Related papers: Reducing the Computational Complexity of Pseudoinv…

This paper considers a class of reinforcement learning problems, which involve systems with two types of states: stochastic and pseudo-stochastic. In such systems, stochastic states follow a stochastic transition kernel while the…

After Strassen presented the first sub-cubic matrix multiplication algorithm, many Strassen-like algorithms are presented. Most of them with low asymptotic cost have large hidden leading coefficient which are thus impractical. To reduce the…

Given a matrix $A$ of dimension $M \times N$ and a vector $\vec{b}$, the quantum linear system (QLS) problem asks for the preparation of a quantum state $|\vec{y}\rangle$ proportional to the solution of $A\vec{y} = \vec{b}$. Existing QLS…

Model-free reinforcement learning has been successfully applied to a range of challenging problems, and has recently been extended to handle large neural network policies and value functions. However, the sample complexity of model-free…

The field of Quantum Machine Learning (QML) has emerged recently in the hopes of finding new machine learning protocols or exponential speedups for classical ones. Apart from problems with vanishing gradients and efficient encoding methods,…

The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…

Recent works on quantum algorithms for solving semidefinite optimization (SDO) problems have leveraged a quantum-mechanical interpretation of positive semidefinite matrices to develop methods that obtain quantum speedups with respect to the…

We propose a soft gradient boosting framework for sequential regression that embeds a learnable linear feature transform within the boosting procedure. At each boosting iteration, we train a soft decision tree and learn a linear input…

We introduce, Q-Sparse, a simple yet effective approach to training sparsely-activated large language models (LLMs). Q-Sparse enables full sparsity of activations in LLMs which can bring significant efficiency gains in inference. This is…

Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of…

This study presents a novel computer system performance optimization and adaptive workload management scheduling algorithm based on Q-learning. In modern computing environments, characterized by increasing data volumes, task complexity, and…

The resurgence of machine learning has increased the demand for high-performance basic linear algebra subroutines (BLAS), which have long depended on libraries to achieve peak performance on commodity hardware. High-performance BLAS…

We study model-free Q-learning in finite-horizon episodic Markov Decision Processes (MDPs) with stationary dynamics across episodes. We identify a central issue in nascent model-free posterior-sampling works: the reliance on delayed…

Humans often think of complex tasks as combinations of simpler subtasks in order to learn those complex tasks more efficiently. For example, a backflip could be considered a combination of four subskills: jumping, tucking knees, rolling…

This paper considers fast algorithms for operations on linearized polynomials. We propose a new multiplication algorithm for skew polynomials (a generalization of linearized polynomials) which has sub-quadratic complexity in the polynomial…

We consider the problem of solving linear systems of equations arising with limited-memory members of the restricted Broyden class of updates and the symmetric rank-one (SR1) update. In this paper, we propose a new approach based on a…

Deep learning models in recommender systems are usually trained in the batch mode, namely iteratively trained on a fixed-size window of training data. Such batch mode training of deep learning models suffers from low training efficiency,…

Obtaining the inverse of a large symmetric positive definite matrix $\mathcal{A}\in\mathbb{R}^{p\times p}$ is a continual challenge across many mathematical disciplines. The computational complexity associated with direct methods can be…

Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…

Reinforcement learning (RL) has emerged as a promising strategy for finetuning small language models (SLMs) to solve targeted tasks such as math and coding. However, RL algorithms tend to be resource-intensive, taking a significant amount…