  In this work we study generalization of neural networks in gradient-based
meta-learning by analyzing various properties of the objective landscapes. 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 an 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 MAML and provide experimental
evidence for its effectiveness.
