Mathieu Bazinet

Mathieu Bazinet, Valentina Zantedeschi, Pascal Germain

The sample compression theory provides generalization guarantees for predictors that can be fully defined using a subset of the training dataset and a (short) message string, generally defined as a binary sequence. Previous works provided generalization bounds for the zero-one loss, which is restrictive notably when applied to deep learning approaches. In this paper, we present a general framework for deriving new sample compression bounds that hold for real-valued unbounded losses. Using the Pick-To-Learn (P2L) meta-algorithm, which transforms the training method of any machine-learning predictor to yield sample-compressed predictors, we empirically demonstrate the tightness of the bounds and their versatility by evaluating them on random forests and multiple types of neural networks.

Mathieu Bazinet, Valentina Zantedeschi, Pascal Germain

Generalization bounds for deep learning models are typically vacuous, not computable or restricted to specific model classes. In this paper, we tackle these issues by providing new disagreement-based certificates for the gap between the true risk of any two predictors. We then bound the true risk of the predictor of interest via a surrogate model that enjoys tight generalization guarantees, and evaluating our disagreement bound on an unlabeled dataset. We empirically demonstrate the tightness of the obtained certificates and showcase the versatility of the approach by training surrogate models leveraging three different frameworks: sample compression, model compression and PAC-Bayes theory. Importantly, such guarantees are achieved without modifying the target model, nor adapting the training procedure to the generalization framework.

Benjamin Leblanc, Mathieu Bazinet, Nathaniel D'Amours et al.

Both PAC-Bayesian and Sample Compress learning frameworks are 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.

Jacob Comeau, Mathieu Bazinet, Pascal Germain et al.

Continual learning algorithms aim to learn from a sequence of tasks, making the training distribution non-stationary. The majority of existing continual learning approaches in the literature rely on heuristics and do not provide learning guarantees. In this paper, we present a new method called Continual Pick-to-Learn (CoP2L), which is able to retain the most representative samples for each task in an efficient way. CoP2L combines the Pick-to-Learn algorithm (rooted in the sample compression theory) and the experience replay continual learning scheme. This allows us to provide non-vacuous upper bounds on the generalization loss of the learned predictors, numerically computable after each task. We empirically evaluate our approach on several standard continual learning benchmarks across Class-Incremental, Task-Incremental, and Domain-Incremental settings. Our results show that CoP2L is highly competitive across all setups, often outperforming existing baselines, and significantly mitigating catastrophic forgetting compared to vanilla experience replay in the Class-Incremental setting. It is possible to leverage the bounds provided by CoP2L in practical scenarios to certify the predictor reliability on previously learned tasks, in order to improve the trustworthiness of the continual learning algorithm.