  Learning-based low rank approximation algorithms can significantly improve
the performance of randomized low rank approximation with sketch matrix. With
the learned value and fixed non-zero positions for sketch matrices from
learning-based algorithms, these matrices can reduce the test error of low rank
approximation significantly. However, there is still no good method to learn
non-zero positions as well as overcome the out-of-distribution performance
loss. In this work, we introduce two new methods Learning Sparsity and Learning
Randomness which try to learn a better sparsity patterns and add randomness to
the value of sketch matrix. These two methods can be applied with any
learning-based algorithms which use sketch matrix directly. Our experiments
show that these two methods can improve the performance of previous
learning-based algorithm for both test error and out-of-distribution test error
without adding too much complexity.
