LIME: Learning Inductive Bias for Primitives of Mathematical Reasoning

Yuhuai Wu, Markus N Rabe, Wenda Li, Jimmy Ba, Roger B Grosse, Christian Szegedy
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:11251-11262, 2021.

Abstract

While designing inductive bias in neural architectures has been widely studied, we hypothesize that transformer networks are flexible enough to learn inductive bias from suitable generic tasks. Here, we replace architecture engineering by encoding inductive bias in the form of datasets. Inspired by Peirce’s view that deduction, induction, and abduction are the primitives of reasoning, we design three synthetic tasks that are intended to require the model to have these three abilities. We specifically design these tasks to be synthetic and devoid of mathematical knowledge to ensure that only the fundamental reasoning biases can be learned from these tasks. This defines a new pre-training methodology called "LIME" (Learning Inductive bias for Mathematical rEasoning). Models trained with LIME significantly outperform vanilla transformers on four very different large mathematical reasoning benchmarks. Unlike dominating the computation cost as traditional pre-training approaches, LIME requires only a small fraction of the computation cost of the typical downstream task. The code for generating LIME tasks is available at https://github.com/tonywu95/LIME.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-wu21c, title = {LIME: Learning Inductive Bias for Primitives of Mathematical Reasoning}, author = {Wu, Yuhuai and Rabe, Markus N and Li, Wenda and Ba, Jimmy and Grosse, Roger B and Szegedy, Christian}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {11251--11262}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/wu21c/wu21c.pdf}, url = {https://proceedings.mlr.press/v139/wu21c.html}, abstract = {While designing inductive bias in neural architectures has been widely studied, we hypothesize that transformer networks are flexible enough to learn inductive bias from suitable generic tasks. Here, we replace architecture engineering by encoding inductive bias in the form of datasets. Inspired by Peirce’s view that deduction, induction, and abduction are the primitives of reasoning, we design three synthetic tasks that are intended to require the model to have these three abilities. We specifically design these tasks to be synthetic and devoid of mathematical knowledge to ensure that only the fundamental reasoning biases can be learned from these tasks. This defines a new pre-training methodology called "LIME" (Learning Inductive bias for Mathematical rEasoning). Models trained with LIME significantly outperform vanilla transformers on four very different large mathematical reasoning benchmarks. Unlike dominating the computation cost as traditional pre-training approaches, LIME requires only a small fraction of the computation cost of the typical downstream task. The code for generating LIME tasks is available at https://github.com/tonywu95/LIME.} }
Endnote
%0 Conference Paper %T LIME: Learning Inductive Bias for Primitives of Mathematical Reasoning %A Yuhuai Wu %A Markus N Rabe %A Wenda Li %A Jimmy Ba %A Roger B Grosse %A Christian Szegedy %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-wu21c %I PMLR %P 11251--11262 %U https://proceedings.mlr.press/v139/wu21c.html %V 139 %X While designing inductive bias in neural architectures has been widely studied, we hypothesize that transformer networks are flexible enough to learn inductive bias from suitable generic tasks. Here, we replace architecture engineering by encoding inductive bias in the form of datasets. Inspired by Peirce’s view that deduction, induction, and abduction are the primitives of reasoning, we design three synthetic tasks that are intended to require the model to have these three abilities. We specifically design these tasks to be synthetic and devoid of mathematical knowledge to ensure that only the fundamental reasoning biases can be learned from these tasks. This defines a new pre-training methodology called "LIME" (Learning Inductive bias for Mathematical rEasoning). Models trained with LIME significantly outperform vanilla transformers on four very different large mathematical reasoning benchmarks. Unlike dominating the computation cost as traditional pre-training approaches, LIME requires only a small fraction of the computation cost of the typical downstream task. The code for generating LIME tasks is available at https://github.com/tonywu95/LIME.
APA
Wu, Y., Rabe, M.N., Li, W., Ba, J., Grosse, R.B. & Szegedy, C.. (2021). LIME: Learning Inductive Bias for Primitives of Mathematical Reasoning. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:11251-11262 Available from https://proceedings.mlr.press/v139/wu21c.html.

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