Joint Embedding Predictive Architectures (JEPAs) learn visual
representations by predicting latent target embeddings from
contextual views, without reconstruction or contrastive negatives.
While effective, existing JEPA predictors are shallow feed-forward
networks applied once per training step, offering limited control
over multi-step latent dynamics and stability. We revisit this
design choice and introduce Learnable Iterated Function Systems
(LIFS), a structured predictor composed of a contractive mixture
of affine maps applied recursively in latent space. LIFS integrates
seamlessly into JEPA without modifying the encoder or objective,
and introduces explicit geometric inductive bias through spectral
control, soft mixture routing, and multi-step refinement. We
provide sufficient conditions for contraction under input-dependent
mixing and empirically verify these conditions during training.
Experiments on CIFAR-10/100 and ImageNet-1K with ResNet-18
and ViT-S/B/16 encoders show that LIFS improves training stability,
accelerates predictive alignment, and yields consistent linear-probe
gains at matched capacity. Analyses of routing entropy, operator
specialization, and FLOPs demonstrate that these improvements stem
from predictor geometry rather than increased depth or parameters.
Our results highlight structured, contractive predictors as a promising
and underexplored design axis for latent-space self-supervised
learning.