GeoERM: Geometry-Aware Multi-Task Representation Learning on Riemannian Manifolds
This addresses robustness issues in multi-task learning for applications like wearable-sensor activity recognition, though it is an incremental improvement by incorporating geometry into existing MTL methods.
The paper tackled the problem of multi-task learning (MTL) methods ignoring non-Euclidean geometry in latent representations, which reduces robustness with heterogeneous or adversarial tasks, and proposed GeoERM, a geometry-aware framework that embeds representations on Riemannian manifolds, resulting in improved accuracy, reduced negative transfer, and stability under noise, outperforming baselines in synthetic and activity-recognition experiments.
Multi-Task Learning (MTL) seeks to boost statistical power and learning efficiency by discovering structure shared across related tasks. State-of-the-art MTL representation methods, however, usually treat the latent representation matrix as a point in ordinary Euclidean space, ignoring its often non-Euclidean geometry, thus sacrificing robustness when tasks are heterogeneous or even adversarial. We propose GeoERM, a geometry-aware MTL framework that embeds the shared representation on its natural Riemannian manifold and optimizes it via explicit manifold operations. Each training cycle performs (i) a Riemannian gradient step that respects the intrinsic curvature of the search space, followed by (ii) an efficient polar retraction to remain on the manifold, guaranteeing geometric fidelity at every iteration. The procedure applies to a broad class of matrix-factorized MTL models and retains the same per-iteration cost as Euclidean baselines. Across a set of synthetic experiments with task heterogeneity and on a wearable-sensor activity-recognition benchmark, GeoERM consistently improves estimation accuracy, reduces negative transfer, and remains stable under adversarial label noise, outperforming leading MTL and single-task alternatives.