# Learning Temporal Abstractions via Variational Homomorphisms in Option-Induced Abstract MDPs

arXiv: https://arxiv.org/abs/2507.16473 · HTML: https://mlsanity.com/paper/2507.16473/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 41 of its 65 references that are in the map.
- First posted on arXiv 22 Jul 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

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

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Diversity is All You Need: Learning Skills without a Reward Function](https://mlsanity.com/paper/1802.06070/) (2018)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [The Option-Critic Architecture](https://mlsanity.com/paper/1609.05140/) (2016)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Relay Policy Learning: Solving Long-Horizon Tasks via Imitation and Reinforcement Learning](https://mlsanity.com/paper/1910.11956/) (2019)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Dynamics-Aware Unsupervised Discovery of Skills](https://mlsanity.com/paper/1907.01657/) (2019)
- [Think before you speak: Training Language Models With Pause Tokens](https://mlsanity.com/paper/2310.02226/) (2023)
- [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://mlsanity.com/paper/2405.14838/) (2024)
- [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://mlsanity.com/paper/2502.21074/) (2025)
- [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://mlsanity.com/paper/2311.01460/) (2023)
- [Equivalence Between Policy Gradients and Soft Q-Learning](https://mlsanity.com/paper/1704.06440/) (2017)
- [OPAL: Offline Primitive Discovery for Accelerating Offline Reinforcement Learning](https://mlsanity.com/paper/2010.13611/) (2020)
- [InfoBot: Transfer and Exploration via the Information Bottleneck](https://mlsanity.com/paper/1901.10902/) (2019)
- [TACO: Learning Task Decomposition via Temporal Alignment for Control](https://mlsanity.com/paper/1803.01840/) (2018)
- [Long-Horizon Visual Planning with Goal-Conditioned Hierarchical Predictors](https://mlsanity.com/paper/2006.13205/) (2020)
- [When Waiting is not an Option : Learning Options with a Deliberation Cost](https://mlsanity.com/paper/1709.04571/) (2017)
- [Self-Consistent Trajectory Autoencoder: Hierarchical Reinforcement Learning with Trajectory Embeddings](https://mlsanity.com/paper/1806.02813/) (2018)
- [Reasoning to Learn from Latent Thoughts](https://mlsanity.com/paper/2503.18866/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) have shown remarkable reasoning ability through explicit Chain-of-Thought (CoT) prompting, but generating these step-by-step textual explanations is computationally expensive and slow. To overcome this, we aim to develop a framework for efficient, implicit reasoning, where the model "thinks" in a latent space without generating explicit text for every step. We propose that these latent thoughts can be modeled as temporally-extended abstract actions, or options, within a hierarchical reinforcement learning framework. To effectively learn a diverse library of options as latent embeddings, we first introduce the Variational Markovian Option Critic (VMOC), an off-policy algorithm that uses variational inference within the HiT-MDP framework. To provide a rigorous foundation for using these options as an abstract reasoning space, we extend the theory of continuous MDP homomorphisms. This proves that learning a policy in the simplified, abstract latent space, for which VMOC is suited, preserves the optimality of the solution to the original, complex problem. Finally, we propose a cold-start procedure that leverages supervised fine-tuning (SFT) data to distill human reasoning demonstrations into this latent option space, providing a rich initialization for the model's reasoning capabilities. Extensive experiments demonstrate that our approach achieves strong performance on complex logical reasoning benchmarks and challenging locomotion tasks, validating our framework as a principled method for learning abstract skills for both language and control.