex Tails","primary_cat":"math.FA","submitted_at":"2026-07-01T07:28:32+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2607.00207","ref_index":65,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Homogenization of $\\ell_2$-Adversarial Training in High-Dimensions: Exact Dynamics under Stochastic Gradient Descent","primary_cat":"math.OC","submitted_at":"2026-06-30T21:38:10+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.25942","ref_index":37,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Elliptical Regularized Hotelling Testing for High Dimensional Data","primary_cat":"stat.ME","submitted_at":"2026-06-24T15:19:15+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.22008","ref_index":56,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"An Optimal Transportation Approach for Improved Confidence Intervals","primary_cat":"stat.ME","submitted_at":"2026-06-20T12:15:24+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"An optimal transport method is proposed to construct confidence intervals with improved coverage, including theoretical consistency results, error bounds, and simulation comparisons.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.17319","ref_index":35,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Tight $L_\\infty$ Sample Complexity for Low-Degree and Sparse Boolean Polynomials","primary_cat":"stat.ML","submitted_at":"2026-06-15T22:00:03+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.24903","ref_index":11,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"A Spectral Phase Diagram for Binary Few-Shot Classification: Intrinsic Dimensionality, Geometric Saturation, and Representational Diagnosis","primary_cat":"cs.LG","submitted_at":"2026-06-12T16:46:24+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.12143","ref_index":28,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Continuous stochastic flows driven by white noise and their duals","primary_cat":"math.PR","submitted_at":"2026-06-10T14:35:16+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Characterizes duals of white-noise-driven continuous stochastic flows by explicit SDEs and introduces a self-dual polynomially self-repelling flow model.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.06483","ref_index":46,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Statistically and Computationally Optimal Estimation and Inference of Common Subspaces","primary_cat":"math.ST","submitted_at":"2026-06-04T17:58:14+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.06333","ref_index":3,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Subspace-Aware Sparse Autoencoders for Effective Mechanistic Interpretability","primary_cat":"cs.LG","submitted_at":"2026-06-04T16:08:25+00:00","verdict":"CONDITIONAL","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.05032","ref_index":37,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Gaussian mean width strong converse bound on the classical identification capacity of quantum channels","primary_cat":"quant-ph","submitted_at":"2026-06-03T16:00:02+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.03807","ref_index":23,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Collision Resistance of Single-Layer Neural Nets","primary_cat":"cs.CR","submitted_at":"2026-06-02T15:52:45+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.30266","ref_index":61,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Wasserstein Least Squares: A Canonical Regression Method for Probability Distributions","primary_cat":"math.ST","submitted_at":"2026-05-28T17:28:30+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.02608","ref_index":31,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Pruning Deep Neural Networks via the Marchenko--Pastur Distribution","primary_cat":"cs.LG","submitted_at":"2026-05-23T19:44:02+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"Marchenko-Pastur random-matrix pruning of DNNs yields theoretical certificates for accuracy preservation under small fine-tuning and empirical ImageNet results with 50-60% MAC reduction and sub-2pp accuracy drops on ViT and CNN models.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.22865","ref_index":32,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Multi-Dimensional Matching in Market Design","primary_cat":"cs.GT","submitted_at":"2026-05-19T19:35:03+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"Proposes SVD-based reduction of multi-dimensional matching to 1D problem for O(N log N) computation that approximates Nash Social Welfare under low effective dimensionality.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.19654","ref_index":85,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Hardness and Approximation for Coloring Digraphs","primary_cat":"cs.DS","submitted_at":"2026-05-19T10:44:44+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.19364","ref_index":41,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Optimal Spectral Algorithms for Correlated Two-view Models in High Dimensions","primary_cat":"math.ST","submitted_at":"2026-05-19T04:55:13+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.18744","ref_index":17,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Lattice random-field Widom--Rowlinson models","primary_cat":"math.PR","submitted_at":"2026-05-18T17:58:51+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Random fields destroy phase transitions in low-dimensional Widom-Rowlinson models but preserve them in high dimensions for large densities.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.10290","ref_index":37,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Characterizing the Generalization Error of Random Feature Regression with Arbitrary Data-Augmentation","primary_cat":"stat.ML","submitted_at":"2026-05-11T09:52:21+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"∂ζξα,λ(0) then follows from an appropriate differentiation lemma, formulated below in the formalism of stochastic domination. Lemma 9(Differentiation under uniform stochastic control).Let (Un)n∈N and (Vn)n∈N be sequences of random holomorphic functions fromCtoC. Fixζ∈Candr >0. Suppose there existsξ n(ζ, r)>0such that sup ζ′∈S(ζ,r) Un(ζ ′)−V n(ζ ′) ≺s ξn(ζ, r).(37) Then, the derivatives atζsatisfy ∂Un ∂ζ (ζ)− ∂Vn ∂ζ (ζ) ≺s ξn(ζ, r) r .