GoKawiilResearcher bets he can find random words that mimic circular embedding geometry
A blog post describes a viral paper by Dhruva Karkada showing that LLM and word2vec embeddings of month names project onto a near-perfect circle, with their Gram matrix closely matching a circulant matrix predicted by a simple analytical theory. The author, skeptical that this pattern is unique to semantically related word sets like months, wagered a beer that he could find ten seemingly unrelated words whose word2vec embeddings would also form a clear circle and circulant structure.
GoKawiil's interpretation of the reporting above, not reported fact.
If arbitrary word sets can produce the same circular geometry, it would suggest the pattern reflects a general statistical property of embedding spaces rather than something special about cyclical concepts like months, potentially complicating claims that models encode meaningful cyclical structure. This kind of adversarial test is a common way researchers probe whether a striking result is genuinely tied to semantics or is an artifact of the embedding method itself.
- A viral paper found month-name embeddings form a circle with a circulant Gram matrix, matched by analytical theory.
- The blog author bet he could replicate this circular pattern using ten unrelated, non-cyclical words.
- The wager tests whether the circle reflects genuine semantic structure or a more general statistical artifact of embeddings.
Source: jamiesimon.io, 2026-09-26
Published there as: “How to win a beer with high-dimensional statistics”
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