A less-popular alternative to batch and layer normalization is weight normalization, which replaces each weight vector w in the model with U where y is a new scalar parameter ||v|| and v is a new vector of parameters with the same shape as w. 1. Derive expressions for V, L and V, L in terms of y, v, and Vw L. 2. Show that applying batch normalization without the shift parameter / to the preactivation ux is equivalent to applying weight normalization if the entries of x are independently distributed with zero mean and unit variance.

A less-popular alternative to batch and layer normalization is weight normalization, which replaces each weight vector w in the model with U where y is a new scalar parameter ||v|| and v is a new vector of parameters with the same shape as w. 1. Derive expressions for V, L and V, L in terms of y, v, and Vw L. 2. Show that applying batch normalization without the shift parameter / to the preactivation ux is equivalent to applying weight normalization if the entries of x are independently distributed with zero mean and unit variance.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

A less-popular alternative to batch and layer normalization is weight normalization, which
replaces each weight vector w in the model with U where y is a new scalar parameter
||v||
and v is a new vector of parameters with the same shape as w.
1. Derive expressions for V, L and V, L in terms of y, v, and Vw L.
2. Show that applying batch normalization without the shift parameter / to the
preactivation ux is equivalent to applying weight normalization if the entries of x are
independently distributed with zero mean and unit variance.

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