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Both PAC-Bayesian and Sample Compress learning frameworks have been shown instrumental for deriving tight (non-vacuous) generalization bound… (voir plus)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.
Reconstruction functions are pivotal in sample compression theory, a framework for deriving tight generalization bounds. From a small sample… (voir plus) 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.
