Arrows of Time for Large Language Models

Vassilis Papadopoulos, Jérémie Wenger, Clément Hongler
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:39509-39528, 2024.

Abstract

We study the probabilistic modeling performed by Autoregressive Large Language Models (LLMs) through the angle of time directionality, addressing a question first raised in (Shannon, 1951). For large enough models, we empirically find a time asymmetry in their ability to learn natural language: a difference in the average log-perplexity when trying to predict the next token versus when trying to predict the previous one. This difference is at the same time subtle and very consistent across various modalities (language, model size, training time, ...). Theoretically, this is surprising: from an information-theoretic point of view, there should be no such difference. We provide a theoretical framework to explain how such an asymmetry can appear from sparsity and computational complexity considerations, and outline a number of perspectives opened by our results.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-papadopoulos24a, title = {Arrows of Time for Large Language Models}, author = {Papadopoulos, Vassilis and Wenger, J\'{e}r\'{e}mie and Hongler, Cl\'{e}ment}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {39509--39528}, 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/papadopoulos24a/papadopoulos24a.pdf}, url = {https://proceedings.mlr.press/v235/papadopoulos24a.html}, abstract = {We study the probabilistic modeling performed by Autoregressive Large Language Models (LLMs) through the angle of time directionality, addressing a question first raised in (Shannon, 1951). For large enough models, we empirically find a time asymmetry in their ability to learn natural language: a difference in the average log-perplexity when trying to predict the next token versus when trying to predict the previous one. This difference is at the same time subtle and very consistent across various modalities (language, model size, training time, ...). Theoretically, this is surprising: from an information-theoretic point of view, there should be no such difference. We provide a theoretical framework to explain how such an asymmetry can appear from sparsity and computational complexity considerations, and outline a number of perspectives opened by our results.} }
Endnote
%0 Conference Paper %T Arrows of Time for Large Language Models %A Vassilis Papadopoulos %A Jérémie Wenger %A Clément Hongler %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-papadopoulos24a %I PMLR %P 39509--39528 %U https://proceedings.mlr.press/v235/papadopoulos24a.html %V 235 %X We study the probabilistic modeling performed by Autoregressive Large Language Models (LLMs) through the angle of time directionality, addressing a question first raised in (Shannon, 1951). For large enough models, we empirically find a time asymmetry in their ability to learn natural language: a difference in the average log-perplexity when trying to predict the next token versus when trying to predict the previous one. This difference is at the same time subtle and very consistent across various modalities (language, model size, training time, ...). Theoretically, this is surprising: from an information-theoretic point of view, there should be no such difference. We provide a theoretical framework to explain how such an asymmetry can appear from sparsity and computational complexity considerations, and outline a number of perspectives opened by our results.
APA
Papadopoulos, V., Wenger, J. & Hongler, C.. (2024). Arrows of Time for Large Language Models. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:39509-39528 Available from https://proceedings.mlr.press/v235/papadopoulos24a.html.

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