Miller (2023) — https://www.evanmiller.org/attention-is-off-by-one.html
Key takeaways
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The complaint. “The problem with using softmax is that it forces each attention head to make an annotation, even if it has no information to add.” Softmax outputs are non-zero even when every input is strongly negative, so a head cannot abstain.
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The proposal. Add one to the denominator:
softmax₁(x)ᵢ = exp(xᵢ) / (1 + Σⱼ exp(xⱼ))which lets the whole output vector go to zero when every score is very negative. The author names the resulting mechanism QuietAttention.
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The connection drawn. Citing Qualcomm research — which is LIT-414, whose authors are at Qualcomm AI Research — that 97%+ of outlier activations occur at whitespace and punctuation positions, i.e. exactly where a head would want to contribute nothing.
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No experiments, and the post is honest about it. “I’m 99.44% sure that it will resolve the outlier feedback loop.” The author proposes ways it might be tested and did not test it, and notes that using it requires retraining.
Standing in the anthology
Filed for provenance and for reach, not for evidence, and the note should not be read as the record endorsing softmax1.
The chronology is the useful content. This post is July 2023 and is downstream of LIT-414, June 2023, which had already diagnosed the no-op mechanism and tested two remedies. What this added was a third proposed remedy, no evidence, and an audience — it is the version of the argument most practitioners have encountered, and it is why the phrase “softmax off by one” appears in LIT-191’s discussion rather than the paper’s name.
And softmax1 specifically is still untested at the scale that would matter. The record holds tested siblings — clipped softmax and gated attention in LIT-414, the head gate at 15B in LIT-138 — and nothing on this exact formulation. That is worth keeping visible, because the popular version of an idea and the evidenced version are not always the same version.