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Statistics of spectral properties of matrix-valued random variables.
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Probability of collision of sums of vectors
Let $S_1$ and $S_2$ be sets of vectors from $\mathbb{R}^d$ that are distinct and let $\sigma(\cdot)$ be a non-linearity, e.g., a componentwise sigmoid function.
Does there exist a random matrix $R \i …
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Probability of collision of sums of vectors multiplied by random matrix
Let $S$ and $T$ be sets of vectors from $\mathbb{R}^d$ such that $S$ and $T$ are at least different in one element.
Does there exist a random matrix $M \in \mathbb{R}^{d \times k}$, e.g., a gaussian …