Given a finite set of sample points, meta-learning algorithms aim to learn an optimal adaptation strategy for new, unseen tasks. Often, this data can be ambiguous as it might belong to different tasks concurrently. This is particularly the case in meta-regression tasks. In such cases, the estimated adaptation strategy is subject to high variance due to the limited amount of support data for each task, which often leads to sub-optimal generalization performance. In this work, we address the problem of variance reduction in gradient-based meta-learning and formalize the class of problems prone to this, a condition we refer to as task overlap. Specifically, we propose a novel approach that reduces the variance of the gradient estimate by weighing each support point individually by the variance of its posterior over the parameters. To estimate the posterior, we utilize the Laplace approximation, which allows us to express the variance in terms of the curvature of the loss landscape of our meta-learner. Experimental results demonstrate the effectiveness of the proposed method and highlight the importance of variance reduction in meta-learning.

We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically correspond to intrinsic data classes and poses respectively. The learner is trained on a loss encouraging equivariance based on supervision from relative symmetry information. The approach is motivated by theoretical results from group theory and guarantees representations that are lossless, interpretable and disentangled. We provide an empirical investigation via experiments involving datasets with a variety of symmetries. Results show that our representations capture the geometry of data and outperform other equivariant representation learning frameworks.

Manipulation of deformable objects has long been a challenging task in robotics. Their high-dimensional configuration space and complex dynamics make them difficult to consider for tasks such as robotic manipulation. In this paper, we address the problem of learning efficient representations of deformable objects which lend themselves better suitable for downstream robotics tasks. In particular, we consider graph-based representations of deformable objects which arise naturally from their point-cloud representation. Through manipulation, we learn to coarsen this graph into a simpler representation which still captures the necessary dynamics of the object. Our model consists of (a) a Cluster Assignment Model which takes the initial graph and coarsens it, (b) a Coarsened Dynamics Model that approximates the dynamics of the coarsened graph and (c) a Forward Prediction Model which predicts the next state of the ground truth graph. After end-to-end training, the Cluster Assignment Model learns to build coarse representations which better capture the dynamics compared to conventional clustering methods such as K-means. We evaluate our method on three sets of experiments: rigid objects, rigid objects with pair-wise interactions and a simulated dataset of a shirt.