GYRO: Anchoring Representations to Simplex Frames for Continual Self-Supervised Learning

Geometric self-supervised learning that use spectral objective provides a principled foundation for extracting robust object manifolds from unlabeled data streams. However, when applied in a continual setting, learned representations rotate freely and drift into established object manifolds. Here, we introduce GYRO, a continual self-supervised learning method that minimizes this drift by anchoring representations to nearest persistent simplex frames. Building on Manifold Capacity Theory, GYRO constrains rotational invariance and enforces geometric stability without requiring class labels, auxiliary alignment losses, or rigid image-to-prototype assignments. Our approach acts directly on the geometry of the embedding space, allowing the network to flexibly adapt its parameters while maintaining separable manifolds. Extensive evaluations across standard benchmarks show that GYRO consistently outperforms replay, distillation, and regularization baselines. Our results highlight that injecting persistent geometric references transforms unconstrained spectral objectives into stable continual learners, demonstrating that representation drift is fundamentally an alignment problem rather than a loss of network capacity.