title: SoftCoT++: Test-Time Scaling with Soft Chain-of-Thought Reasoning
summary: 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.
paper_authors._id: 682b7826e9f4a26b02e74091
paper_authors.name: Yige Xu
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-05-20T07:22:07.334Z
paper_authors._id: 6448d7e5e87a77e872e47982
paper_authors.avatarUrl: /avatars/7405ceef3bf7468cb3e977c4669d81a4.svg
paper_authors.fullname: Yige Xu
paper_authors.type: user
paper_authors.user: xuyige
paper_authors._id: 682b7826e9f4a26b02e74092
paper_authors.name: Xu Guo
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-05-21T15:17:49.054Z
paper_authors._id: 5f3b74d7a4dd343b63a6009f
paper_authors.avatarUrl: /avatars/198d38cad20ea38f47f53e1433d9607c.svg
paper_authors.fullname: Xu Guo
paper_authors.type: user
paper_authors.user: xuxuxu
paper_authors._id: 682b7826e9f4a26b02e74093
paper_authors.name: Zhiwei Zeng
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2025-05-20T08:52:04.331Z
paper_authors._id: 664b5d83edcadf9fa5e0615d
paper_authors.avatarUrl: /avatars/5fdfc87a78b68f1eb54e1ed7d144952a.svg
paper_authors.fullname: zeng zhiwei
paper_authors.type: user
paper_authors.user: Aver3
paper_authors._id: 682b7826e9f4a26b02e74094
paper_authors.name: Chunyan Miao
paper_title: SoftCoT++: Test-Time Scaling with Soft Chain-of-Thought Reasoning
paper_summary: 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.
paper_ai_summary: SoftCoT++ enhances continuous-space reasoning in Test-Time Scaling by introducing diverse exploration through perturbed latent thoughts and contrastive learning.
paper_ai_keywords: Test-Time Scaling discrete token space continuous latent space SoftCoT latent thoughts autoregressive token generation continuous-space reasoning self-consistency scaling contrastive learning LLM architectures