# Training Continuous Chain of Thought Models: A Tale of Two Regimes

arXiv: https://arxiv.org/abs/2607.16972 · HTML: https://mlsanity.com/paper/2607.16972/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 55 references that are in the map.
- First posted on arXiv 18 Jul 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 29 of 29)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://mlsanity.com/paper/2405.14838/) (2024)
- [Compressed Chain of Thought: Efficient Reasoning Through Dense Representations](https://mlsanity.com/paper/2412.13171/) (2024)
- [Let's Think Dot by Dot: Hidden Computation in Transformer Language Models](https://mlsanity.com/paper/2404.15758/) (2024)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [Soft Thinking: Unlocking the Reasoning Potential of LLMs in Continuous Concept Space](https://mlsanity.com/paper/2505.15778/) (2025)
- [LightThinker: Thinking Step-by-Step Compression](https://mlsanity.com/paper/2502.15589/) (2025)
- [Reasoning by Superposition: A Theoretical Perspective on Chain of Continuous Thought](https://mlsanity.com/paper/2505.12514/) (2025)
- [PonderLM: Pretraining Language Models to Ponder in Continuous Space](https://mlsanity.com/paper/2505.20674/) (2025)
- [LLMs are Single-threaded Reasoners: Demystifying the Working Mechanism of Soft Thinking](https://mlsanity.com/paper/2508.03440/) (2025)
- [Continuous Chain of Thought Enables Parallel Exploration and Reasoning](https://mlsanity.com/paper/2505.23648/) (2025)
- [Soft Tokens, Hard Truths](https://mlsanity.com/paper/2509.19170/) (2025)
- [Hybrid Latent Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2505.18454/) (2025)
- [SwiReasoning: Switch-Thinking in Latent and Explicit for Pareto-Superior Reasoning LLMs](https://mlsanity.com/paper/2510.05069/) (2025)
- [Think-at-Hard: Dynamic Looped Transformers for Improved Reasoning](https://mlsanity.com/paper/2511.08577/) (2025)
- [Multiplex Thinking: Reasoning via Token-wise Branch-and-Merge](https://mlsanity.com/paper/2601.08808/) (2026)
- [A Formal Comparison Between Chain of Thought and Latent Thought](https://mlsanity.com/paper/2509.25239/) (2025)
- [Continuous Autoregressive Language Models](https://mlsanity.com/paper/2510.27688/) (2025)
- [ThinkRouter: Efficient Reasoning via Routing Thinking between Latent and Discrete Spaces](https://mlsanity.com/paper/2602.11683/) (2026)
- [Capabilities and Fundamental Limits of Latent Chain-of-Thought](https://mlsanity.com/paper/2602.01148/) (2026)
- [Self-Distillation for Multi-Token Prediction](https://mlsanity.com/paper/2603.23911/) (2026)
- [LightThinker++: From Reasoning Compression to Memory Management](https://mlsanity.com/paper/2604.03679/) (2026)

## Built on by (most cited first, 2 of 2)

- [AURAL: Adaptive Latent Reasoning with Joint Chunk for Speech Language Models](https://mlsanity.com/paper/2610.01560/) (2026)
- [The Dynamics of Continuous Mixture Collapse in Language Models](https://mlsanity.com/paper/2609.02049/) (2026)

## Abstract (arXiv)

Continuous Chain-of-Thought methods replace verbose reasoning traces with a short sequence of dense latent representations. Earlier continuous CoT methods indirectly supervise the latent representations such that its final state match that of verbose reasoning traces, requiring autoregressive, slow generation during training. We introduce C-MTP, a simpler, faster direct supervision approach that models each latent as an average of the embeddings in the CoT traces to be compressed. Our approach outperforms a prior direct supervision method that approximates the distribution of compressed tokens, and performs competitively to slower indirect supervision approaches in existing evaluation setup with simplified CoT traces (less than 100 tokens). Lastly, we extend the evaluation of Continuous CoT methods to complex tasks with longer reasoning traces (≥ few hundreds reasoning tokens). We find both direct and indirect supervision training methods perform poorly (roughly 65% performance drop) in this setting, revealing the limitations of current continuous CoT methods. The code and checkpoints are released at https://github.com/Varun221/cmtpresearch