Rotate2Think: Geometric Priming via Orthogonal Rotation to Improve Language Model Reasoning

A team of researchers has introduced Rotate2Think, a training-free method that improves language model reasoning by injecting a geometric primer at the start of the reasoning trace, according to a paper posted to arXiv on 2 June 2026 [1][2]. The method is built on an analysis of how a model's hidden representations differ during thinking versus when processing the input prompt. The authors report that both input embeddings and thinking embeddings — mean-pooled last-layer hidden states over the prompt and reasoning trace, respectively — exhibit extremely high conicity, with all vectors clustering tightly around a single mean direction [2]. Critically, these mean input and thinking directions are non-collinear, with thinking embeddings occupying a geometrically distinct region of embedding space across many different models and benchmark tasks [2]. This observation led the team to cast the input-to-thinking transition as a rotation problem admitting a closed-form solution via orthogonal Procrustes analysis [2]. Rotate2Think estimates this rotation from a small set of correctly solved examples and injects the resulting synthetic thinking vector between thinking delimiters at inference time, providing a geometric primer at the onset of the reasoning trace [1][2]. The approach requires no additional training or fine-tuning of the underlying model [1]. Evaluated across multiple benchmarks and model families, Rotate2Think improved accuracy in 30 of 32 model-benchmark configurations across mathematics, science, and code tasks [1][2]. The method also generalized zero-shot to multimodal reasoning on the MATH-Vision benchmark [1][2]. The paper does not report specific numeric accuracy gains in its abstract, and no external benchmarks or independent replications were available in the research bundle at the time of this report. The work contributes to a growing body of research examining the internal geometry of language model representations. While the research bundle included several other arXiv papers, their excerpts contained only platform navigation text for tools such as CatalyzeX and DagsHub and provided no substantive content related to Rotate2Think or geometric priming methods [3][4][5]. Two Wikipedia entries on sustainable development goals and transcription factors were also present in the bundle but are unrelated to the machine learning domain of the primary paper [6][7].