Towards Understanding Generalization in Gradient-Based Meta-Learning
In this master's thesis, we study the generalization of neural networks in gradient-based meta-learning by analyzing various properties of the objective landscapes. Meta-learning, a challenging paradigm where models not only have to learn a task but beyond that, are trained for ``learning to learn" as they must adapt to new tasks and environments with very limited data about them. With research on the objective landscapes of neural networks in classical supervised having provided some answers regarding their ability to generalize for new data points, we propose similar analyses aimed at understanding generalization in meta-learning. We first introduce the literature on objective landscapes of neural networks in Section \ref{sec:intro:objective_landscapes}. We then introduce the literature of meta-learning in Section \ref{chap:prof_forcing}, concluding our introduction with the approach of gradient-based meta-learning, a meta-learning setup that bears strong similarities to the traditional supervised learning setup through stochastic gradient-based optimization. At the time of writing of this thesis, and to the best of our knowledge, this is the first work to empirically study the objective landscapes in gradient-based meta-learning, especially in the context of deep learning. We notably provide some insights on some properties of those landscapes that appear correlated to the generalization to new tasks. We experimentally demonstrate that as meta-training progresses, the meta-test solutions, obtained after adapting the meta-train solution of the model, to new tasks via few steps of gradient-based fine-tuning, become flatter, lower in loss, and further away from the meta-train solution. We also show that those meta-test solutions become flatter even as generalization starts to degrade, thus providing experimental evidence against the correlation between generalization and flat minima in the paradigm of gradient-based meta-leaning. Furthermore, we provide empirical evidence that generalization to new tasks is correlated with the coherence between their adaptation trajectories in parameter space, measured by the average cosine similarity between task-specific trajectory directions, starting from a same meta-train solution. We also show that coherence of meta-test gradients, measured by the average inner product between the task-specific gradient vectors evaluated at meta-train solution, is also correlated with generalization. Based on these observations, we propose a novel regularizer for the Model Agnostic Meta-Learning (MAML) algorithm and provide experimental evidence for its effectiveness.
Deep learning Meta-learning Objective landscapes Generalization Few-shot learning