A*-Thought-V2：透過大型語言模型幾何動力學的高效潛在推理

摘要

思維鏈（Chain-of-Thought, CoT）提升大型語言模型（Large Language Models, LLMs）的推理能力，但會帶來可觀的計算與上下文成本。現有方法不是透過硬剪枝流失中間資訊，就是缺乏連續壓縮的原則性準則。我們提出 A*-Thought-V2，一個由 LLM 幾何動力學引導的框架，將 CoT 建模為隱藏狀態軌跡，並以顯式-隱式交錯的潛在架構取代硬刪除。將問題、步驟與解答表徵投影到三維 PCA 空間後，該框架衡量每個局部轉移與全域問題到解答方向之間的對齊程度。對齊的步驟保留為顯式文字，而偏離的步驟則壓縮為連續潛在符元。方向角同時捕捉局部語義與推理動態：小角度表示直接執行與答案形成，而大角度更常涉及檢查、修正與分支探索；其時間變化揭示探索、收斂與精煉階段。為訓練此架構，我們引入逐步嵌入強制，將每個冗餘步驟池化為單一潛在嵌入，以及標籤強制，以軟性多峰詞彙分布監督該潛在符元，而非硬性獨熱標籤。在 Qwen3.5-9B 與 Qwen3.6-27B 上、跨越六個域內與域外基準測試的實驗顯示，A*-Thought-V2 將平均準確率最多提升 2.6%，同時將回應長度最多縮減一半，使每計算單位準確率提升至 2.29 倍，並分別將預處理與訓練時間減少 94.6% 與最多 80.3%。表徵分析顯示，潛在狀態形成一個與文字狀態不同的緊湊區域，而潛在符元位置較高的熵則反映更廣泛的軟目標，鼓勵更豐富的步驟級特徵學習。

English

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 2.29times, 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.