arXiv research

New algorithms achieve optimal regret in sliding window model with limited memory.

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

Mirzakhani volumes of moduli spaces are polylogarithmic.

Study higher genus polylogarithms under Riemann surface degenerations.

Investigates webs related to cluster algebras and polylogarithms.

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

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

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…

New constraints on space and adaptivity in bandits force more batches and memory use.

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

We consider the problem of online prediction in a marginally stable linear dynamical system subject to bounded adversarial or (non-isotropic) stochastic perturbations. This poses two challenges. Firstly, the system is in general unidentifiable, so recent and classical results on parameter recovery do not apply. Secondl…

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

QATS efficiently decodes HMMs with polylogarithmic complexity.

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

New method compresses non-Gaussian distributions exponentially.

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…

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…

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…

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

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 GNN simulation of WL test with exponentially lower complexity.

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

New algorithms minimize regret in both adversarial and stochastic contexts.

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

Improved bounds for estimating discrete distributions in KL divergence.

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

Improved guarantees for misspecified kernelized bandit optimization.

Efficiently estimates binary product distributions with privacy.

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

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

Optimal hidden-target learning for online inventory optimization on general convex sets.

New algorithms optimize without tuning, matching tuned SGD performance.

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 …

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…

Study growth of systoles in arithmetic manifolds, focusing on $k$-dimensional cases.

We show how to solve a number of problems in numerical linear algebra, such as least squares regression, $\ell_p$-regression for any $p \geq 1$, low rank approximation, and kernel regression, in time $T(A) \poly(\log(nd))$, where for a given input matrix $A \in \mathbb{R}^{n \times d}$, $T(A)$ is the time needed to com…

Heretofore, neural networks with external memory are restricted to single memory with lossy representations of memory interactions. A rich representation of relationships between memory pieces urges a high-order and segregated relational memory. In this paper, we propose to separate the storage of individual experience…

In this paper, we propose a dual memory structure for reinforcement learning algorithms with replay memory. The dual memory consists of a main memory that stores various data and a cache memory that manages the data and trains the reinforcement learning agent efficiently. Experimental results show that the dual memory …

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

Stable Hadamard Memory improves reinforcement learning by efficiently managing memory.

New memory allocation scheme improves image generation performance.

DAM with MRL improves relational reasoning in MANNs.

New algorithms for privately learning decision lists and halfspaces.

We discuss memory models which are based on tensor decompositions using latent representations of entities and events. We show how episodic memory and semantic memory can be realized and discuss how new memory traces can be generated from sensory input: Existing memories are the basis for perception and new memories ar…

mGRN improves multivariate time series prediction by managing marginal and joint memories.

Model combines long-term and short-term memory using conceptors.

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