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Quantization became a necessary tool for serving ever-increasing Large Language Models (LLMs). RTN (Round-to-Nearest) is perhaps the simplest quantization technique that has been around well before LLMs surged to the forefront of machine…

Quantum measurements are a fundamental component of quantum computing. However, on modern-day quantum computers, measurements can be more error prone than quantum gates, and are susceptible to non-unital errors as well as non-local…

We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…

Recent advances in large language models (LLMs), such as OpenAI-o1 and DeepSeek-R1, have demonstrated the effectiveness of test-time scaling, where extended reasoning processes substantially enhance model performance. Despite this, current…

Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…

We study nearly-linear time approximation algorithms for non-preemptive scheduling problems in two settings: the unrelated machine setting, and the identical machine with job precedence constraints setting, under the well-studied objectives…

The inverse-free extreme learning machine (ELM) algorithm proposed in [4] was based on an inverse-free algorithm to compute the regularized pseudo-inverse, which was deduced from an inverse-free recursive algorithm to update the inverse of…

A common approach in the design of MapReduce algorithms is to minimize the number of rounds. Indeed, there are many examples in the literature of monolithic MapReduce algorithms, which are algorithms requiring just one or two rounds.…

GEneral Matrix Multiply (GEMM) is a central operation in deep learning and corresponds to the largest chunk of the compute footprint. Therefore, improving its efficiency is an active topic of ongoing research. A popular strategy is the use…

We propose a more accurate variant of an algorithm for multiplying 4x4 matrices using 48 multiplications over any ring containing an inverse of 2. This algorithm has an error bound exponent of only log 4 $\gamma$$\infty$,2 $\approx$ 2.386.…

The automatic generation of loop invariants is a fundamental challenge in software verification. While this task is undecidable in general, it is decidable for certain restricted classes of programs. This work focuses on invariant…

Reinforcement Learning algorithms that learn from human feedback (RLHF) need to be efficient in terms of statistical complexity, computational complexity, and query complexity. In this work, we consider the RLHF setting where the feedback…

1-bit LLM quantization offers significant advantages in reducing storage and computational costs. However, existing methods typically train 1-bit LLMs from scratch, failing to fully leverage pre-trained models. This results in high training…

Retrieval-augmented language models (RALMs) improve performance by accessing long-tail and up-to-date knowledge from external data stores, but are challenging to build. Existing approaches require either expensive retrieval-specific…

Recently there has been significant interest in training machine-learning models at low precision: by reducing precision, one can reduce computation and communication by one order of magnitude. We examine training at reduced precision, both…

Loop invariants are properties of a program loop that hold before and after each iteration of the loop. They are often employed to verify programs and ensure that algorithms consistently produce correct results during execution.…

We present an algorithm for synthesizing program loops satisfying a given polynomial loop invariant. The class of loops we consider can be modeled by a system of algebraic recurrence equations with constant coefficients. We turn the task of…

We study ROUND-UFP and ROUND-SAP, two generalizations of the classical BIN PACKING problem that correspond to the unsplittable flow problem on a path (UFP) and the storage allocation problem (SAP), respectively. We are given a path with…

Reinforcement learning (RL) has become the de facto standard practice for sequential decision-making problems by improving future acting policies with feedback. However, RL algorithms may require extensive trial-and-error interactions to…

Matrix multiplication computation acceleration has been a research hotspot across various domains. Due to the characteristics of some applications, approximate matrix multiplication can achieve significant performance improvements without…