# SoftCoT++: Test-Time Scaling with Soft Chain-of-Thought Reasoning

arXiv: https://arxiv.org/abs/2505.11484 · HTML: https://mlsanity.com/paper/2505.11484/

## Key facts

- Cited by 41 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 33 of its 34 references that are in the map.
- First posted on arXiv 16 May 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 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [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)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [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)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [Compressed Chain of Thought: Efficient Reasoning Through Dense Representations](https://mlsanity.com/paper/2412.13171/) (2024)
- [The Effect of Sampling Temperature on Problem Solving in Large Language Models](https://mlsanity.com/paper/2402.05201/) (2024)
- [Stream of Search (SoS): Learning to Search in Language](https://mlsanity.com/paper/2404.03683/) (2024)
- [SoftCoT: Soft Chain-of-Thought for Efficient Reasoning with LLMs](https://mlsanity.com/paper/2502.12134/) (2025)
- [S*: Test Time Scaling for Code Generation](https://mlsanity.com/paper/2502.14382/) (2025)

## Built on by (most cited first, 30 of 41)

- [MemGen: Weaving Generative Latent Memory for Self-Evolving Agents](https://mlsanity.com/paper/2509.24704/) (2025)
- [Reasoning Beyond Language: A Comprehensive Survey on Latent Chain-of-Thought Reasoning](https://mlsanity.com/paper/2505.16782/) (2025)
- [Implicit Reasoning in Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2509.02350/) (2025)
- [The Latent Space: Foundation, Evolution, Mechanism, Ability, and Outlook](https://mlsanity.com/paper/2604.02029/) (2026)
- [SwiReasoning: Switch-Thinking in Latent and Explicit for Pareto-Superior Reasoning LLMs](https://mlsanity.com/paper/2510.05069/) (2025)
- [SofT-GRPO: Surpassing Discrete-Token LLM Reinforcement Learning via Gumbel-Reparameterized Soft-Thinking Policy Optimization](https://mlsanity.com/paper/2511.06411/) (2025)
- [Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning](https://mlsanity.com/paper/2605.21488/) (2026)
- [Stop When Enough: Adaptive Early-Stopping for Chain-of-Thought Reasoning](https://mlsanity.com/paper/2510.10103/) (2025)
- [Parallel Test-Time Scaling for Latent Reasoning Models](https://mlsanity.com/paper/2510.07745/) (2025)
- [When and How Much to Imagine: Adaptive Test-Time Scaling with World Models for Visual Spatial Reasoning](https://mlsanity.com/paper/2602.08236/) (2026)
- [Slim-SC: Thought Pruning for Efficient Scaling with Self-Consistency](https://mlsanity.com/paper/2509.13990/) (2025)
- [Bridging the Gap Between Latent and Explicit Reasoning with Looped Transformers](https://mlsanity.com/paper/2606.31779/) (2026)
- [From Efficiency to Adaptivity: A Deeper Look at Adaptive Reasoning in Large Language Models](https://mlsanity.com/paper/2511.10788/) (2025)
- [The Art of Scaling Test-Time Compute for Large Language Models](https://mlsanity.com/paper/2512.02008/) (2025)
- [MedSynapse-V: Bridging Visual Perception and Clinical Intuition via Latent Memory Evolution](https://mlsanity.com/paper/2604.26283/) (2026)
- [LatentEvolve: Self-Evolving Test-Time Scaling in Latent Space](https://mlsanity.com/paper/2509.24771/) (2025)
- [LatentChem: From Textual CoT to Latent Thinking in Chemical Reasoning](https://mlsanity.com/paper/2602.07075/) (2026)
- [Measuring Reasoning Utility in LLMs via Conditional Entropy Reduction](https://mlsanity.com/paper/2508.20395/) (2025)
- [The Silent Thought: Modeling Internal Cognition in Full-Duplex Spoken Dialogue Models via Latent Reasoning](https://mlsanity.com/paper/2603.17837/) (2026)
- [Do Vision-Language Models Truly Perform Vision Reasoning? A Rigorous Study of the Modality Gap](https://mlsanity.com/paper/2604.16256/) (2026)
- [Capabilities and Fundamental Limits of Latent Chain-of-Thought](https://mlsanity.com/paper/2602.01148/) (2026)
- [Mem-W: Latent Memory-Native GUI Agents](https://mlsanity.com/paper/2605.09317/) (2026)
- [Latent Thought Flow: Efficient Latent Reasoning in Large Language Models](https://mlsanity.com/paper/2606.16222/) (2026)
- [Explore-Execute Chain: Towards an Efficient Structured Reasoning Paradigm](https://mlsanity.com/paper/2509.23946/) (2025)
- [IV-CoT: Implicit Visual Chain-of-Thought for Structure-Aware Text-to-Image Generation](https://mlsanity.com/paper/2606.24849/) (2026)
- [MUX: Continuous Reasoning via Multiplexed Tokens](https://mlsanity.com/paper/2607.18264/) (2026)
- [Latent Abstraction for Retrieval-Augmented Generation](https://mlsanity.com/paper/2604.17866/) (2026)
- [Tyler: Typed Latent Reasoning for Language Models -- When to Think, What to Compute, and How Much to Allocate](https://mlsanity.com/paper/2606.16360/) (2026)
- [RuPLaR : Efficient Latent Compression of LLM Reasoning Chains with Rule-Based Priors From Multi-Step to One-Step](https://mlsanity.com/paper/2605.09346/) (2026)
- [Geometric Latent Reasoning Induces Shorter Generations in LLMs](https://mlsanity.com/paper/2606.02248/) (2026)

## Abstract (arXiv)

Test-Time Scaling (TTS) refers to approaches that improve reasoning performance by allocating extra computation during inference, without altering the model's parameters. While existing TTS methods operate in a discrete token space by generating more intermediate steps, recent studies in Coconut and SoftCoT have demonstrated that thinking in the continuous latent space can further enhance the reasoning performance. Such latent thoughts encode informative thinking without the information loss associated with autoregressive token generation, sparking increased interest in continuous-space reasoning. Unlike discrete decoding, where repeated sampling enables exploring diverse reasoning paths, latent representations in continuous space are fixed for a given input, which limits diverse exploration, as all decoded paths originate from the same latent thought. To overcome this limitation, we introduce SoftCoT++ to extend SoftCoT to the Test-Time Scaling paradigm by enabling diverse exploration of thinking paths. Specifically, we perturb latent thoughts via multiple specialized initial tokens and apply contrastive learning to promote diversity among soft thought representations. Experiments across five reasoning benchmarks and two distinct LLM architectures demonstrate that SoftCoT++ significantly boosts SoftCoT and also outperforms SoftCoT with self-consistency scaling. Moreover, it shows strong compatibility with conventional scaling techniques such as self-consistency. Source code is available at https://github.com/xuyige/SoftCoT.