Related papers: Combining Precision Boosting with LP Iterative Ref…
Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive…
Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While…
Solving linear systems is a ubiquitous task in science and engineering. Because directly inverting a large-scale linear system can be computationally expensive, iterative algorithms are often used to numerically find the inverse. To…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
The latest research on Large Language Models (LLMs) has demonstrated significant advancement in the field of Natural Language Processing (NLP). However, despite this progress, there is still a lack of reliability in these models. This is…
Optimizing Large Language Model (LLM) performance requires well-crafted prompts, but manual prompt engineering is labor-intensive and often ineffective. Automated prompt optimization techniques address this challenge but the majority of…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer…
Linear Predictive Clustering (LPC) partitions samples based on shared linear relationships between feature and target variables, with numerous applications including marketing, medicine, and education. Greedy optimization methods, commonly…
We propose a totally corrective boosting algorithm with explicit cardinality regularization. The resulting combinatorial optimization problems are not known to be efficiently solvable with existing classical methods, but emerging quantum…
This paper introduces scalable, sampling-based algorithms that optimize trained neural networks with ReLU activations. We first propose an iterative algorithm that takes advantage of the piecewise linear structure of ReLU neural networks…
Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…
Large Language Models (LLMs) are showing remarkable performance in generating source code, yet the generated code often has issues like compilation errors or incorrect code. Researchers and developers often face wasted effort in…
Mixed-Integer Programming (MIP), particularly Mixed-Integer Linear Programming (MILP) and Mixed-Integer Quadratic Programming (MIQP), has found extensive applications in domains such as portfolio optimization and network flow control, which…
Maximum a posteriori (MAP) inference in discrete-valued Markov random fields is a fundamental problem in machine learning that involves identifying the most likely configuration of random variables given a distribution. Due to the…
Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…
Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…
Large Language Models' (LLM) reasoning can be improved using test-time aggregation strategies, i.e., generating multiple samples and voting among generated samples. While these improve performance, they often reach a saturation point.…
In the dynamic linear program (LP) problem, we are given an LP undergoing updates and we need to maintain an approximately optimal solution. Recently, significant attention (e.g., [Gupta et al. STOC'17; Arar et al. ICALP'18, Wajc STOC'20])…
Gradient boosting is a state-of-the-art prediction technique that sequentially produces a model in the form of linear combinations of simple predictors---typically decision trees---by solving an infinite-dimensional convex optimization…