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We study the problem of optimizing Large Language Model (LLM) inference scheduling to minimize total latency. LLM inference is an online and multi-task service process and also heavily energy consuming by which a pre-trained LLM processes…

Machine Learning · Computer Science 2025-09-03 Zixi Chen , Yinyu Ye , Zijie Zhou

Large language models (LLMs) enable researchers to analyze text at unprecedented scale and minimal cost. Researchers can now revisit old questions and tackle novel ones with rich data. We provide an econometric framework for realizing this…

Econometrics · Economics 2025-12-08 Jens Ludwig , Sendhil Mullainathan , Ashesh Rambachan

While scaling training compute has led to remarkable improvements in large language models (LLMs), scaling inference compute has not yet yielded analogous gains. We hypothesize that a core missing component is a lack of diverse LLM outputs,…

Machine Learning · Computer Science 2024-10-22 Evan Wang , Federico Cassano , Catherine Wu , Yunfeng Bai , Will Song , Vaskar Nath , Ziwen Han , Sean Hendryx , Summer Yue , Hugh Zhang

Recently, test-time scaling has garnered significant attention from the research community, largely due to the substantial advancements of the o1 model released by OpenAI. By allocating more computational resources during the inference…

We introduce a scaling law for fine-tuning large language models (LLMs) under fixed compute budgets that explicitly accounts for data composition. Conventional approaches measure training data solely by total tokens, yet the number of…

Computation and Language · Computer Science 2025-06-04 Ryan Lagasse , Aidan Kierans , Avijit Ghosh , Shiri Dori-Hacohen

Recent developments in large language models have shown advantages in reallocating a notable share of computational resource from training time to inference time. However, the principles behind inference time scaling are not well…

Machine Learning · Computer Science 2026-02-13 Indranil Halder , Cengiz Pehlevan

We propose a statistical framework built on latent variable modeling for scaling laws of large language models (LLMs). Our work is motivated by the rapid emergence of numerous new LLM families with distinct architectures and training…

In this paper, we investigate the underlying factors that potentially enhance the mathematical reasoning capabilities of large language models (LLMs). We argue that the data scaling law for math reasoning capabilities in modern LLMs is far…

Artificial Intelligence · Computer Science 2024-07-18 Liang Zeng , Liangjun Zhong , Liang Zhao , Tianwen Wei , Liu Yang , Jujie He , Cheng Cheng , Rui Hu , Yang Liu , Shuicheng Yan , Han Fang , Yahui Zhou

Scaling model size and training data has led to great advances in the performance of Large Language Models (LLMs). However, the diminishing returns of this approach necessitate alternative methods to improve model capabilities, particularly…

Machine Learning · Computer Science 2025-11-05 Daman Arora , Andrea Zanette

While Large Language Models (LLMs) have exhibited remarkable emergent capabilities through extensive pre-training, they still face critical limitations in generalizing to specialized domains and handling diverse linguistic variations, known…

Computation and Language · Computer Science 2025-05-28 Jinwu Hu , Zhitian Zhang , Guohao Chen , Xutao Wen , Chao Shuai , Wei Luo , Bin Xiao , Yuanqing Li , Mingkui Tan

Large language models (LLMs) have made remarkable advances in recent years, with scaling laws playing a critical role in this rapid progress. In this paper, we empirically investigate how a critical hyper-parameter, i.e., the global batch…

Computation and Language · Computer Science 2024-12-03 Xian Shuai , Yiding Wang , Yimeng Wu , Xin Jiang , Xiaozhe Ren

This paper presents a method to analyze the inference patterns used by Large Language Models (LLMs) for judgment in a case study on legal LLMs, so as to identify potential incorrect representations of the LLM, according to human domain…

Artificial Intelligence · Computer Science 2025-05-21 Lu Chen , Yuxuan Huang , Yixing Li , Dongrui Liu , Qihan Ren , Shuai Zhao , Kun Kuang , Zilong Zheng , Quanshi Zhang

In recent years, language models have drastically grown in size, and the abilities of these models have been shown to improve with scale. The majority of recent scaling laws studies focused on high-compute high-parameter count settings,…

Computation and Language · Computer Science 2023-06-01 Vijeta Deshpande , Dan Pechi , Shree Thatte , Vladislav Lialin , Anna Rumshisky

Pretraining large language models (LLMs) is resource-intensive, often requiring months of training time even with high-end GPU clusters. There are two approaches of mitigating such computational demands: reusing smaller models to train…

Machine Learning · Computer Science 2025-06-17 Seng Pei Liew , Takuya Kato , Sho Takase

Small language models (SLMs) enable low-cost, private, on-device inference, but they often fail on problems that require specialized domain knowledge or multi-step reasoning. Existing approaches for improving reasoning either rely on scale…

Computation and Language · Computer Science 2026-01-08 Kenan Alkiek , David Jurgens , Vinod Vydiswaran

In recent years, the state-of-the-art in deep learning has been dominated by very large models that have been pre-trained on vast amounts of data. The paradigm is very simple: investing more computational resources (optimally) leads to…

Machine Learning · Computer Science 2024-05-24 Sotiris Anagnostidis , Gregor Bachmann , Imanol Schlag , Thomas Hofmann

Large language models (LLMs) now exhibit strong multi-step reasoning abilities, but existing inference-time scaling methods remain computationally expensive, often relying on extensive sampling or external evaluators. We propose a…

Artificial Intelligence · Computer Science 2026-03-10 Nicolas Legrand , Kenneth Enevoldsen , Márton Kardos , Kristoffer Nielbo

Although Large Language Models (LLMs) have demonstrated strong ability, they are further supposed to be controlled and guided by in real-world scenarios to be safe, accurate, and intelligent. This demands the possession of capability of…

Computation and Language · Computer Science 2024-10-18 Wangtao Sun , Chenxiang Zhang , XueYou Zhang , Xuanqing Yu , Ziyang Huang , Pei Chen , Haotian Xu , Shizhu He , Jun Zhao , Kang Liu

As neural networks continue to grow in size but datasets might not, it is vital to understand how much performance improvement can be expected: is it more important to scale network size or data volume? Thus, neural network scaling laws,…

Machine Learning · Computer Science 2024-09-10 Akhilan Boopathy , Ila Fiete

The performance gains of LLMs have historically been driven by scaling up model size and training data. However, the rapidly diminishing availability of high-quality training data is introducing a fundamental bottleneck, shifting the focus…

Computation and Language · Computer Science 2025-10-14 Zhichao Wang , Cheng Wan , Dong Nie