JEPA world models commonly predict the next latent state with one regressor. Under stochastic transitions, squared and cosine regression return the conditional mean and its normalized direction, respectively: a single compromise that may match no valid successor. MoP-JEPA instead uses K hard-assigned heads and a context-only router to produce a finite candidate set in one pass. On held-out OGBench transitions, graph search with single-output predictors succeeds on 0.02--0.09 of queries, whereas MoP-JEPA reaches 0.85. To distinguish useful successors from indiscriminate coverage, we also measure verified-route success (\emph{realroute}), which checks after graph construction whether the proposal contains a path of real transitions. MoP-JEPA leads this same-protocol metric on all three mazes; an MDN attains high raw coverage but predicts many nonexistent edges.
Joint-Embedding Predictive Architectures (JEPAs) learn world models by predicting in representation space rather than reconstructing pixels, making them a natural backbone for latent model predictive control from offline demonstration logs. JEPA-style training optimizes short-horizon latent prediction, whereas planning requires a multi-step ranking of imagined futures by goal progress. Prior JEPA planners often inherit that ranking from embedding geometry, typically latent Euclidean distance, which arises as a byproduct of representation learning rather than as a progress cost mined from the logs. We propose Temporal-Distance-JEPA, which retains the LeWM encoder--predictor backbone and mines a directed temporal cost from reward-free trajectories: same-trajectory step order supplies positive targets, cross-trajectory pairs act as heuristic negatives, and a rollout-consistency term matches the planner horizon. The mined supervision serves two roles: as the deployed planning cost when progress is topological, and as a representation signal that improves Euclidean planning when contact geometry dominates. Under locked evaluation, deploying the mined cost raises Two-Room success to 100.0% versus LeWM's 97.4%, while shared Euclidean planning on the same temporally trained checkpoint raises OGB-Cube by 14.2 points over LeWM and improves Push-T. Against LeWM and the concurrent RC-aux baseline under locked evaluation, Temporal-Distance-JEPA matches or exceeds both methods on every environment. Ablations show that the directed head, cross-trajectory negatives, and rollout consistency each contribute. Temporal-Distance-JEPA narrows the train--plan gap for JEPA world-model planners by discovering temporal progress structure in offline logs and co-designing cost form with plan-time deployment. Code is available at https://github.com/HKBU-KnowComp/Temporal-Distance-JEPA.
World models construct latent states that support prediction, planning, and reasoning about an underlying system. Joint-embedding predictive architectures (JEPAs) offer a direct way to learn such states by predicting targets in representation space instead of reconstructing every detail of the observation. Standard JEPAs, however, organize all predictable content through one target embedding and one prediction pathway. In complex systems, this monolithic state can allocate redundant capacity to dominant signals while providing weak or conflicting gradients to less dominant predictive structure. We introduce \method, a latent world-modeling framework based on orthogonal predictive factorization. Learned basis matrices analyze each target state into multiple components, and a dedicated prediction branch estimates each component from a shared context representation. Predictive regression preserves the factor magnitudes required for state synthesis, an orthogonality objective discourages repeated directions, factor-activity regularization maintains variation in projected targets, and online variance regularization discourages coordinate-wise encoder collapse. Predicted components are synthesized into a complete latent state that can be used by a readout, decoder, planner, or autoregressive rollout. The same predictive-state mechanism applies when the target is temporally future, spatially hidden, or another partial observation of the same system. Experiments on controlled vision, single-cell transcriptomics, longitudinal health records, continuous control, and molecular dynamics evaluate representation quality, forecasting, planning, and long-horizon stability.
Joint Embedding Predictive Architectures (JEPAs) have recently emerged as a promising paradigm for world modeling by learning predictive dynamics in a latent space rather than generating future observations at the input level. Despite their empirical success, the theoretical understanding of JEPA-based world models remains limited. In this paper, we develop the first generalization theory for JEPA-based world models. We formulate JEPA pretraining as a conditional spectral graph learning problem and show that the JEPA objective is equivalent to a low-rank factorization of an action-conditioned co-occurrence matrix. Building on this characterization, we establish a connection between JEPA pretraining error and downstream planning regret, leading to a finite-sample generalization bound for JEPA-based world models. Our analysis reveals an inherent trade-off between approximation and sample errors with respect to the latent dimension, providing theoretical insights into the advantages and limitations of latent predictive models compared with input-level predictive approaches.