Appendix for "Episodic Multi-T ask Learning with Heterogeneous Neural Processes" In this section, we list frequently asked questions from researchers who help proofread this manuscript. As shown in Table 1, we use "Heterogeneous tasks" to distinguish the different branches of multi-task Meanwhile, "Episodic training" is used to describe the data-feeding strategy. Thus, "Heterogeneous tasks" is not available here (-). In episodic multi-task learning, we restrict the scope of the problem to the case where tasks in the same episode are related and share the same target space. This also implies that tasks with the same target space are related.

Standard few-shot learning methods employ geometric similarity metrics such as cosine similarity and negative Euclidean distance to gauge the semantic relatedness between two features.

Specifically, a set of prototypes is optimized to achieve per-task prototype overfit-ting, enabling accurately obtaining the overfitted prototypes for individual tasks. Furthermore, we introduce a task-guided diffusion process within the prototype space, enabling the meta-learning of a generative process that transitions from a vanilla prototype to an overfitted prototype.

Articulated object manipulation is a fundamental yet challenging task in robotics. Due to significant geometric and semantic variations across object categories, previous manipulation models struggle to generalize to novel categories. Few-shot learning is a promising solution for alleviating this issue by allowing robots to perform a few interactions with unseen objects.

Gaussian processes with deep neural networks demonstrate to be a strong learner for few-shot learning since they combine the strength of deep learning and kernels while being able to well capture uncertainty. However, it remains an open problem to leverage the shared knowledge provided by related tasks. In this paper, we propose to learn Gaussian processes with dense inducing variables by meta-learning for few-shot learning. In contrast to sparse Gaussian processes, we define a set of dense inducing variables to be of a much larger size than the support set in each task, which collects prior knowledge from experienced tasks. The dense inducing variables specify a shared Gaussian process prior over prediction functions of all tasks, which are learned in a variational inference framework and offer a strong inductive bias for learning new tasks. To achieve task-specific prediction functions, we propose to adapt the inducing variables to each task by efficient gradient descent. We conduct extensive experiments on common benchmark datasets for a variety of few-shot learning tasks. Our dense Gaussian processes present significant improvements over vanilla Gaussian processes and comparable or even better performance with state-of-the-art methods.