# Towards Inference-time Scaling for Continuous Space Reasoning

arXiv: https://arxiv.org/abs/2510.12167 · HTML: https://mlsanity.com/paper/2510.12167/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 25 of its 27 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 25 of 25)

- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://mlsanity.com/paper/2502.21074/) (2025)
- [Compressed Chain of Thought: Efficient Reasoning Through Dense Representations](https://mlsanity.com/paper/2412.13171/) (2024)
- [Token Assorted: Mixing Latent and Text Tokens for Improved Language Model Reasoning](https://mlsanity.com/paper/2502.03275/) (2025)
- [A Survey on Latent Reasoning](https://mlsanity.com/paper/2507.06203/) (2025)
- [Continuous Chain of Thought Enables Parallel Exploration and Reasoning](https://mlsanity.com/paper/2505.23648/) (2025)
- [Large language models implicitly learn to straighten neural sentence trajectories to construct a predictive representation of natural language](https://mlsanity.com/paper/2311.04930/) (2023)
- [CoTFormer: A Chain-of-Thought Driven Architecture with Budget-Adaptive Computation Cost at Inference](https://mlsanity.com/paper/2310.10845/) (2023)
- [Stable Anisotropic Regularization](https://mlsanity.com/paper/2305.19358/) (2023)

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

- [GTS: Inference-Time Scaling of Latent Reasoning with a Learnable Gaussian Thought Sampler](https://mlsanity.com/paper/2602.14077/) (2026)
- [LLM Reasoning Is Latent, Not the Chain of Thought](https://mlsanity.com/paper/2604.15726/) (2026)

## Abstract (arXiv)

Inference-time scaling through multiple sample generation in combination with Process- or Outcome-Reward Model (PRM or ORM) re-ranking has proven effective for text-based reasoning in large language models. This paper investigates whether such established techniques can be successfully adapted to reasoning in the continuous space, using COCONUT (Hao et al. 2024) continuous space reasoning LM as the backbone. We demonstrate the feasibility of generating diverse reasoning paths through dropout-based sampling. Our Pass@N analysis on the generated samples reveals the potential that could enable a significant gain in performance akin to observed gain in the discrete space. However, we highlight unique challenges faced for materializing this gain in the continuous thought space. In particular, working recipes for data generation and training PRM and ORM models in the discrete space unlocks only marginal improvements in the continuous space. Through probing various aspects including geometric properties and trajectory dynamics we identify the underlying reasons that prevent effective discrimination between correct and incorrect reasoning (essential for the functioning of PRM and ORM). Our findings reveal that current limitations stem from the absence of key inductive biases in continuous thought representations. We argue that the training frameworks for continuous reasoning LMs require not only to optimize for accuracy but also to explicitly incorporate inductive biases that could be utilized during inference-time for discrimination of correct and incorrect thoughts.footnoteOur code and data will be publicly available.