# A*-Thought-V2: Efficient Latent Reasoning via Geometric Dynamics of LLM

arXiv: https://arxiv.org/abs/2609.07821 · HTML: https://mlsanity.com/paper/2609.07821/

## Key facts

- Cited by 1 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 30 of its 32 references that are in the map.
- First posted on arXiv 7 Sep 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, 30 of 30)

- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [TokenSkip: Controllable Chain-of-Thought Compression in LLMs](https://mlsanity.com/paper/2502.12067/) (2025)
- [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://mlsanity.com/paper/2502.21074/) (2025)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [When More is Less: Understanding Chain-of-Thought Length in LLMs](https://mlsanity.com/paper/2502.07266/) (2025)
- [CoT-Valve: Length-Compressible Chain-of-Thought Tuning](https://mlsanity.com/paper/2502.09601/) (2025)
- [LightThinker: Thinking Step-by-Step Compression](https://mlsanity.com/paper/2502.15589/) (2025)
- [Large Concept Models: Language Modeling in a Sentence Representation Space](https://mlsanity.com/paper/2412.08821/) (2024)
- [Think Silently, Think Fast: Dynamic Latent Compression of LLM Reasoning Chains](https://mlsanity.com/paper/2505.16552/) (2025)
- [TreeRL: LLM Reinforcement Learning with On-Policy Tree Search](https://mlsanity.com/paper/2506.11902/) (2025)
- [Reasoning by Superposition: A Theoretical Perspective on Chain of Continuous Thought](https://mlsanity.com/paper/2505.12514/) (2025)
- [SIM-CoT: Supervised Implicit Chain-of-Thought](https://mlsanity.com/paper/2509.20317/) (2025)
- [Efficient Inference for Large Reasoning Models: A Survey](https://mlsanity.com/paper/2503.23077/) (2025)
- [PonderLM: Pretraining Language Models to Ponder in Continuous Space](https://mlsanity.com/paper/2505.20674/) (2025)
- [Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lens](https://mlsanity.com/paper/2505.18237/) (2025)
- [Ada-R1: Hybrid-CoT via Bi-Level Adaptive Reasoning Optimization](https://mlsanity.com/paper/2504.21659/) (2025)
- [Let LRMs Break Free from Overthinking via Self-Braking Tuning](https://mlsanity.com/paper/2505.14604/) (2025)
- [Parallel Continuous Chain-of-Thought with Jacobi Iteration](https://mlsanity.com/paper/2506.18582/) (2025)
- [SwiReasoning: Switch-Thinking in Latent and Explicit for Pareto-Superior Reasoning LLMs](https://mlsanity.com/paper/2510.05069/) (2025)
- [Latent Thinking Optimization: Your Latent Reasoning Language Model Secretly Encodes Reward Signals in Its Latent Thoughts](https://mlsanity.com/paper/2509.26314/) (2025)
- [Dynamic Large Concept Models: Latent Reasoning in an Adaptive Semantic Space](https://mlsanity.com/paper/2512.24617/) (2025)
- [ReCUT: Balancing Reasoning Length and Accuracy in LLMs via Stepwise Trails and Preference Optimization](https://mlsanity.com/paper/2506.10822/) (2025)
- [Next Concept Prediction in Discrete Latent Space Leads to Stronger Language Models](https://mlsanity.com/paper/2602.08984/) (2026)
- [A*-Thought: Efficient Reasoning via Bidirectional Compression for Low-Resource Settings](https://mlsanity.com/paper/2505.24550/) (2025)
- [CopT: Contrastive On-Policy Thinking with Continuous Spaces for General and Agentic Reasoning](https://mlsanity.com/paper/2605.20075/) (2026)

## Built on by (most cited first, 1 of 1)

- [SYNLAT: Syntax-Aligned Text-Latent Compression for Chain-of-Thought Reasoning](https://mlsanity.com/paper/2610.03839/) (2026)

## Abstract (arXiv)

Chain-of-Thought (CoT) improves the reasoning ability of Large Language Models (LLMs) but incurs substantial computation and context costs. Existing methods either lose intermediate information through hard pruning or lack a principled criterion for continuous compression. We present A*-Thought-V2, a geometric dynamics of LLM guided framework that models CoT as a hidden-state trajectory and replaces hard deletion with an explicit-implicit interleaved latent architecture. After projecting question, step, and solution representations into a 3D PCA space, it measures alignment between each local transition and global question-to-solution direction. Aligned steps remain explicit text, whereas deviating steps are compressed into continuous latent tokens. Directional angles capture both local semantics and reasoning dynamics: small angles indicate direct execution and answer formation, while large angles more frequently involve checking, correction, and branch exploration; their temporal variation reveals exploration, convergence, and refinement stages. To train this architecture, we introduce stepwise embedding forcing, which pools each redundant step into a single latent embedding, and label forcing, which supervises that latent token with a soft multi-modal vocabulary distribution instead of a hard one-hot label. Experiments on Qwen3.5-9B and Qwen3.6-27B across six in-domain and out-of-domain benchmarks show that A*-Thought-V2 improves average accuracy by up to 2.6% while reducing response length by up to half, increasing Accuracy per Computation Unit by 2.29×, and reducing preprocessing and training time by 94.6% and up to 80.3%, respectively. Representation analyses suggest that latent states form a compact region distinct from textual states, while higher entropy at latent-token positions reflects broader soft targets that encourage richer step-level feature learning.