# DiscoLoop: Looping Discrete Embeddings and Continuous Hidden States for Multi-hop Reasoning

arXiv: https://arxiv.org/abs/2607.00341 · HTML: https://mlsanity.com/paper/2607.00341/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 39 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

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

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://mlsanity.com/paper/2502.02737/) (2025)
- [Think before you speak: Training Language Models With Pause Tokens](https://mlsanity.com/paper/2310.02226/) (2023)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [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)
- [Do Large Language Models Latently Perform Multi-Hop Reasoning?](https://mlsanity.com/paper/2402.16837/) (2024)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [Physics of Language Models: Part 3.2, Knowledge Manipulation](https://mlsanity.com/paper/2309.14402/) (2023)
- [Soft Thinking: Unlocking the Reasoning Potential of LLMs in Continuous Concept Space](https://mlsanity.com/paper/2505.15778/) (2025)
- [Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process](https://mlsanity.com/paper/2407.20311/) (2024)
- [Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalization](https://mlsanity.com/paper/2405.15071/) (2024)
- [Hopping Too Late: Exploring the Limitations of Large Language Models on Multi-Hop Queries](https://mlsanity.com/paper/2406.12775/) (2024)
- [Reasoning by Superposition: A Theoretical Perspective on Chain of Continuous Thought](https://mlsanity.com/paper/2505.12514/) (2025)
- [Qwen3-Coder-Next Technical Report](https://mlsanity.com/paper/2603.00729/) (2026)
- [Guiding Language Model Reasoning with Planning Tokens](https://mlsanity.com/paper/2310.05707/) (2023)
- [PonderLM: Pretraining Language Models to Ponder in Continuous Space](https://mlsanity.com/paper/2505.20674/) (2025)
- [Loop, Think, & Generalize: Implicit Reasoning in Recurrent-Depth Transformers](https://mlsanity.com/paper/2604.07822/) (2026)
- [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)
- [How do Transformers Learn Implicit Reasoning?](https://mlsanity.com/paper/2505.23653/) (2025)
- [Emergence of Superposition: Unveiling the Training Dynamics of Chain of Continuous Thought](https://mlsanity.com/paper/2509.23365/) (2025)
- [Extractive Structures Learned in Pretraining Enable Generalization on Finetuned Facts](https://mlsanity.com/paper/2412.04614/) (2024)
- [Generalization or Hallucination? Understanding Out-of-Context Reasoning in Transformers](https://mlsanity.com/paper/2506.10887/) (2025)

## Built on by (most cited first, 4 of 4)

- [Loop the Loopies!](https://mlsanity.com/paper/2607.16051/) (2026)
- [DeepLoop: Depth Scaling for Looped Transformers](https://mlsanity.com/paper/2607.13491/) (2026)
- [The Ignition Is Real, and It Lives at the Readout: Latent composition, difficulty-clocked ignition, and the interface-constituted commit in a recurrent-depth reasoner](https://mlsanity.com/paper/2608.03263/) (2026)
- [Improving Test-Time Scaling with Adaptive Looped Transformers](https://mlsanity.com/paper/2609.35748/) (2026)

## Abstract (arXiv)

Large language models achieve strong performance on many reasoning tasks when allowed to externalize intermediate steps as Chain-of-Thought (CoT). However, many questions require the model to internalize the multi-step reasoning within a single forward pass before generating the answer. We study this challenge through two-hop reasoning, a representative task where the model must compose multiple pieces of parametric knowledge within a single forward pass. Standard non-recurrent Transformers suffer from a depth-local storage problem: facts learned in earlier layers are unavailable where second-hop retrieval happens. We found that Looped Transformers mitigate this issue by reusing the same memory, but still generalize imperfectly. We show that the remaining bottleneck is representational. In the two-hop reasoning task, the first loop often makes the correct bridge entity nearly perfectly decodable, yet the corresponding hidden state remains poorly aligned with the bridge token embedding. Surprisingly, an easy training-free realignment intervention nearly closes the generalization gap. Building upon this insight, we propose DiscoLoop, a looping architecture whose recurrence carries both a discrete embedding channel and a continuous hidden-state channel. DiscoLoop achieves near-perfect accuracy with substantially fewer training steps across symbolic and synthetic-language multi-hop reasoning tasks. When applied to real-world pretraining, DiscoLoop attains lower training loss and stronger benchmark performance than looped-transformer baselines, suggesting that the mixed-channel design transfers to practical language modeling.