FastPrep
Problem · Matrix

Prefix Matrix Products and Autograd

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Problem statement

You are given a sequence of square integer matrices matrices with shape [N, D, D]. Define the inclusive prefix products

P[i] = matrices[0] @ matrices[1] @ ... @ matrices[i],

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Examples

Example 1

matrices = [[[1,2],[3,4]]]upstream = [[[2,0],[1,-1]]]return = [[1,2,3,4],[2,0,1,-1]]

There is one prefix, so P[0] = matrices[0]. Because that prefix is the input itself, its gradient is exactly upstream[0].

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Reported in 1 OpenAI interview this week

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FastPrep Pro gives you full access to interview problems reported within the last week.

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