Learning from Students: Applying t-Distributions to Explore Accurate and Efficient Formats for LLMs

Jordan Dotzel, Yuzong Chen, Bahaa Kotb, Sushma Prasad, Gang Wu, Sheng Li, Mohamed S Abdelfattah, Zhiru Zhang
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:11573-11591, 2024.

Abstract

The increasing size of large language models (LLMs) traditionally requires low-precision integer formats to meet strict latency and power demands. Yet recently, alternative formats such as Normal Float (NF4) have increased model accuracy at the cost of increased chip area. In this work, we first conduct a large-scale analysis of LLM weights and activations across 30 networks and conclude that most distributions follow a Student’s t-distribution. We then derive a new theoretically optimal format, Student Float (SF4), that improves over NF4 across modern LLMs, for example increasing the average accuracy on LLaMA2-7B by 0.76% across tasks. Using this format as a high-accuracy reference, we then propose augmenting E2M1 with two variants of supernormal support for higher model accuracy. Finally, we explore the quality and efficiency frontier across 11 datatypes by evaluating their model accuracy and hardware complexity. We discover a Pareto curve composed of INT4, E2M1, and E2M1 with supernormal support, which offers a continuous tradeoff between model accuracy and chip area. For example, E2M1 with supernormal support increases the accuracy of Phi-2 by up to 2.19% with 1.22% area overhead, enabling more LLM-based applications to be run at four bits. The supporting code is hosted at https://github.com/cornell-zhang/llm-datatypes.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-dotzel24a, title = {Learning from Students: Applying t-Distributions to Explore Accurate and Efficient Formats for {LLM}s}, author = {Dotzel, Jordan and Chen, Yuzong and Kotb, Bahaa and Prasad, Sushma and Wu, Gang and Li, Sheng and Abdelfattah, Mohamed S and Zhang, Zhiru}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {11573--11591}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/dotzel24a/dotzel24a.pdf}, url = {https://proceedings.mlr.press/v235/dotzel24a.html}, abstract = {The increasing size of large language models (LLMs) traditionally requires low-precision integer formats to meet strict latency and power demands. Yet recently, alternative formats such as Normal Float (NF4) have increased model accuracy at the cost of increased chip area. In this work, we first conduct a large-scale analysis of LLM weights and activations across 30 networks and conclude that most distributions follow a Student’s t-distribution. We then derive a new theoretically optimal format, Student Float (SF4), that improves over NF4 across modern LLMs, for example increasing the average accuracy on LLaMA2-7B by 0.76% across tasks. Using this format as a high-accuracy reference, we then propose augmenting E2M1 with two variants of supernormal support for higher model accuracy. Finally, we explore the quality and efficiency frontier across 11 datatypes by evaluating their model accuracy and hardware complexity. We discover a Pareto curve composed of INT4, E2M1, and E2M1 with supernormal support, which offers a continuous tradeoff between model accuracy and chip area. For example, E2M1 with supernormal support increases the accuracy of Phi-2 by up to 2.19% with 1.22% area overhead, enabling more LLM-based applications to be run at four bits. The supporting code is hosted at https://github.com/cornell-zhang/llm-datatypes.} }
Endnote
%0 Conference Paper %T Learning from Students: Applying t-Distributions to Explore Accurate and Efficient Formats for LLMs %A Jordan Dotzel %A Yuzong Chen %A Bahaa Kotb %A Sushma Prasad %A Gang Wu %A Sheng Li %A Mohamed S Abdelfattah %A Zhiru Zhang %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-dotzel24a %I PMLR %P 11573--11591 %U https://proceedings.mlr.press/v235/dotzel24a.html %V 235 %X The increasing size of large language models (LLMs) traditionally requires low-precision integer formats to meet strict latency and power demands. Yet recently, alternative formats such as Normal Float (NF4) have increased model accuracy at the cost of increased chip area. In this work, we first conduct a large-scale analysis of LLM weights and activations across 30 networks and conclude that most distributions follow a Student’s t-distribution. We then derive a new theoretically optimal format, Student Float (SF4), that improves over NF4 across modern LLMs, for example increasing the average accuracy on LLaMA2-7B by 0.76% across tasks. Using this format as a high-accuracy reference, we then propose augmenting E2M1 with two variants of supernormal support for higher model accuracy. Finally, we explore the quality and efficiency frontier across 11 datatypes by evaluating their model accuracy and hardware complexity. We discover a Pareto curve composed of INT4, E2M1, and E2M1 with supernormal support, which offers a continuous tradeoff between model accuracy and chip area. For example, E2M1 with supernormal support increases the accuracy of Phi-2 by up to 2.19% with 1.22% area overhead, enabling more LLM-based applications to be run at four bits. The supporting code is hosted at https://github.com/cornell-zhang/llm-datatypes.
APA
Dotzel, J., Chen, Y., Kotb, B., Prasad, S., Wu, G., Li, S., Abdelfattah, M.S. & Zhang, Z.. (2024). Learning from Students: Applying t-Distributions to Explore Accurate and Efficient Formats for LLMs. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:11573-11591 Available from https://proceedings.mlr.press/v235/dotzel24a.html.

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