# SJEPA: Learning Elegant Latent Dynamics with Hybrid Symbolic-Neural Predictors

arXiv: https://arxiv.org/abs/2608.04060 · HTML: https://mlsanity.com/paper/2608.04060/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 37 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Builds on (most cited first, 26 of 26)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Recurrent World Models Facilitate Policy Evolution](https://mlsanity.com/paper/1809.01999/) (2018)
- [Revisiting Feature Prediction for Learning Visual Representations from Video](https://mlsanity.com/paper/2404.08471/) (2024)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [MC-JEPA: A Joint-Embedding Predictive Architecture for Self-Supervised Learning of Motion and Content Features](https://mlsanity.com/paper/2307.12698/) (2023)
- [Audio-JEPA: Joint-Embedding Predictive Architecture for Audio Representation Learning](https://mlsanity.com/paper/2507.02915/) (2025)
- [VJEPA: Variational Joint Embedding Predictive Architectures as Probabilistic World Models](https://mlsanity.com/paper/2601.14354/) (2026)
- [3D-JEPA: A Joint Embedding Predictive Architecture for 3D Self-Supervised Representation Learning](https://mlsanity.com/paper/2409.15803/) (2024)
- [ACT-JEPA: Novel Joint-Embedding Predictive Architecture for Efficient Policy Representation Learning](https://mlsanity.com/paper/2501.14622/) (2025)
- [T-SHRED: Symbolic Regression for Regularization and Model Discovery with Transformer Shallow Recurrent Decoders](https://mlsanity.com/paper/2506.15881/) (2025)
- [From Observation to Insight: Mechanistic World Models and the Quest for Autonomous Discovery](https://mlsanity.com/paper/2607.12474/) (2026)
- [Knowledge, Rules and Their Embeddings: Two Paths towards Neuro-Symbolic JEPA](https://mlsanity.com/paper/2603.13265/) (2026)
- [Extracting Governing Equations from Latent Dynamics via Multi-View Contrastive Learning](https://mlsanity.com/paper/2606.13260/) (2026)

## Built on by (most cited first, 1 of 1)

- [Vision-Predictor-Action: Towards Efficient Embodied AI via Neuro-Symbolic JEPA Predictors](https://mlsanity.com/paper/2610.15556/) (2026)

## Abstract (arXiv)

Joint-embedding predictive architectures learn abstract states by predicting target embeddings from context embeddings, but their transition models are typically opaque neural maps. We introduce SJEPA, a reconstruction-free JEPA framework that learns predictive representations whose induced dynamics admit compact symbolic descriptions. Its hybrid transition combines a symbolic law with a regularised neural correction for dynamics outside the selected grammar. The central principle is to learn the simplest adequate dynamics: representation constraints preserve informative, non-collapsed predictive coordinates, while operator compression favours low-complexity symbolic-neural transitions that remain predictively adequate. We formalise this principle through induced-dynamics complexity, analyse predictive-coordinate non-identifiability, and show that unconstrained operator compression creates a direct shortcut to representation collapse. The framework supports both alternating representation-equation learning and symbolic dynamics fitted to fixed representations. In controlled pendulum experiments, joint learning discovers substantially simpler symbolic dynamics with lower long-horizon rollout error and divergence than post-hoc fitting, while an unconstrained one-step diagnostic realises the predicted collapse shortcut. Under grammar misspecification, correction regularisation preserves the representable symbolic mechanism and directs the neural component towards residual dynamics. The results expose a controllable trade-off among predictive fidelity, representation quality, symbolic parsimony, and symbolic-neural allocation.