---
title: "Towards Inference-time Scaling for Continuous Space Reasoning"
description: "The paper asks whether standard test-time scaling for text reasoning carries over to models that reason in latent space. 30 references."
authors: ["Minghan Wang", "Thuy-Trang Vu", "Ehsan Shareghi", "Gholamreza Haffari"]
year: 2026
venue: "Findings of the Association for Computational Linguistics: ACL 2026"
source: "https://aclanthology.org/2026.findings-acl.1338/"
doi: "10.18653/v1/2026.findings-acl.1338"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/wang-2026-inference-time-scaling-continuous-space/"
---
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# Towards Inference-time Scaling for Continuous Space Reasoning

**Authors:** [Minghan Wang](https://md.research.elamur.ai/free/en/authors/minghan-wang/), [Thuy-Trang Vu](https://md.research.elamur.ai/free/en/authors/thuy-trang-vu/), [Ehsan Shareghi](https://md.research.elamur.ai/free/en/authors/ehsan-shareghi/) and [Gholamreza Haffari](https://md.research.elamur.ai/free/en/authors/gholamreza-haffari/) · **Year:** 2026 · **Venue:** [Findings of the Association for Computational Linguistics: ACL 2026](https://md.research.elamur.ai/free/en/venues/findings/) ([Findings of the Association for Computational Linguistics 2026](https://md.research.elamur.ai/free/en/venues/findings/2026/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2026.findings-acl.1338/) · [PDF](https://aclanthology.org/2026.findings-acl.1338.pdf) · [DOI 10.18653/v1/2026.findings-acl.1338](https://doi.org/10.18653/v1/2026.findings-acl.1338) · [OpenAlex](https://openalex.org/W4415269707)

**Citations:** 0 citations (OpenAlex, 2026-10-14)

## Summary
The paper asks whether standard test-time scaling for text reasoning carries over to models that reason in latent space. That recipe samples many solutions and reranks them with a Process or Outcome Reward Model (PRM/ORM). The authors use COCONUT on GPT-2, trained on GSM8k-aug. COCONUT's latent reasoning is normally deterministic, so they create diverse trajectories by keeping dropout active only while continuous thoughts are generated.

Pass@N grows quickly with more samples, which suggests large potential gains. However, PRM/ORM models trained with MATH-Shepherd-style automatic step labels deliver only small improvements. Probing the geometry and dynamics of the latent trajectories explains why: correct and incorrect reasoning look nearly identical in latent space, so reward models have little signal to separate them.

As a test of this explanation, a short post-training step adds a margin-based geometric regularizer. This partly restores separability and modestly improves scaling. The broader lesson is that continuous reasoners need training objectives with explicit geometric inductive biases before reranking can pay off.

## Key points
- **Setup:** GPT-2 backbone, following the original COCONUT protocol on GSM8k-aug (385k training / 1319 test examples).
  - Inference uses 6 continuous thought steps (3 stages × c = 2).
  - Dropout rate is 0.1, applied only during latent reasoning.
  - Sample sizes range from N = 1 to 32.
- **Sampling results:** Deterministic COCONUT trails text CoT by roughly 10 points.
  - With dropout, Pass@1 is slightly below the deterministic baseline.
  - Pass@32 surpasses text CoT.
  - The number of distinct answers grows roughly logarithmically with N, so reranking stays cheap.
- **Reward models:** PRM and ORM trained via automatic step annotation (adapted from MATH-Shepherd) give only marginal gains. The authors attribute this to geometric homogeneity of the latent thoughts.
- **Post-training fix:**
  - Data: 5000 GSM8k training examples, one epoch.
  - Only the last Transformer block is updated.
  - Rollouts: 32 per prompt.
  - Loss: cross-entropy on correct trajectories plus a hinge regularizer (γ = 1, λ = 1). The regularizer pushes apart correct and incorrect trajectories on four metrics: compactness, straightness, local smoothness, and curvature.
  - Outcome: larger correct/incorrect gaps on these metrics and better Pass@N.
- **Scope and code:** The study covers a single benchmark (GSM8k). Code is released as LatentITS on GitHub (yuriak/LatentITS).

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [University College London](https://md.research.elamur.ai/free/en/universities/university-college-london/) — University, London, United Kingdom · 88 works · 19,432 citations
- [Monash University](https://md.research.elamur.ai/free/en/universities/monash-university/) — University, Melbourne, Australia · 60 works · 54,866 citations

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🧭 Topics (1): [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/) · 1,426 works

## Cite

Cite as: Minghan Wang, Thuy-Trang Vu, Ehsan Shareghi and Gholamreza Haffari. 2026. Towards Inference-time Scaling for Continuous Space Reasoning. Findings of the Association for Computational Linguistics: ACL 2026.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{wang2026inference,
  title = {{Towards Inference-time Scaling for Continuous Space Reasoning}},
  author = {Minghan Wang, Thuy-Trang Vu, Ehsan Shareghi and Gholamreza Haffari},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2026},
  year = {2026},
  doi = {10.18653/v1/2026.findings-acl.1338},
  url = {https://doi.org/10.18653/v1/2026.findings-acl.1338}
}
```

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30. ID % Correct Iso+ Iso-Hoyer+ Hoyer-p-value Cohen’s d 1 2 3 4 5 6 7 8 53.9 52.3 47.7 46.1 42.1 41.4 41.4 40.6 0.014 0.011 0.007 0.010 0.019 0.016 0.019 0.019 0.014 0.010 0.004 0.008 0.021 0.015 0.016 0.018 0.370 0.480 0.432 0.437 0.365 0.455 0.466 0.398 0.359 0.496 0.429 0.447 0.357 0.467 0.460 0.401… [find](https://scholar.google.com/scholar?q=ID+%25+Correct+Iso%2B+Iso%2DHoyer%2B+Hoyer%2Dp%2Dvalue+Cohen%E2%80%99s+d+1+2+3+4+5+6+7+8+53%2E9+52%2E3+47%2E7+46%2E1+42%2E1+41%2E4+41%2E4+40%2E6+0%2E014+0%2E011+0%2E007+0%2E010+0%2E019+0%2E016+0%2E019+0%2E019+0%2E014+0%2E010+0%2E004+0%2E008+0%2E021+0%2E015+0%2E016+0)

*Updated 1 November 2026*