Measure Less, Know More: Self-Supervised Test-Time Feature Acquisition

Recent progress in multimodal, high-dimensional learning has enabled foundation models to process heterogeneous, large-scale data. However, at test time, acquiring all features or modalities can be prohibitively costly and often redundant. Sequentially selecting informative modalities is therefore critical, yet challenging when the downstream task or prediction target is unknown. To this end, we introduce ECHO-$k$, a task-agnostic and self-supervised learning principle for modality acquisition: we use a deep model’s internal pretrained representations (e.g., from a foundation model) as proxy targets that summarize cross-modal information. We provide theoretical guarantees in a linear model setting that motivate a reinforcement learning (RL) policy for sequential modality selection. Across benchmarks, the resulting acquisition strategies transfer reliably and achieve state-of-the-art performance on downstream tasks that are entirely unseen during selection. Our method provides a principled route to cost-aware test-time deployment, with implications for any multimodal system where measurements are expensive or time-constrained, and downstream tasks unknown a priori.