# Geometric Latent Reasoning Induces Shorter Generations in LLMs

arXiv: https://arxiv.org/abs/2606.02248 · HTML: https://mlsanity.com/paper/2606.02248/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 27 of its 30 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## 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, 27 of 27)

- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://mlsanity.com/paper/2502.21074/) (2025)
- [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://mlsanity.com/paper/2311.01460/) (2023)
- [Soft Thinking: Unlocking the Reasoning Potential of LLMs in Continuous Concept Space](https://mlsanity.com/paper/2505.15778/) (2025)
- [SoftCoT: Soft Chain-of-Thought for Efficient Reasoning with LLMs](https://mlsanity.com/paper/2502.12134/) (2025)
- [Token Assorted: Mixing Latent and Text Tokens for Improved Language Model Reasoning](https://mlsanity.com/paper/2502.03275/) (2025)
- [SoftCoT++: Test-Time Scaling with Soft Chain-of-Thought Reasoning](https://mlsanity.com/paper/2505.11484/) (2025)
- [Hybrid Latent Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2505.18454/) (2025)

## Abstract (arXiv)

Large language models solve complex problems by generating lengthy chains of explicit reasoning tokens. While effective, this makes reasoning expensive, length-sensitive, and constrained to (discrete) natural language. While latent reasoning offers a continuous alternative, determining useful structures for intermediate latent states is an open challenge. In this paper, we formulate latent reasoning as a geometric path-approximation problem within the model's pretrained token-embedding space. We introduce Geometric Latent Reasoning (GLR), which uses a lightweight transition head to predict iterative direction updates in embedding space. Using textual chain-of-thought traces as anchors, GLR learns to approximate discrete reasoning trajectories while permitting continuous deviations from exact token embeddings. Evaluations on mathematical reasoning benchmarks using Qwen3 models reveal an emergent phenomenon: geometric latent reasoning induces substantially shorter generations without an explicit length objective. By replacing early explicit reasoning with continuous latent steps, models often reach correct answers using substantially fewer total generation steps. These findings suggest that continuous trajectories act as compact intermediate reasoning states, exposing a new tradeoff between latent computation budget, output length, and accuracy.