New partition designs reduce star discrepancy in high-dimensional sampling.
problem Improving the expected star discrepancy in high-dimensional sampling.
method Developed non-equal volume partitions to achieve lower expected star discrepancy.
result Explicit upper bounds for expected star discrepancy under non-equal volume partitions.
Improved SGD learning for single index models reduces sample complexity.
problem Learning a single index model with optimal sample complexity.
method Using smoothed loss in online SGD to reduce sample complexity.
result Online SGD with smoothed loss achieves optimal sample complexity of d k ⋆ / 2 d^{k^\star/2} d k ⋆ /2 . Let f ⋆ f^{\star} f ⋆ be a function on R d \mathbb{R}^d R d with an assumption of a spectral norm v f ⋆ v_{f^{\star}} v f ⋆ . For various noise settings, we show that E ∥ f ^ − f ⋆ ∥ 2 ≤ ( v f ⋆ 4 log d n ) 1 / 3 \mathbb{E}\|\hat{f} - f^{\star} \|^2 \leq \left(v^4_{f^{\star}}\frac{\log d}{n}\right)^{1/3} E ∥ f ^ − f ⋆ ∥ 2 ≤ ( v f ⋆ 4 n l o g d ) 1/3 , where n n n is the sample size and f ^ \hat{f} f ^ is either a penalized lea…
Neural networks can achieve optimal sample complexity for learning single-index models.
problem Achieving optimal computational-statistical tradeoff in learning Gaussian single-index models.
method Unified gradient-based algorithm for training a two-layer neural network, adaptable to various loss and activation functions.
result Sample complexity of d s ⋆ / 2 ∨ d d^{s^\star/2} \lor d d s ⋆ /2 ∨ d matches the SQ lower bound up to a polylogarithmic factor. This work improves Q-learning for average-reward MDPs, reducing sample and communication complexities in federated settings.
problem Improving sample complexity of Q-learning for average-reward MDPs.
method Simple Q-learning algorithm with carefully chosen parameters for both single-agent and federated scenarios.
result Established first federated Q-learning algorithm for average-reward MDPs with provable efficiency in sample and communication complexities.
Study optimizes KSD estimation from samples, revealing Hilbert-Schmidt vs trace scales.
problem Optimizing estimation of Kernel Stein Discrepancy from samples.
method Identifying and comparing minimax scales for U-statistic and V-statistic.
result Hilbert-Schmidt norm of Stein covariance operator gives optimal scale.
A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include K K K -fold cross-validation ( K K K -CV), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Though these methods work well for lo…
The paper introduces methods to quantify uncertainty in sampling without replacement.
problem Accurately estimating parameters from finite populations sampled without replacement.
method Develops confidence sequences using Bayesian and empirical methods.
result Improved confidence intervals and sequences for sampling without replacement.
Sharp Lipschitz bounds for flow-matching and diffusion models with optimal sampling rates.
problem Establishing optimal Lipschitz regularity for flow-matching and diffusion models.
method Sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores.
result Achieves optimal sampling rate of d / N \sqrt{d}/N d / N for Euler-type samplers in dimension d d d . Introduces Star-Shaped DDPMs for non-Gaussian distributions.
problem Difficulties in defining DDPMs for non-Gaussian distributions.
method Star-shaped diffusion process, duality with specific Markovian diffusions, efficient algorithms.
result SS-DDPMs can model distributions like Beta, von Mises-Fisher, Dirichlet, Wishart.
Rotation invariant algorithms fail with hard labels sampled from sparse targets.
problem Rotation invariant algorithms fail to learn from hard labels sampled from sparse targets.
method Proving the excess risk of rotation invariant algorithms and proposing a simple non-rotation invariant algorithm.
result Rotation invariant algorithms incur an excess risk of $Ω\left(\frac{d-1}{n}
ight)$ , while non-rotation invariant algorithms have an excess risk of $O\left(\frac{s\log d}{n}
ight).
This paper bridges offline and online RL by studying policy finetuning with a reference policy.
problem Sample-efficient reinforcement learning in online and offline settings.
method Design of policy finetuning algorithms and analysis of sample complexity.
result Theoretical analysis shows that the optimal policy finetuning algorithm is either offline reduction or purely online RL.
The paper provides guarantees for learning nonlinear representations from multiple non-identically distributed data sources.
problem Learning from non-identically distributed and dependent data.
method Established statistical guarantees for learning general nonlinear representations from multiple data sources.
result The excess risk of the estimated function decays as a function of the sample complexity and task diversity.
Study shows computational and statistical gaps in Gaussian Single-Index Models.
problem Statistical and computational trade-offs in high-dimensional regression problems.
method Analysis of SQ and LDP frameworks, partial-trace algorithm.
result Computational algorithms require significantly more samples than information-theoretic limits.
Injective flows for star-like manifolds improve variational inference efficiency.
problem Efficiently modeling densities on star-like manifolds with exact Jacobian computation.
method Proposed injective flows for star-like manifolds with exact Jacobian computation.
result Exact Jacobian computation for star-like manifolds reduces computational cost to NFs.
