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In recent years fused-multiply-add (FMA) units with lower-precision multiplications and higher-precision accumulation have proven useful in machine learning/artificial intelligence applications, most notably in training deep neural networks…

Mathematical Software · Computer Science 2019-04-16 Greg Henry , Ping Tak Peter Tang , Alexander Heinecke

We propose an adaptive mixed precision and dynamically scaled preconditioned conjugate gradient algorithm (AMP-PCG). It dynamically adjusts the precision for storing vectors and computing, exploiting low precision when appropriate, while…

Numerical Analysis · Mathematics 2025-05-08 Yichen Guo , Eric de Sturler , Tim Warburton

We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…

Numerical Analysis · Mathematics 2024-05-07 Jean-Michel Muller , Bruno Salvy

Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one…

Logic in Computer Science · Computer Science 2026-05-07 Yichen Tao , Hongfei Fu , Jiawei Chen , Jean-Baptiste Jeannin

The rapid scaling of large language models (LLMs) has made low-precision training essential for reducing memory, improving efficiency, and enabling larger models and datasets. Existing convergence theories for adaptive optimizers, however,…

Machine Learning · Computer Science 2026-03-03 Xuan Tang , Jichu Li , Difan Zou

Large neural networks spend most computation on floating point tensor multiplications. In this work, we find that a floating point multiplier can be approximated by one integer adder with high precision. We propose the linear-complexity…

Computation and Language · Computer Science 2024-10-03 Hongyin Luo , Wei Sun

Powerful foundation models, including large language models (LLMs), with Transformer architectures have ushered in a new era of Generative AI across various industries. Industry and research community have witnessed a large number of new…

The trade-off between accuracy and interpretability has long been a challenge in machine learning (ML). This tension is particularly significant for emerging interpretable-by-design methods, which aim to redesign ML algorithms for…

Machine Learning · Computer Science 2025-05-28 Geyu Liang , Senne Michielssen , Salar Fattahi

We present and evaluate a technique for computing path-sensitive interference conditions during abstract interpretation of concurrent programs. In lieu of fixed point computation, we use prime event structures to compactly represent causal…

Programming Languages · Computer Science 2017-05-02 Marcelo Sousa , César Rodríguez , Vijay D'Silva , Daniel Kroening

Locating and editing knowledge in large language models (LLMs) is crucial for enhancing their accuracy, safety, and inference rationale. We introduce ``concept editing'', an innovative variation of knowledge editing that uncovers…

Computation and Language · Computer Science 2024-08-23 Nura Aljaafari , Danilo S. Carvalho , André Freitas

Answering multi-hop reasoning questions requires retrieving and synthesizing information from diverse sources. Language models (LMs) struggle to perform such reasoning consistently. We propose an approach to pinpoint and rectify multi-hop…

Computation and Language · Computer Science 2024-11-11 Mansi Sakarvadia

In this paper, we explore FP8 low-bit data formats for efficient training of large language models (LLMs). Our key insight is that most variables, such as gradients and optimizer states, in LLM training can employ low-precision data formats…

Making large language models (LLMs) more efficient in memory, latency, and serving cost is crucial for edge deployment, interactive applications, and sustainable inference at scale. Pruning is a promising technique, but existing pruning…

Computation and Language · Computer Science 2025-10-13 Eugene Kwek , Wenpeng Yin

Transformer-based Large Language Models (LLMs) traditionally rely on final-layer loss for training and final-layer representations for predictions, potentially overlooking the predictive power embedded in intermediate layers. Surprisingly,…

Computation and Language · Computer Science 2024-10-18 Haoyan Luo , Lucia Specia

Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…

Machine Learning · Computer Science 2021-10-29 Abhishek Sharma , Catherine Zeng , Sanjana Narayanan , Sonali Parbhoo , Finale Doshi-Velez

Large language models like GPT-4 exhibit emergent capabilities across general-purpose tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks are not explicitly encoded by the unsupervised, next-token…

Machine Learning · Computer Science 2023-07-10 Nayoung Lee , Kartik Sreenivasan , Jason D. Lee , Kangwook Lee , Dimitris Papailiopoulos

Transformers trained on huge text corpora exhibit a remarkable set of capabilities, e.g., performing basic arithmetic. Given the inherent compositional nature of language, one can expect the model to learn to compose these capabilities,…

Machine Learning · Computer Science 2024-02-07 Rahul Ramesh , Ekdeep Singh Lubana , Mikail Khona , Robert P. Dick , Hidenori Tanaka

Large pre-trained transformers have revolutionized artificial intelligence across various domains, and fine-tuning remains the dominant approach for adapting these models to downstream tasks due to the cost of training from scratch.…

Computer Vision and Pattern Recognition · Computer Science 2025-07-16 Wei Chen , Jingxi Yu , Zichen Miao , Qiang Qiu

The Rapid Iterative FiTting (RIFT) parameter inference algorithm provides a simulation-based inference approach to efficient, highly-parallelized parameter inference for GW sources. Previous editions of RIFT have conservatively optimized…

Instrumentation and Methods for Astrophysics · Physics 2025-05-20 Katelyn J. Wagner , R. O'Shaughnessy , A. Yelikar , N. Manning , D. Fernando , J. Lange , V. Tiwari , A. Fernando , D. Williams

Feature transformation plays a critical role in enhancing machine learning model performance by optimizing data representations. Recent state-of-the-art approaches address this task as a continuous embedding optimization problem, converting…

Machine Learning · Computer Science 2025-08-29 Yang Gao , Dongjie Wang , Scott Piersall , Ye Zhang , Liqiang Wang