The vanishing and exploding gradient problems are well-studied obstacles that make it difficult for recurrent neural networks to learn long-term time dependencies. We propose a reparameterization of standard recurrent neural networks to update linear transformations in a provably norm-preserving way through Givens rotations. Additionally, we use the absolute value function as an element-wise no...

The sequence alignment is a fundamental problem in computational biology. Many sequence alignment methods have been proposed, such as pair-wise sequence alignment, multiple sequence alignment (MSA), syntenic alignment, constraint multiple sequence alignment, and etc. Among them, pair-wise sequence alignment is a most commonly used method. Recently, MSA is more and more important which has been ...

In this ‘on-going’ work, I explore certain theoretical and empirical implications of data transformations under the PCA. In particular, I state and prove three theorems about PCA, which I paraphrase as follows: 1). PCA without discarding eigenvector rows is injective, but looses this injectivity when eigenvector rows are discarded 2). PCA without discarding eigenvector rows preserves pair-wise ...