Learning to Extrapolate to New Tasks: A Relational Approach to Task Extrapolation
Authors: Adam Ousherovitch, Yixin Wang
Organizations: Department of Statistics, University of Michigan, Ann Arbor.
Abstract
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.
We present Zeus, a unified tuning-free Time Series Foundation Model (TSFM) that delivers superior performance across diverse analysis tasks without any task-specific fine-tuning. Unlike prior studies that primarily focus on zero-shot forecasting but require task-specific tuning for other tasks, Zeus bridges this gap by addressing two fundamental challenges in multi-task generalization. First, to reconcile point-level granularity with long-sequence scalability, Zeus incorporates a multi-scale Transformer featuring point-wise tokenization and a U-shaped hierarchy, effectively balancing fine-grained fidelity with computational efficiency. Second, to accommodate varying inductive biases across different tasks, Zeus introduces Multi-Objective Temporal Masking (MOTM), a unified strategy that supports heterogeneous tasks (e.g., extrapolation, interpolation, and global abstraction) within a single framework. Extensive experiments across five representative tasks demonstrate that Zeus consistently achieves competitive results in tuning-free settings, underscoring its potential as a general-purpose TSFM.
Recent advancements in large language models demonstrate that injecting perturbations can substantially enhance extrapolation performance. However, current approaches often rely on discrete perturbations with fixed designs, which limits their flexibility. In this work, we propose a framework where token prefixes are perturbed by a learnable transformation of a continuous latent vector within an embedding space. To overcome the challenge of an intractable marginal likelihood, we derive unbiased estimating equations for model parameters and optimize them via stochastic gradient descent. We establish the statistical properties of the resulting estimator in over-parameterized regimes. Empirical evaluations on both synthetic and real-world datasets demonstrate that our proposal yields significant gains in out-of-domain settings over a range of state-of-the-art baseline methods.
Multi-task model merging aims to consolidate several task-specific experts into a unified model, yet static merging consistently suffers from parameter interference. While dynamic merging models aim to bridge this gap, many works rely on the costly storage and loading of redundant expert components at inference. In this work, from the perspective of task expert, we view parameter interference as parameter perturbation introduced to each expert during merging process. We show that such parameter perturbations can be modeled as affine transformation, which can be approximated as additive offsets. Motivated by these, we propose Recover Task eXpert (ReTeX), a framework that predicts those offsets, in order to undo parameter interference and recover task-expert performance from a single merged checkpoint. To recover the appropriate expert when task identity is unknown, we introduce a router-free task identifier based on SVD subspace signatures computed offline before inference. At inference, the identifier selects the task whose subspace yields the smallest projection residual for a given input. As a result, ReTeX recovers over 95% of individual-expert performance in both vision and NLP domains, while significantly improving generalization to unseen tasks. Crucially, we also show that the parameter offset prediction leads to emergent adaptive interpolation of expert knowledge for out-of-distribution (OOD) tasks. ReTeX adaptively interpolates seen expert knowledge to handle unseen tasks. Our code is available at https://github.com/BAIKLAB/ReTeX