# Constrained latent state modeling: A unifying perspective on representation learning under competing constraints

arXiv: https://arxiv.org/abs/2605.15995 · HTML: https://mlsanity.com/paper/2605.15995/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 97 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 30 of 39)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [ViLBERT: Pretraining Task-Agnostic Visiolinguistic Representations for Vision-and-Language Tasks](https://mlsanity.com/paper/1908.02265/) (2019)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [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)
- [Multimodal Machine Learning: A Survey and Taxonomy](https://mlsanity.com/paper/1705.09406/) (2017)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Data-Efficient Image Recognition with Contrastive Predictive Coding](https://mlsanity.com/paper/1905.09272/) (2019)
- [Multimodal Transformer for Unaligned Multimodal Language Sequences](https://mlsanity.com/paper/1906.00295/) (2019)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Revisiting Feature Prediction for Learning Visual Representations from Video](https://mlsanity.com/paper/2404.08471/) (2024)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [Context Autoencoder for Self-Supervised Representation Learning](https://mlsanity.com/paper/2202.03026/) (2022)
- [Multimodal Deep Learning](https://mlsanity.com/paper/2301.04856/) (2023)
- [Emergence of Invariance and Disentanglement in Deep Representations](https://mlsanity.com/paper/1706.01350/) (2017)
- [Multimodal Generative Models for Scalable Weakly-Supervised Learning](https://mlsanity.com/paper/1802.05335/) (2018)
- [Variational Mixture-of-Experts Autoencoders for Multi-Modal Deep Generative Models](https://mlsanity.com/paper/1911.03393/) (2019)
- [State Representation Learning for Control: An Overview](https://mlsanity.com/paper/1802.04181/) (2018)

## Abstract (arXiv)

Learning latent representations from temporal, multimodal, and partially observed data requires specifying what information a latent state should retain, discard, and organize. Existing approaches encode these requirements through heterogeneous objectives, making methods difficult to compare and learned representations difficult to interpret. We propose Constrained Latent State Modeling (CLSM), a conceptual framework that characterizes latent states through six complementary properties: predictive sufficiency, minimality, temporal coherence, observation compatibility, invariance to nuisance factors, and structural constraints. CLSM separates these properties from the surrogate objectives used to induce them and from the diagnostics used to evaluate them, and clarifies how combinations of constraints can improve identifiability by restricting the space of admissible representations. We reinterpret major representation-learning families through this common design space and illustrate the framework with a controlled synthetic benchmark. The experiments show how objectives produce distinct latent organizations and empirical trade-offs depending on the prediction target, surrogate formulation, parameterization, and optimization. Companion repository containing the reference implementation, reproducible experiments, documentation, and model cards: https://github.com/gwenole-quellec/clsm