Generalization Bounds via Meta-Learned Model Representations: PAC-Bayes and Sample Compression Hypernetworks

Benjamin Leblanc, Mathieu Bazinet, Nathaniel D’Amours, Alexandre Drouin, Pascal Germain
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:32830-32852, 2025.

Abstract

Both PAC-Bayesian and Sample Compress learning frameworks have been shown instrumental for deriving tight (non-vacuous) generalization bounds for neural networks. We leverage these results in a meta-learning scheme, relying on a hypernetwork that outputs the parameters of a downstream predictor from a dataset input. The originality of our approach lies in the investigated hypernetwork architectures that encode the dataset before decoding the parameters: (1) a PAC-Bayesian encoder that expresses a posterior distribution over a latent space, (2) a Sample Compress encoder that selects a small sample of the dataset input along with a message from a discrete set, and (3) a hybrid between both approaches motivated by a new Sample Compress theorem handling continuous messages. The latter theorem exploits the pivotal information transiting at the encoder-decoder junction in order to compute generalization guarantees for each downstream predictor obtained by our meta-learning scheme.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-leblanc25a, title = {Generalization Bounds via Meta-Learned Model Representations: {PAC}-{B}ayes and Sample Compression Hypernetworks}, author = {Leblanc, Benjamin and Bazinet, Mathieu and D'Amours, Nathaniel and Drouin, Alexandre and Germain, Pascal}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {32830--32852}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/leblanc25a/leblanc25a.pdf}, url = {https://proceedings.mlr.press/v267/leblanc25a.html}, abstract = {Both PAC-Bayesian and Sample Compress learning frameworks have been shown instrumental for deriving tight (non-vacuous) generalization bounds for neural networks. We leverage these results in a meta-learning scheme, relying on a hypernetwork that outputs the parameters of a downstream predictor from a dataset input. The originality of our approach lies in the investigated hypernetwork architectures that encode the dataset before decoding the parameters: (1) a PAC-Bayesian encoder that expresses a posterior distribution over a latent space, (2) a Sample Compress encoder that selects a small sample of the dataset input along with a message from a discrete set, and (3) a hybrid between both approaches motivated by a new Sample Compress theorem handling continuous messages. The latter theorem exploits the pivotal information transiting at the encoder-decoder junction in order to compute generalization guarantees for each downstream predictor obtained by our meta-learning scheme.} }
Endnote
%0 Conference Paper %T Generalization Bounds via Meta-Learned Model Representations: PAC-Bayes and Sample Compression Hypernetworks %A Benjamin Leblanc %A Mathieu Bazinet %A Nathaniel D’Amours %A Alexandre Drouin %A Pascal Germain %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-leblanc25a %I PMLR %P 32830--32852 %U https://proceedings.mlr.press/v267/leblanc25a.html %V 267 %X Both PAC-Bayesian and Sample Compress learning frameworks have been shown instrumental for deriving tight (non-vacuous) generalization bounds for neural networks. We leverage these results in a meta-learning scheme, relying on a hypernetwork that outputs the parameters of a downstream predictor from a dataset input. The originality of our approach lies in the investigated hypernetwork architectures that encode the dataset before decoding the parameters: (1) a PAC-Bayesian encoder that expresses a posterior distribution over a latent space, (2) a Sample Compress encoder that selects a small sample of the dataset input along with a message from a discrete set, and (3) a hybrid between both approaches motivated by a new Sample Compress theorem handling continuous messages. The latter theorem exploits the pivotal information transiting at the encoder-decoder junction in order to compute generalization guarantees for each downstream predictor obtained by our meta-learning scheme.
APA
Leblanc, B., Bazinet, M., D’Amours, N., Drouin, A. & Germain, P.. (2025). Generalization Bounds via Meta-Learned Model Representations: PAC-Bayes and Sample Compression Hypernetworks. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:32830-32852 Available from https://proceedings.mlr.press/v267/leblanc25a.html.

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