# World Modeling through Spectral Alignment

arXiv: https://arxiv.org/abs/2610.15429 · HTML: https://mlsanity.com/paper/2610.15429/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 41 of its 51 references that are in the map.
- First posted on arXiv 11 Oct 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 30 of 41)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [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)
- [MOReL : Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2005.05951/) (2020)
- [CALVIN: A Benchmark for Language-Conditioned Policy Learning for Long-Horizon Robot Manipulation Tasks](https://mlsanity.com/paper/2112.03227/) (2021)
- [TD-MPC2: Scalable, Robust World Models for Continuous Control](https://mlsanity.com/paper/2310.16828/) (2023)
- [World Action Models are Zero-shot Policies](https://mlsanity.com/paper/2602.15922/) (2026)
- [Learning Invariant Representations for Reinforcement Learning without Reconstruction](https://mlsanity.com/paper/2006.10742/) (2020)
- [DINO-WM: World Models on Pre-trained Visual Features enable Zero-shot Planning](https://mlsanity.com/paper/2411.04983/) (2024)
- [Causal World Modeling for Robot Control](https://mlsanity.com/paper/2601.21998/) (2026)
- [Data-Efficient Reinforcement Learning with Self-Predictive Representations](https://mlsanity.com/paper/2007.05929/) (2020)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [Cosmos Policy: Fine-Tuning Video Models for Visuomotor Control and Planning](https://mlsanity.com/paper/2601.16163/) (2026)
- [LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels](https://mlsanity.com/paper/2603.19312/) (2026)
- [Contrastive Learning as Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2206.07568/) (2022)
- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [Contrastive and Non-Contrastive Self-Supervised Learning Recover Global and Local Spectral Embedding Methods](https://mlsanity.com/paper/2205.11508/) (2022)
- [URLB: Unsupervised Reinforcement Learning Benchmark](https://mlsanity.com/paper/2110.15191/) (2021)
- [Training Agents Inside of Scalable World Models](https://mlsanity.com/paper/2509.24527/) (2025)
- [Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learning](https://mlsanity.com/paper/2304.01203/) (2023)
- [V-JEPA 2.1: Unlocking Dense Features in Video Self-Supervised Learning](https://mlsanity.com/paper/2603.14482/) (2026)
- [Learning One Representation to Optimize All Rewards](https://mlsanity.com/paper/2103.07945/) (2021)
- [Does Zero-Shot Reinforcement Learning Exist?](https://mlsanity.com/paper/2209.14935/) (2022)

## Abstract (arXiv)

How do we tell a world model what information to preserve? We study this question through the lens of spectral representation learning. We introduce SpecWM, a JEPA framework that explicitly specifies desired relationships between observations through a target similarity kernel and trains the encoder to reproduce those relationships in its embedding geometry. Different kernels provide different supervision, ranging from physical state information to a fully self-supervised temporal kernel requiring only the ordering of observations within trajectories. We characterize the global optima of the objective, establish conditions for linear recoverability and invariance to nuisance information, and connect temporal-kernel similarity to the behavioral successor measure under an idealized setting. Empirically, the choice of kernel strongly controls which physical quantities are recoverable from the representation. More importantly, temporal spectral alignment improves CEM planning success over LeWorldModel from 52% to 68% on OGBench Cube, 49% to 77% on OGBench Scene, and 29% to 51% on CALVIN. These results suggest that explicitly specifying representation geometry provides a simple way to steer what latent world models preserve for control.