RADAR: Relative Angular Divergence Across Representations
Authors: Xavier Cadet, Mateusz Nowak, Peter Chin
Organizations: Dartmouth College
Abstract
Machine learning methods rely on data. However, gathering suitable data can be challenging due to availability constraints, cost, or the need for domain expertise. Expanding datasets with additional sources is a common response to limited data, yet this practice does not always improve downstream performance and can sometimes lead to a loss of performance, known as negative transfer. We propose RADAR, a simple, geometrically grounded metric for estimating cross-domain transferability in foundation models. RADAR analyzes the layer-wise evolution of representations by measuring angular alignments and relative changes in distance along layer-to-layer displacement trajectories, and by comparing empirical distributions of within-domain and cross-domain dynamics. We hypothesize that domain transferability is related to the divergence between these trajectory distributions. We evaluate the metric across multiple modalities, including cross-lingual sentiment classification with text embedding models and cross-domain image classification with foundation vision models. Across several settings, RADAR provides competitive predictive performance relative to existing transferability metrics on several vision and text benchmarks, with particularly strong results when domain transitions are smooth or cleanly separated. Our ablations further suggest that the effectiveness of transferability estimation depends on the geometry of the model's internal representation space, with different modalities favoring different topological formulations.
The growing availability of trajectory datasets has fueled major advances in data-driven motion prediction. Yet, models trained on one dataset often fail to generalize beyond their training domain as a result of differences in scene layouts, agent behaviors, and sensing conditions. A framework that learns latent representations of datasets and quantifies their similarity using distributional metrics is presented. This large-scale study covers 24 major datasets, including the most widely used motion-prediction benchmarks, and shows that the resulting transferability scores strongly correlate with cross-dataset model performance. The results provide practical guidance for dataset selection, pretraining, and large-scale foundation models for motion prediction, paving the way toward more generalizable and robust predictive systems.
Domain transfer (DT) maps source to target distributions and supports tasks such as unsupervised image-to-image translation, single-cell analysis, and cross-platform medical imaging. However, DT is fundamentally ill-posed: push-forward mappings are generally non-identifiable, as measure-preserving automorphisms (MPAs) preserve marginals while altering cross-domain correspondences, leading to content-misaligned translation. Recent work shows that MPAs can be eliminated by jointly transferring multiple corresponding source/target conditional distributions, but supervision signals labeling such conditionals are not always available in practice. We develop an alternative route to DT identifiability. Under a structural sparsity condition on the Jacobian support pattern, we show that distribution matching together with a single paired anchor sample suffices to identify the ground-truth transfer -- requiring substantially less supervision than prior approaches. To enable practical high-dimensional learning, we further propose an efficient Jacobian sparsity regularizer based on randomized masked finite differences, yielding a scalable surrogate without explicit Jacobian evaluation. Empirical results on synthetic and real-world DT tasks validate the theory.
Cross-lingual transfer is a model's ability to generalize capabilities from well-represented source languages to under-represented target languages. Existing measures of a model's transfer strength conflate improvements in transfer with general improvements to accuracy in the source language. We advocate for an alternate metric that reliably captures transfer strength called Hardness Adjusted Transfer (HAT) Score, and use it to derive multiple insights on factors influencing transfer strength. Our analysis across twenty diverse language models and three popular mainstream multilingual benchmarks argues that 1) transfer in small models is not broken, 2) we are making slower than expected progress in cross-lingual transfer with model size, and 3) we have made clear progress over time.
Prasoon Bajpai, Eleftheria Briakou, Colin Cherry +2