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How Many Thoughts Can a Vector Hold? The Capacity of Reasoning by Superposition
摘要
arXiv:2609.13747v1 Announce Type: new Abstract: Large language models solve hard problems through intermediate computations across multi-step reasoning. Traditional chain-of-thought encodes these computations as tokens. Recent continuous and recurrent methods instead move partial computations into fixed-dimensional latent states, where a single thought can superpose multiple alternatives. This raises a fundamental design question:what should continuous thoughts preserve as reasoning proceeds? An intuitive approach discards past computations and keeps only the current reasoning frontier. Storing more items seems to dilute states and waste limited representational capacity. We show this intuition can be incorrect. Under identical downstream computations, cumulative superposition retaining full reasoning history can require lower representational dimensions than frontier-only superposition holding only current alternatives. At fixed hidden width, this advantage allows latent reasoners to retain more valid evidence, distinguish more plausible downstream outcomes, and delay the point where compressed states turn unreliable. This counter-intuitive effect emerges because informative historical components coherently reinforce each other, while unrelated alternatives bring random interference. This perspective also answers a practical design question: how should models weight memories accumulated inside latent states when their future use is unknown? Across reusable weighted superpos