arXiv research

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

Mirzakhani volumes of moduli spaces are polylogarithmic.

Study higher genus polylogarithms under Riemann surface degenerations.

Investigates webs related to cluster algebras and polylogarithms.

QATS efficiently decodes HMMs with polylogarithmic complexity.

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

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

Improved GNN simulation of WL test with exponentially lower complexity.

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

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…

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

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

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…

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

Efficiently estimates binary product distributions with privacy.

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

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

Constructs manifolds from quantum codes with novel geometric properties.

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

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…

Improved guarantees for misspecified kernelized bandit optimization.

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

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

In this paper, we study local solutions F=(F1,..,Fn) of a general functional equation of the form F1(U1(x,y))+....+Fn(Un(x,y))=0. A such equation will be called an ``abelian functional equation'' (Afe). We will restrict ourselves to the case when the inner functions Ui's are real rational functions. First we prove that…

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 …

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 …

Private optimization faster on interpolation problems with quadratic growth.

New algorithms minimize regret in both adversarial and stochastic contexts.

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

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}…

Paper presents a faster classical algorithm for principal component regression.

Machine learning has recently emerged as a fruitful area for finding potential quantum computational advantage. Many of the quantum enhanced machine learning algorithms critically hinge upon the ability to efficiently produce states proportional to high-dimensional data points stored in a quantum accessible memory. Eve…

In this paper, we give improved bounds for the computational complexity of computing with planar algebraic curves. More specifically, for arbitrary coprime polynomials $f$, $g \in \mathbb{Z}[x,y]$ and an arbitrary polynomial $h \in \mathbb{Z}[x,y]$, each of total degree less than $n$ and with integer coefficients of ab…

Efficient active learning with abstention reduces label complexity exponentially.

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 …

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

Improved bounds for estimating discrete distributions in KL divergence.

This work proves that large models can be compressed significantly without losing performance.

We study the question of whether parallelization in the exploration of the feasible set can be used to speed up convex optimization, in the local oracle model of computation. We show that the answer is negative for both deterministic and randomized algorithms applied to essentially any of the interesting geometries and…

A new method for efficient Gaussian process inference using sparse approximations.

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

New algorithms optimize without tuning, matching tuned SGD performance.

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

New method controls linear systems with adversarial disturbances.

Within the framework of statistical learning theory it is possible to bound the minimum number of samples required by a learner to reach a target accuracy. We show that if the bound on the accuracy is taken into account, quantum machine learning algorithms for supervised learning---for which statistical guarantees are …

New algorithm reduces matrix multiplication time for sparse matrices.

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