Table of Contents Definitions Proof of Lemma 1 TODO Proof of Lemma 2 This is a proof that Tensor Embedding (Joudaki, Rätsch, and Kahles 2020) with $ℓ^2$-norm preserves the Hamming distance. This is in collaboration with Amir Joudaki. \begin{equation*} \newcommand{\I}{\mathcal I} \newcommand{\EE}{\mathbb E} \newcommand{\var}{\operatorname{Var}} \end{equation*} Definitions NotationThe alphabet is \(\Sigma\), of size \(|\Sigma| = \sigma\). The set of indices is \(\I := \{(i_1, \dots, i_t) \in...
