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The exp-normal distribution is infinitely divisible
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abstract
Let $Z$ be a standard normal random variable (r.v.). It is shown that the distribution of the r.v. $\ln|Z|$ is infinitely divisible; equivalently, the standard normal distribution considered as the distribution on the multiplicative group over $\mathbb{R}\setminus\{0\}$ is infinitely divisible.
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Deep Weight Factorization: Sparse Learning Through the Lens of Artificial Symmetries
Factorizing weights into D≥2 multiplicative factors and applying L2 weight decay induces a non-convex sparse L2/D penalty, and with tailored initialization and learning rates, achieves superior sparsity-accuracy tradeoffs.
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