Joint-Embedding Predictive Architectures (JEPAs), a powerful class of self-supervised models, exhibit an unexplained ability to cluster time-series data by their underlying dynamical regimes. We propose a novel theoretical explanation for this phenomenon, hypothesizing that JEPA's predictive objective implicitly drives it to learn the invariant subspace of the system's Koopman operator. We prove that an idealized JEPA loss is minimized when the encoder represents the system's regime indicator functions, which are Koopman eigenfunctions. This theory was validated on synthetic data with known dynamics, demonstrating that constraining the JEPA's linear predictor to be a near-identity operator is the key inductive bias that forces the encoder to learn these invariants. We further discuss that this constraint is critical for selecting this interpretable solution from a class of mathematically equivalent but entangled optima, revealing the predictor's role in representation disentanglement. This work demystifies a key behavior of JEPAs, provides a principled connection between modern self-supervised learning and dynamical systems theory, and informs the design of more robust and interpretable time-series models.

While the current machine fault diagnosis is affected by the rarity of cross conditional fault data in practice, efficient implementation of these diagnosis models on resource constrained devices is another active challenge. Given such constraints, an ideal fault diagnosis model should not be either generalizable across the shifting domains or lightweight, but rather a combination of both, generalizable while being minimalistic. Preferably being uninformed about the domain shift. Addressing these computational and data centric challenges, we propose a novel methodology, Convolutional Auto-encoder and Nearest Neighbors based self adaptation (SCAE-NN), that adapts its fault diagnosis model to the changing conditions of a machine. We implemented SCAE-NN for various cross-domain fault diagnosis tasks and compared its performance against the state-of-the-art domain invariant models. Compared to the SOTA, SCAE-NN is at least 6− 7% better at predicting fault classes across conditions, while being more than 10 times smaller in size and latency. Moreover, SCAE-NN does not need any labelled target domain data for the adaptation, making it suitable for practical data scarce scenarios.