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Re:Show HN: Word2Bits – Quantized Word Vectors by yorwba on Tuesday March 20, 2018 @09:05PM (#16634370)
Say you have a function f(q(x)) where q quantizes x into one of s_1, ..., s_n. Then if q(x) = s_i for a certain x, df/ds_i = df/dq and df/ds_j = 0 for all j != i.

That breaks down for values of x precisely at the boundary between steps, so I should have qualified "differentiable" with "almost everywhere".

It also occurs to me that this might interact strangely with the approximation dq/dx = 1, but since the quantization steps are globally shared, I think it should be stable anyway.

If the evaluation suite for your code doesn't require too much manual interaction, I might try and see for myself.

Re:Show HN: Word2Bits – Quantized Word Vectors by maxlam on Wednesday March 21, 2018 @12:11PM (#16639436)
That's definitely an interesting idea -- it seems this would allow for boundaries that "change" along with the data (instead of having static boundaries as it is). Would be interested to know how that turns out!