(38) Proof.By Cauchy's integral formula for the derivative of a holomorphic function, ∂ ∂ζ (Un −V n)(ζ) = 1 2πi I ζ′∈S(ζ,r) Un(ζ ′)−V n(ζ ′) (ζ ′ −ζ) 2 dζ ′ . Taking the module and noting that the maximum of |Un(ζ ′)−V n(ζ ′)| over the circle S(ζ, r) controls the integral, we"},{"citing_arxiv_id":"2605.08485","ref_index":78,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Sinkhorn Treatment Effects: A Causal Optimal Transport Measure","primary_cat":"stat.ML","submitted_at":"2026-05-08T21:03:11+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.05591","ref_index":102,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"In-Context Positive-Unlabeled Learning","primary_cat":"stat.ML","submitted_at":"2026-05-07T02:17:53+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.01632","ref_index":22,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Perturb and Correct: Post-Hoc Ensembles using Affine Redundancy","primary_cat":"cs.LG","submitted_at":"2026-05-02T22:48:11+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.26913","ref_index":49,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Generalization of Zeroth-Order Method for Quotients of Quadratic Functions","primary_cat":"math.OC","submitted_at":"2026-04-29T17:23:40+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"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.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"it holds w.r.t. (13) that Exk∼X k|V k=vk[ D ATAvk, xk E xk] = 2 d−1 PBTBv k ATAvk = 2 d−1 grad∥Avk∥2.(14) Here, since we are not aware ofBTBand, hence, working on the generalized sphere [9] is not possible, we propose a more general and unconstrained sampling approach. More precisely, we chosexk ∼ U(S d−1)uniformly distributed on the entire unit sphere [49, Ex. 3.3.7] given by xk := x ∥x∥ , x∼ N(0, I d)(15) with propertyEx∼N(0,I d)[xk(xk)T] =E xk∼U(S d−1)[xk(xk)T] = 1 d Id. Therefore, we resolved the issue for discussing conditional distributions as we havePX k|V k=· =P X k =U(S d−1), which is necessary for the construction in [8, 9], cf. (13). Afterwards, we aim to solve the following optimal step size problem in each iterationk∈Ngiven by"},{"citing_arxiv_id":"2604.18181","ref_index":147,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Spectral approximation for the separable covariance mixture model","primary_cat":"math.ST","submitted_at":"2026-04-20T12:38:04+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"which is used in most works on eigen inference (cf. Ding et al. (2024); El Karoui (2008); Kong and Valiant (2017); Ledoit and Wolf (2015)). Assumption (A3) is a standard moment bound on the entries ofX. Such assumptions on the mo- ments or tail behavior of the entries also arise in most works on random matrix theory (RMT) (cf. Bai and Silverstein (2010); Vershynin (2018); Yao et al. (2015)). Proving results of RMT under minimal moment assumptions can be highly challenging (cf. Khorunzhy et al. (1996); Tao and Vu (2010)) and some results, such as local laws, commonly assume the existence of all moments (cf. Alt et al. (2017); Knowles and Yin (2017)). Assumption (A4) is specific to the model under consideration and thus cannot immediately be"},{"citing_arxiv_id":"2604.14277","ref_index":50,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Entanglement and circuit complexity in finite-depth random linear optical networks","primary_cat":"quant-ph","submitted_at":"2026-04-15T18:00:00+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"In finite-depth random linear optical circuits, entanglement grows at most diffusively and robust circuit complexity scales similarly, with depth bounds ensuring near-maximal subsystem entanglement and closeness to Haar unitaries.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.12563","ref_index":29,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Latent community paths in VAR-type models via dynamic directed spectral co-clustering","primary_cat":"stat.ME","submitted_at":"2026-04-14T10:45:35+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"[wm]ij ˜Am,ℓ(i,j) ) ≤E ( [wm]2 ij ˜Am,ℓ(i,j) ) ≤c1 ˜Am,ℓ(i,j). Therefore the matrix-variance parameter satisfies v2 :=  ∑ m,ℓ,i,j E [ Xm,ℓ(i,j) 2] ≤max m=1,...,s c1 δm +τm max   max i ∑ j ˜Am,ℓ(i,j) [Om]ii +τm ,max j ∑ i ˜Am,ℓ(i,j) [Pm]jj +τm   ≤c1 c2 , since each normalized row and column sum is at most1. By the matrix Bernstein inequality (Vershynin, 2018, Theorem 5.4.1), P ( ∥¯CS−˜ΦS∥≥a ) ≤4sqexp ( − a2 2v2 + 2 3La ) . Take a=M √ c1 log(8sq/ϵ) c2 withM >0sufficiently large. Since Assumption 4.7 givesc 2≍sqBsq andB sq = Ω(log(sq)/(sq)), we have c2 ≳log(sq), so the linear term 2 3Lais of smaller order thana 2 and the exponent is bounded above by −log(8sq/ϵ)forMlarge enough. Hence P ( ∥¯CS−˜ΦS∥≤a ) ≥1−ϵ"},{"citing_arxiv_id":"2602.05742","ref_index":15,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Fast Rates for Nonstationary Weighted Risk Minimization","primary_cat":"stat.ML","submitted_at":"2026-02-05T15:10:07+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2512.22997","ref_index":31,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Generalised Entanglement Entropies from Unit-Invariant Singular Value Decomposition","primary_cat":"hep-th","submitted_at":"2025-12-28T16:51:19+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2511.01680","ref_index":56,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Making Interpretable Discoveries from Unstructured Data: A High-Dimensional Multiple Hypothesis Testing Approach","primary_cat":"econ.EM","submitted_at":"2025-11-03T15:42:32+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2507.21883","ref_index":63,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Sampling (noisy) quantum circuits through randomized rounding","primary_cat":"quant-ph","submitted_at":"2025-07-29T14:56:17+00:00","verdict":"CONDITIONAL","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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].","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2308.02480","ref_index":70,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Statistical Inference for Linear Functions of Eigenvectors with Small Eigengaps","primary_cat":"math.ST","submitted_at":"2023-08-04T17:48:10+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Proves approximate Gaussianity of debiased linear forms of eigenvectors in matrix denoising and spiked PCA models under Gaussian noise, then constructs bias/variance estimators yielding minimax-optimal confidence intervals without sample splitting.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}