Method identifies galaxies with recent star formation variations.
problem Identify galaxies with recent star formation variations.
method Approximate Bayesian Computation (ABC) with machine learning.
result Flexible star formation histories are needed for accurate modeling.
Improved sampling for diffusion models and log-concave distributions.
problem Efficient sampling for diffusion models and log-concave distributions.
method Algorithms for sampling with δ δ δ -error in p o l y l o g ( 1 / δ ) \mathrm{polylog}(1/δ) polylog ( 1/ δ ) steps using accurate score estimates. result Exponential improvement in complexity over previous results.
New lower bound shows bandit convex optimization is harder than linear bandits.
problem Establishing a lower bound for stochastic bandit convex optimization.
method Constructing a hard class of convex functions and analyzing posterior spread of Fisher information matrices.
result A Ω ~ ( d 5 / 4 T ) \widetildeΩ(d^{5/4}\sqrt{T}) Ω ( d 5/4 T ) lower bound on minimax expected regret. New lower bound shows bandit convex optimization is harder than previously thought.
problem Establishing a lower bound on the minimax expected regret for bandit convex optimization.
method Constructing a hard class of convex functions and analyzing the posterior spread of Fisher information matrices.
result A Ω ~ ( d 5 / 4 T ) \widetildeΩ(d^{5/4}\sqrt{T}) Ω ( d 5/4 T ) lower bound on the minimax expected regret. Three-layer networks learn complex hierarchical polynomials of multiple nonlinear features.
problem Understanding how neural networks learn hierarchical features of multiple nonlinear inputs.
method Examine a broad class of functions using three-layer neural networks, showing complete recovery and efficient learning.
result Three-layer neural networks trained via gradient descent can learn hierarchical polynomials of multiple nonlinear features efficiently.
Introduces Star-Shaped deviation measures for risk analysis.
problem Risk measurement and analysis in finance.
method Characterizes Star-Shaped deviation measures through acceptance sets and convex deviation measures.
result Exposes the relationship between Star-Shaped risk measures and deviation measures.
Gradient descent learns over-param neural nets better than NTK.
problem Learning over-parametrized neural networks with ReLU activations.
method Gradient descent from random initialization on a Gaussian input distribution.
result Gradient descent achieves population loss o ( 1 / d ) o(1/d) o ( 1/ d ) , while NTK achieves Ω ( 1 / d ) Ω(1/d) Ω ( 1/ d ) . This paper is concerned with offline reinforcement learning (RL), which learns using pre-collected data without further exploration. Effective offline RL would be able to accommodate distribution shift and limited data coverage. However, prior algorithms or analyses either suffer from suboptimal sample complexities or …
New method for LLMs to learn reasoning by optimizing latent variables.
problem Teaching LLMs to generate logical justifications for answers.
method Formalized reasoning as latent variable model, derived FEM objective, designed sampling schemes.
result Prompt Posterior Sampling (PPS) outperforms other schemes in learning to reason.
This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix M ⋆ ∈ R n × n \mathbf{M}^{\star}\in \mathbb{R}^{n\times n} M ⋆ ∈ R n × n , yet only a randomly perturbed version M \mathbf{M} M is observed. The noise matrix $\mathbf{M}-\mathbf{M}^{\s…
Neural networks can learn useful representations that kernels can't.
problem Learning functions that depend on only a few relevant directions.
method Gradient descent on a two-layer neural network.
result Improved sample complexity for learning polynomials.
New metrics boost A/B-test power by up to 210%.
problem High cost and type-II errors in A/B-tests.
method Learn metrics from short-term signals to maximize power.
result Statistical power increased by up to 210%.
Algorithm achieves optimal regret for unknown Lipschitz convex losses.
problem Online learning with unknown Lipschitz constant and target vector norm.
method Develops an online learning algorithm without knowledge of G G G or ∥ w ⋆ ∥ \|w_\star\| ∥ w ⋆ ∥ . result Matches optimal regret bound G ∥ w ⋆ ∥ T G\|w_\star\|\sqrt{T} G ∥ w ⋆ ∥ T up to logarithmic factors. Test-time training improves sampling efficiency in generative AI.
problem Efficient sampling from complex probability distributions.
method Test-time training (TTT) updates model weights based on partial generations and feedback.
result TTT can adapt to specific sampling tasks, improving sampling efficiency.
New star-shaped acceptability indexes generalize existing methods.
problem Generalizing existing acceptability measures.
method Characterizing acceptability indexes through star-shaped risk measures and sets.
result Introducing concrete examples linked to various financial measures.
A new method uses Shapley values to select important features for classification.
problem Feature selection for improving classification models.
method Classification game with Shapley value apportioning of hinge loss.
result Threshold 0 on SVEA value identifies significant features.
