Learning self-supervised representations that are invariant and equivariant to transformations is crucial for advancing beyond traditional visual classification tasks. However, many methods rely on predictor architectures to encode equivariance, despite evidence that architectural choices, such as capsule networks, inherently excel at learning interpretable pose-aware representations. To explore this, we introduce EquiCaps (Equivariant Capsule Network), a capsule-based approach to pose-aware self-supervision that eliminates the need for a specialised predictor for enforcing equivariance. Instead, we leverage the intrinsic pose-awareness capabilities of capsules to improve performance in pose estimation tasks. To further challenge our assumptions, we increase task complexity via multi-geometric transformations to enable a more thorough evaluation of invariance and equivariance by introducing 3DIEBench-T, an extension of a 3D object-rendering benchmark dataset. Empirical results demonstrate that EquiCaps outperforms prior state-of-the-art equivariant methods on rotation prediction, achieving a supervised-level $R^2$ of 0.78 on the 3DIEBench rotation prediction benchmark and improving upon SIE and CapsIE by 0.05 and 0.04 $R^2$, respectively. Moreover, in contrast to non-capsule-based equivariant approaches, EquiCaps maintains robust equivariant performance under combined geometric transformations, underscoring its generalisation capabilities and the promise of predictor-free capsule architectures.

Humans and animals have the ability to continuously learn new information over their lifetime without losing previously acquired knowledge. However, artificial neural networks struggle with this due to new information conflicting with old knowledge, resulting in catastrophic forgetting. The complementary learning systems (CLS) theory (McClelland and McNaughton, 1995; Kumaran et al. 2016) suggests that the interplay between hippocampus and neocortex systems enables long-term and efficient learning in the mammalian brain, with memory replay facilitating the interaction between these two systems to reduce forgetting. The proposed Lifelong Self-Supervised Domain Adaptation (LLEDA) framework draws inspiration from the CLS theory and mimics the interaction between two networks: a DA network inspired by the hippocampus that quickly adjusts to changes in data distribution and an SSL network inspired by the neocortex that gradually learns domain-agnostic general representations. LLEDA’s latent replay technique facilitates communication between these two networks by reactivating and replaying the past memory latent representations to stabilize long-term generalization and retention without interfering with the previously learned information. Extensive experiments demonstrate that the proposed method outperforms several other methods resulting in a long-term adaptation while being less prone to catastrophic forgetting when transferred to new domains.