arXiv research

Study shows sample complexity for multicalibration is Θ(ε^-3) with polylogarithmic factors.

New method uses higher-order Langevin dynamics for efficient parallel sampling.

Paper solves no-swap regret minimization for combinatorial bandits with polylogarithmic dependence on N.

Recent theoretical work has guaranteed that overparameterized networks trained by gradient descent achieve arbitrarily low training error, and sometimes even low test error. The required width, however, is always polynomial in at least one of the sample size $n$, the (inverse) target error $1/ε$, and the (inverse) fail…

New algorithm selects best distribution privately in nearly-linear time.

Sampling logconcave functions arising in statistics and machine learning has been a subject of intensive study. Recent developments include analyses for Langevin dynamics and Hamiltonian Monte Carlo (HMC). While both approaches have dimension-independent bounds for the underlying $\mathit{continuous}$ processes under s…

Quantum machine learning can't achieve polylogarithmic runtimes, even with quantum data access.

Neural networks can achieve optimal sample complexity for learning single-index models.

Mirzakhani volumes of moduli spaces are polylogarithmic.

Study higher genus polylogarithms under Riemann surface degenerations.

Investigates webs related to cluster algebras and polylogarithms.

Efficiently estimates binary product distributions with privacy.

QATS efficiently decodes HMMs with polylogarithmic complexity.

Private optimization faster on interpolation problems with quadratic growth.

A new algorithm estimates mean adaptively to covariance, faster and more flexible than existing methods.

In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $γ\in(0,1)$ we provide an algorithm that computes an $ε$-optimal strategy with high-probability given $\tilde{O}((1 - γ)^{-3}…

We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix. We circumvent the non-convex optimization problem using improper learning: carefully overparameterize the class of LDSs by a polylogarithmic factor, in exchange for con…

Standard results in stochastic convex optimization bound the number of samples that an algorithm needs to generate a point with small function value in expectation. More nuanced high probability guarantees are rare, and typically either rely on "light-tail" noise assumptions or exhibit worse sample complexity. In this …

A wide range of fundamental machine learning tasks that are addressed by the maximum a posteriori estimation can be reduced to a general minimum conical hull problem. The best-known solution to tackle general minimum conical hull problems is the divide-and-conquer anchoring learning scheme (DCA), whose runtime complexi…

New algorithm reduces regret in online portfolio and quantum state learning.

Improved GNN simulation of WL test with exponentially lower complexity.

Piecewise polynomial interpolation-based gradient descent reduces oracle complexity for smooth loss functions.

New method proves fast regret bounds for online RLHF with generalized preferences.

Optimal sampling bounds for various classification losses under different regularization terms.

We prove optimal subspace embedding conjecture up to sub-polylogarithmic factors.

The paper explores the geometry of the Spence-Kummer trilogarithm equation and its Galois analogue.

Neural network learns low-dimensional polynomials with SGD near information-theoretic limit.

Motivated by a sampling problem basic to computational statistical inference, we develop a nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical analysis. Given an $n\times n$ SDDM matrix ${\bf \mathbf{M}}$, and a constant $-1 \leq p \leq 1$, our algorithm gives efficient access to a…

A recent line of research on deep learning focuses on the extremely over-parameterized setting, and shows that when the network width is larger than a high degree polynomial of the training sample size $n$ and the inverse of the target error $ε^{-1}$, deep neural networks learned by (stochastic) gradient descent enjoy …

Improved sampling from high-dimensional Gaussians using smoothed scores.

New algorithm for RL with horizon-free reward-free exploration for linear MDPs.

Paper presents a faster classical algorithm for principal component regression.

Protocol learns pure quantum states with minimal disturbance.

We present a novel parallelisation scheme that simplifies the adaptation of learning algorithms to growing amounts of data as well as growing needs for accurate and confident predictions in critical applications. In contrast to other parallelisation techniques, it can be applied to a broad class of learning algorithms …

Efficiently estimates Gaussian distributions privately and robustly.

Kähler information manifolds for signal filters in weighted Hardy spaces are explored.

Paper analyzes online tensorial ICA convergence with stochastic approximation.

New bounds show current methods overestimate system parameter errors.

Constructs manifolds from quantum codes with novel geometric properties.

Sparse covariance estimation in the vertical-split model achieves exponential improvement over dense estimates.

Quantum algorithm speeds up Lasso regression by quadratically faster per iteration.

New study reveals a polynomial penalty for adapting to unknown margin parameters in batched nonparametric bandits.

The paper analyzes GD for KANs, deriving bounds for training, generalization, and privacy.

Improved guarantees for misspecified kernelized bandit optimization.

Privacy improves robustness in statistical estimation.

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in $\mathbb{R}^{n_1 \times n_2 \times \cdots \times n_d}$. It focuses on the task of estimatin…

New algorithms for privately learning decision lists and halfspaces.

Gradient descent learns a neuron in noisy data.