Paper proves conjecture about star-shaped curves evolving under GAPF, but not always preserves star shape.
problem What conditions guarantee global existence of Gage's area-preserving flow for nonconvex initial curves?
method Using Dittberner's singularity analysis theory, constructed a ``flying wing'' curve to show limitations.
result Gage's area-preserving flow does not always preserve star-shapedness of evolving curves.
HyperAgent improves RL exploration in large-scale problems.
problem Efficient exploration in large-scale reinforcement learning problems.
method Hypermodel framework for incremental posterior approximation without conjugacy.
result HyperAgent achieves logarithmic per-step computational complexity and sublinear regret.
Algorithm learns weight matrix from single trajectory of nonlinear dynamical system.
problem Learning weight matrix from a single trajectory of nonlinear dynamical system.
method Algorithm uses global stability and well-conditioned covariance to recover weight matrix.
result Algorithm recovers weight matrix with optimal sample complexity and linear running time.
In this article, we introduce the notion of star-Ricci tensors in the real hypersurfaces of complex quadric Q m Q^m Q m . It is proved that there exist no Hopf hypersurfaces in Q m , m ≥ 3 Q^m,m\geq3 Q m , m ≥ 3 , with commuting star-Ricci tensor or parallel star-Ricci tensor. As a generalization of star-Einstein metric, star-Ricci solitons on M M M …
Classifies star products on Lie algebroid duals and extends to projectable quantizations.
problem Classifying and extending quantizations on Lie algebroid duals.
method Classification through second Lie algebroid cohomology, extension to projectable quantizations.
result Quantization commutes with reduction in the considered setting.
New set-valued star-shaped risk measures introduced for better risk assessment.
problem Improving risk assessment in financial contexts.
method Developed new set-valued star-shaped risk measures and proved their representation theorems.
result Set-valued star-shaped risk measures can be represented as unions of set-valued convex risk measures.
Flow turns star-shaped curves into circles.
problem Transforming star-shaped curves into circles.
method Gage's area-preserving flow.
result Curves evolve into circles over time.
The paper studies dynamic star-shaped risk measures and their representation.
problem Representing dynamic star-shaped risk measures and their properties.
method Representation theorems for dynamic monetary and star-shaped risk measures.
result Dynamic star-shaped risk measures can be represented as the lower envelope of a family of dynamic convex risk measures.
Paper disproves symmetry of stars at infinity in a specific graph.
problem Symmetry of stars at infinity in a specific graph.
method Defined incidence geometry of stars at infinity; provided an example.
result Relation of one boundary point being included in a star of another is not symmetric.
Study star products on Poisson manifolds compatible with reduction.
problem Finding star products compatible with coisotropic reduction.
method Compute second constraint Hochschild cohomology of constraint algebra.
result Determine infinitesimal star products on Poisson manifolds.
Study shows sample complexity for learning optimal policies in SSP with generative model.
problem Learning optimal policies in Stochastic Shortest Path problems.
method Derive and prove lower and upper bounds on sample complexity.
result Lower bound of Ω ( S A B ⋆ 3 / ( c min ε 2 ) ) Ω(SAB_{\star}^3/(c_{\min}ε^2)) Ω ( S A B ⋆ 3 / ( c m i n ε 2 )) samples for general case, and up to logarithmic factors for bounded hitting time condition. The paper characterizes dynamic return and star-shaped risk measures via BSDEs.
problem Characterizing dynamic return and star-shaped risk measures.
method Characterization of star-shaped functionals and BSDEs.
result Existence of convex BSDEs with non-empty set of supersolutions.
Deform moment map on symplectic connections using star product algebras.
problem Understanding symplectic connections and their deformations.
method Study vector bundle of Fedosov star product algebras, formal connection, curvature, and star product trace.
result Showed star product trace as a formal symplectic form and moment map.
CasVAE outperforms supervised methods for star-galaxy classification.
problem Challenges in machine learning for astronomy data.
method Cascade Variational Auto-Encoder (CasVAE) for unsupervised star-galaxy classification.
result CasVAE outperforms baseline models in accuracy and stability.
Paper analyzes Birkhoff relaxation for graph alignment, providing theoretical guarantees.
problem Finding vertex correspondence between two graphs to maximize edge overlap.
method Birkhoff relaxation as a convex relaxation of the quadratic assignment problem (QAP).
result Theoretical guarantees on the performance of Birkhoff relaxation under specific conditions.
Study shows offline RL under Q ⋆ Q^\star Q ⋆ -approximation and partial coverage is harder than previously thought.
problem Theoretical limits of offline reinforcement learning under Q ⋆ Q^\star Q ⋆ -approximation and partial coverage. method Introduced a decision-estimation framework to decompose offline RL complexity into decision and value estimation errors.
result Answered the open question by proving sample inefficiency under partial coverage is not guaranteed by Q ⋆ Q^\star Q ⋆ -realizability and Bellman completeness. We compare the star surgery operations introduced in [KS] to the generalized rational blow-down. We show that star surgery shares the properties that make rational blow-down useful for constructions of small exotic symplectic 4-manifolds. Then we show that star surgery operations provide a strictly more general class o…