# Intrinsic-Energy Joint Embedding Predictive Architectures Induce Quasimetric Spaces

arXiv: https://arxiv.org/abs/2602.12245 · HTML: https://mlsanity.com/paper/2602.12245/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Builds on (most cited first, 9 of 9)

- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learning](https://mlsanity.com/paper/2304.01203/) (2023)
- [Improved Representation of Asymmetrical Distances with Interval Quasimetric Embeddings](https://mlsanity.com/paper/2211.15120/) (2022)
- [Value-guided action planning with JEPA world models](https://mlsanity.com/paper/2601.00844/) (2025)
- [Model Predictive Optimized Path Integral Strategies](https://mlsanity.com/paper/2203.16633/) (2022)
- [Physics of Learning: A Lagrangian perspective to different learning paradigms](https://mlsanity.com/paper/2509.21049/) (2025)
- [PA-MPPI: Perception-Aware Model Predictive Path Integral Control for Quadrotor Navigation in Unknown Environments](https://mlsanity.com/paper/2509.14978/) (2025)

## Abstract (arXiv)

Joint-Embedding Predictive Architectures (JEPAs) aim to learn representations by predicting target embeddings from context embeddings, inducing a scalar compatibility energy in a latent space. In contrast, Quasimetric Reinforcement Learning (QRL) studies goal-conditioned control through directed distance values (cost-to-go) that support reaching goals under asymmetric dynamics. In this short article, we connect these viewpoints by restricting attention to a principled class of JEPA energy functions : intrinsic (least-action) energies, defined as infima of accumulated local effort over admissible trajectories between two states. Under mild closure and additivity assumptions, any intrinsic energy is a quasimetric. In goal-reaching control, optimal cost-to-go functions admit exactly this intrinsic form ; inversely, JEPAs trained to model intrinsic energies lie in the quasimetric value class targeted by QRL. Moreover, we observe why symmetric finite energies are structurally mismatched with one-way reachability, motivating asymmetric (quasimetric) energies when directionality matters.