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

A*-Thought-V2. Efficient Latent Reasoning via Geometric Dynamics of LLM. By Xiaoang Xu and fifteen others, from the Beijing University of Posts and Telecommunications, the Hong Kong Polytechnic University, and three other institutions. Published on the seventh of September. Its code repository is worked out: about three hundred and fifty source files, with a readme.

Chain-of-Thought, or CoT, improves the reasoning of Large Language Models, but it is expensive in computation and in context. Existing ways of trimming it fall into two camps. Hard pruning deletes steps and loses the intermediate information in them. Continuous compression keeps information in latent form but lacks a principled criterion for what to compress. One approach throws away too much, and the other has no good rule for deciding what to keep.

A star Thought V2 supplies that criterion from the geometry of the model's own dynamics. It treats a chain of thought as a trajectory through hidden states. Question, step, and solution representations are projected into a three- dimensional PCA space, and each local transition is measured for how well it aligns with the overall direction from question to solution. Steps that align stay as explicit text. Steps that deviate are compressed into continuous latent tokens. In place of hard deletion, the result is an architecture that interleaves explicit and implicit steps. The chain keeps its shape. Some of its links are words, and some are compact latent tokens standing in for the words that were there.

The directional angles carry meaning of their own. Small angles indicate direct execution and forming the answer. Large angles more often involve checking, correction, and exploring branches. How the angles vary over time reveals stages of exploration, convergence, and refinement. That gives the criterion a reading beyond efficiency: a step off the direct line is often one where the model is checking its work or trying an alternative, and those are the steps folded into latent form.

Two training techniques support the architecture. Stepwise embedding forcing pools each redundant step into a single latent embedding. Label forcing supervises that latent token with a soft distribution over the vocabulary, multi-modal rather than a hard one-hot label.

Experiments on two models, Qwen three point five at nine billion parameters and Qwen three point six at twenty-seven billion parameters, across six in- domain and out-of-domain benchmarks, show average accuracy improving by up to two point six percent. Response length falls by up to half, and Accuracy per Computation Unit rises by two point two nine times.

Preprocessing time falls by ninety-four point six percent, and training time by up to eighty point three percent. Representation analyses suggest the latent states form a compact region distinct from textual states. Higher entropy at latent-token positions reflects the broader soft targets, which encourage richer feature learning at the level of steps.

The geometry does the deciding. A step that heads straight toward the answer is kept in words, a step that wanders is folded into a latent token, and nothing is simply thrown away. The model reasons in shorter text without discarding the detours it took.