Modern learning systems excel at interpolation but struggle to generalize to unseen tasks outside the training distribution's support. This failure occurs even in simple settings, such as handling task parameters beyond the training range, and persists despite advances in foundation models. To this end, we develop the Relational Task Extrapolator (RTE), an algorithm designed to enable systematic extrapolation to novel tasks. The key observation is that extrapolation is inherently relational: extrapolating to unseen tasks requires learning how tasks transform into one another. If a model learns the transformation between tasks A and B during training, it can apply that same transformation to relate known tasks to unseen ones at test time. RTE operationalizes this idea by decomposing each target task into a known anchor task and a transformation linking the anchor and target. It then learns a relational operator, mapping an anchor-transformation pair to predictions for the target task. We instantiate RTE across multiple task extrapolation regimes in function prediction, e.g. where target tasks use out-of-range parameters (parameter extrapolation), have greater compositional depth (length extrapolation), and/or recombine function primitives in unseen ways (compositional extrapolation). We further extend RTE to sequence prediction, integrating it into fine-tuning algorithms for foundation models. Across empirical studies, we find that RTE substantially outperforms existing approaches on extrapolation to novel, unseen tasks.

Representation learning based on multi-task pretraining has become a powerful approach in many domains. In particular, task-aware representation learning aims to learn an optimal representation for a specific target task by sampling data from a set of source tasks, while task-agnostic representation learning seeks to learn a universal representation for a class of tasks. In this paper, we propose a general and versatile algorithmic and theoretic framework for active representation learning, where the learner optimally chooses which source tasks to sample from. This framework, along with a tractable meta algorithm, allows most arbitrary target and source task spaces (from discrete to continuous), covers both task-aware and task-agnostic settings, and is compatible with deep representation learning practices. We provide several instantiations under this framework, from bilinear and feature-based nonlinear to general nonlinear cases. In the bilinear case, by leveraging the non-uniform spectrum of the task representation and the calibrated source-target relevance, we prove that the sample complexity to achieve ε-excess risk on target scales with (k)2 v 22ε 2 where k is the effective dimension of the target and v 22 (0,1] represents the connection between source and target space. Compared to the passive one, this can save up to 1dW of sample complexity, where dW is the task space dimension. Finally, we demonstrate different instantiations of our meta algorithm in synthetic datasets and robotics problems, from pendulum simulations to real-world drone flight datasets. On average, our algorithms outperform baselines by 20% 70%. 1

Large pretrained language models (LMs) like BERT have improved performance in many disparate natural language processing (NLP) tasks. However, fine tuning such models requires a large number of training examples for each target task. Simultaneously, many realistic NLP problems are "few shot", without a sufficiently large training set. In this work, we propose a novel conditional neural process-based approach for few-shot text classification that learns to transfer from other diverse tasks with rich annotation. Our key idea is to represent each task using gradient information from a base model and to train an adaptation network that modulates a text classifier conditioned on the task representation. While previous task-aware few-shot learners represent tasks by input encoding, our novel task representation is more powerful, as the gradient captures input-output relationships of a task. Experimental results show that our approach outperforms traditional fine-tuning, sequential transfer learning, and state-of-the-art meta learning approaches on a collection of diverse few-shot tasks. We further conducted analysis and ablations to justify our design choices.

Modern kernel-based two-sample tests have shown great success in distinguishing complex, high-dimensional distributions by learning appropriate kernels (or, as a special case, classifiers). Previous work, however, has assumed that many samples are observed from both of the distributions being distinguished. In realistic scenarios with very limited numbers of data samples, it can be challenging to identify a kernel powerful enough to distinguish complex distributions. We address this issue by introducing the problem of meta two-sample testing (M2ST), which aims to exploit (abundant) auxiliary data on related tasks to find an algorithm that can quickly identify a powerful test on new target tasks. We propose two specific algorithms for this task: a generic scheme which improves over baselines, and a more tailored approach which performs even better. We provide both theoretical justification and empirical evidence that our proposed meta-testing schemes outperform learning kernel-based tests directly from scarce observations, and identify when such schemes will be successful.