How Spurious Features are Memorized: Precise Analysis for Random and NTK Features

Simone Bombari, Marco Mondelli
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:4267-4299, 2024.

Abstract

Deep learning models are known to overfit and memorize spurious features in the training dataset. While numerous empirical studies have aimed at understanding this phenomenon, a rigorous theoretical framework to quantify it is still missing. In this paper, we consider spurious features that are uncorrelated with the learning task, and we provide a precise characterization of how they are memorized via two separate terms: (i) the stability of the model with respect to individual training samples, and (ii) the feature alignment between the spurious pattern and the full sample. While the first term is well established in learning theory and it is connected to the generalization error in classical work, the second one is, to the best of our knowledge, novel. Our key technical result gives a precise characterization of the feature alignment for the two prototypical settings of random features (RF) and neural tangent kernel (NTK) regression. We prove that the memorization of spurious features weakens as the generalization capability increases and, through the analysis of the feature alignment, we unveil the role of the model and of its activation function. Numerical experiments show the predictive power of our theory on standard datasets (MNIST, CIFAR-10).

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-bombari24a, title = {How Spurious Features are Memorized: Precise Analysis for Random and {NTK} Features}, author = {Bombari, Simone and Mondelli, Marco}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {4267--4299}, 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/bombari24a/bombari24a.pdf}, url = {https://proceedings.mlr.press/v235/bombari24a.html}, abstract = {Deep learning models are known to overfit and memorize spurious features in the training dataset. While numerous empirical studies have aimed at understanding this phenomenon, a rigorous theoretical framework to quantify it is still missing. In this paper, we consider spurious features that are uncorrelated with the learning task, and we provide a precise characterization of how they are memorized via two separate terms: (i) the stability of the model with respect to individual training samples, and (ii) the feature alignment between the spurious pattern and the full sample. While the first term is well established in learning theory and it is connected to the generalization error in classical work, the second one is, to the best of our knowledge, novel. Our key technical result gives a precise characterization of the feature alignment for the two prototypical settings of random features (RF) and neural tangent kernel (NTK) regression. We prove that the memorization of spurious features weakens as the generalization capability increases and, through the analysis of the feature alignment, we unveil the role of the model and of its activation function. Numerical experiments show the predictive power of our theory on standard datasets (MNIST, CIFAR-10).} }
Endnote
%0 Conference Paper %T How Spurious Features are Memorized: Precise Analysis for Random and NTK Features %A Simone Bombari %A Marco Mondelli %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-bombari24a %I PMLR %P 4267--4299 %U https://proceedings.mlr.press/v235/bombari24a.html %V 235 %X Deep learning models are known to overfit and memorize spurious features in the training dataset. While numerous empirical studies have aimed at understanding this phenomenon, a rigorous theoretical framework to quantify it is still missing. In this paper, we consider spurious features that are uncorrelated with the learning task, and we provide a precise characterization of how they are memorized via two separate terms: (i) the stability of the model with respect to individual training samples, and (ii) the feature alignment between the spurious pattern and the full sample. While the first term is well established in learning theory and it is connected to the generalization error in classical work, the second one is, to the best of our knowledge, novel. Our key technical result gives a precise characterization of the feature alignment for the two prototypical settings of random features (RF) and neural tangent kernel (NTK) regression. We prove that the memorization of spurious features weakens as the generalization capability increases and, through the analysis of the feature alignment, we unveil the role of the model and of its activation function. Numerical experiments show the predictive power of our theory on standard datasets (MNIST, CIFAR-10).
APA
Bombari, S. & Mondelli, M.. (2024). How Spurious Features are Memorized: Precise Analysis for Random and NTK Features. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:4267-4299 Available from https://proceedings.mlr.press/v235/bombari24a.html.

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