[2505.23648] Continuous Chain of Thought Enables Parallel Exploration and Reasoning

Computer Science > Machine Learning arXiv:2505.23648 (cs) [Submitted on 29 May 2025 (v1), last revised 5 Mar 2026 (this version, v3)] Title:Continuous Chain of Thought Enables Parallel Exploration and Reasoning Authors:Halil Alperen Gozeten, M. Emrullah Ildiz, Xuechen Zhang, Hrayr Harutyunyan, Ankit Singh Rawat, Samet Oymak View a PDF of the paper titled Continuous Chain of Thought Enables Parallel Exploration and Reasoning, by Halil Alperen Gozeten and 5 other authors View PDF HTML (experimental) Abstract:Modern language models generate chain-of-thought traces by autoregressively sampling tokens from a finite vocabulary. While this discrete sampling has achieved remarkable success, conducting chain-of-thought with continuously-valued tokens (CoT2) offers a richer and more expressive alternative. Our work provides new theoretical guarantees and algorithms for CoT2, motivated by logical reasoning tasks that inherently require search capabilities. Theoretically, we establish how CoT2 facilitates the model to track multiple discrete traces in parallel; and quantify the level of achievable parallelism and its benefits for inference efficiency. We also provide a CoT2-based one-layer transformer construction that solves the combinatorial "subset sum problem" given a sufficient embedding dimension. These insights arise from a novel and effective supervision strategy where we match the language model outputs to the empirical token distributions of a set of target traces. Complemen...