Stolen Probability: A Structural Weakness of Neural Language Models

NNLMs produce a distribution for the next word by taking the dot product of its representation with all word vectors in a high dimensional embedding space. This paper theoretically shows that the norm of a word vector placed interior to the convex hull will put an upper bound on its softmax probability, meaning that the probability of some words will never be predicted as 1 even if the context provides very certain clues. This finding is confirmed with empirical experiments on some small sized NNLMs, showing that infrequent words are placed inside the convex hull.


  • Very good paper with both theoretical and experimental results.
  • I’m wondering if the case of large models like Transformers will be any better. Maybe MaskedLMs will arrange the embedding space such that more words are on the convex hull?
  • 5: Transformative: This paper is likely to change our field. It should be considered for a best paper award.
  • 4.5: Exciting: It changed my thinking on this topic. I would fight for it to be accepted.
  • 4: Strong: I learned a lot from it. I would like to see it accepted.
  • 3.5: Leaning positive: It can be accepted more or less in its current form. However, the work it describes is not particularly exciting and/or inspiring, so it will not be a big loss if people don’t see it in this conference.
  • 3: Ambivalent: It has merits (e.g., it reports state-of-the-art results, the idea is nice), but there are key weaknesses (e.g., I didn’t learn much from it, evaluation is not convincing, it describes incremental work). I believe it can significantly benefit from another round of revision, but I won’t object to accepting it if my co-reviewers are willing to champion it.
  • 2.5: Leaning negative: I am leaning towards rejection, but I can be persuaded if my co-reviewers think otherwise.
  • 2: Mediocre: I would rather not see it in the conference.
  • 1.5: Weak: I am pretty confident that it should be rejected.
  • 1: Poor: I would fight to have it rejected.

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