Neural Networks Learn Statistics of Increasing Complexity

Nora Belrose, Quintin Pope, Lucia Quirke, Alex Troy Mallen, Xiaoli Fern
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:3382-3409, 2024.

Abstract

The distributional simplicity bias (DSB) posits that neural networks learn low-order moments of the data distribution first, before moving on to higher-order correlations. In this work, we present compelling new evidence for the DSB by showing that networks automatically learn to perform well on maximum-entropy distributions whose low-order statistics match those of the training set early in training, then lose this ability later. We also extend the DSB to discrete domains by proving an equivalence between token $n$-gram frequencies and the moments of embedding vectors, and by finding empirical evidence for the bias in LLMs. Finally we use optimal transport methods to surgically edit the low-order statistics of one class to match those of another, and show that early-training networks treat the edited samples as if they were drawn from the target class. Code is available at https://github.com/EleutherAI/features-across-time.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-belrose24a, title = {Neural Networks Learn Statistics of Increasing Complexity}, author = {Belrose, Nora and Pope, Quintin and Quirke, Lucia and Mallen, Alex Troy and Fern, Xiaoli}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {3382--3409}, 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/belrose24a/belrose24a.pdf}, url = {https://proceedings.mlr.press/v235/belrose24a.html}, abstract = {The distributional simplicity bias (DSB) posits that neural networks learn low-order moments of the data distribution first, before moving on to higher-order correlations. In this work, we present compelling new evidence for the DSB by showing that networks automatically learn to perform well on maximum-entropy distributions whose low-order statistics match those of the training set early in training, then lose this ability later. We also extend the DSB to discrete domains by proving an equivalence between token $n$-gram frequencies and the moments of embedding vectors, and by finding empirical evidence for the bias in LLMs. Finally we use optimal transport methods to surgically edit the low-order statistics of one class to match those of another, and show that early-training networks treat the edited samples as if they were drawn from the target class. Code is available at https://github.com/EleutherAI/features-across-time.} }
Endnote
%0 Conference Paper %T Neural Networks Learn Statistics of Increasing Complexity %A Nora Belrose %A Quintin Pope %A Lucia Quirke %A Alex Troy Mallen %A Xiaoli Fern %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-belrose24a %I PMLR %P 3382--3409 %U https://proceedings.mlr.press/v235/belrose24a.html %V 235 %X The distributional simplicity bias (DSB) posits that neural networks learn low-order moments of the data distribution first, before moving on to higher-order correlations. In this work, we present compelling new evidence for the DSB by showing that networks automatically learn to perform well on maximum-entropy distributions whose low-order statistics match those of the training set early in training, then lose this ability later. We also extend the DSB to discrete domains by proving an equivalence between token $n$-gram frequencies and the moments of embedding vectors, and by finding empirical evidence for the bias in LLMs. Finally we use optimal transport methods to surgically edit the low-order statistics of one class to match those of another, and show that early-training networks treat the edited samples as if they were drawn from the target class. Code is available at https://github.com/EleutherAI/features-across-time.
APA
Belrose, N., Pope, Q., Quirke, L., Mallen, A.T. & Fern, X.. (2024). Neural Networks Learn Statistics of Increasing Complexity. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:3382-3409 Available from https://proceedings.mlr.press/v235/belrose24a.html.

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