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\\( \newcommand{\upto}{,\ldots,} \\)
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\\( \newcommand{\prob}{\mathbb{P}} \\)
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## Motivation
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The singular value decomposition is a neat way to understand what is happening with matrix operations, and one good direction to interpret LLMs under the hood. We begin with a motivating example: the movie ratings data. The below is a snippet of preferences (from 1-5 where 5 is best) of 26 movies rated by 61 students (anonymized):
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