Benjamin Leblanc

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

Nathaniel D'Amours

Both PAC-Bayesian and Sample Compress learning frameworks have been shown instrumental for deriving tight (non-vacuous) generalization bound… (see more)s 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.

2025-05-01

ICML.cc/2025/Conference (poster)

openreview.net

Sample Compression Hypernetworks: From Generalization Bounds to Meta-Learning

Nathaniel D'Amours

Reconstruction functions are pivotal in sample compression theory, a framework for deriving tight generalization bounds. From a small sample… (see more) of the training set (the compression set) and an optional stream of information (the message), they recover a predictor previously learned from the whole training set. While usually fixed, we propose to learn reconstruction functions. To facilitate the optimization and increase the expressiveness of the message, we derive a new sample compression generalization bound for real-valued messages. From this theoretical analysis, we then present a new hypernetwork architecture that outputs predictors with tight generalization guarantees when trained using an original meta-learning framework. The results of promising preliminary experiments are then reported.

2024-10-09

NeurIPS.cc/2024/Workshop/Compression (published)

openreview.net