On the zeros of solutions of any order of derivative of second order linear differential equations taking small functions

In this paper, we investigate the hyper-exponent of convergence of zeros of $f^{(j)}(z)-\varphi(z) (j\in N)$, where $f$ is a solution of second or $k(\geq2)$ order linear differential equation, $\varphi(z)\not\equiv0$ is an entire function satisfying $\sigma(\varphi)<\sigma(f)$ or $\sigma_{2}(\varphi)<\sigma_{2}(f)$. We obtain some precise results which improve the previous results in [3, 5] and revise the previous results in [11, 13]. More importantly, these results also provide us a method to investigate the hyper-exponent of convergence of zeros of $f^{(j)}(z)-\varphi(z)(j\in N)$

Distilling Word Embeddings: An Encoding Approach

Distilling knowledge from a well-trained cumbersome network to a small one has recently become a new research topic, as lightweight neural networks with high performance are particularly in need in various resource-restricted systems. This paper addresses the problem of distilling word embeddings for NLP tasks. We propose an encoding approach to distill task-specific knowledge from a set of high-dimensional embeddings, which can reduce model complexity by a large margin as well as retain high accuracy, showing a good compromise between efficiency and performance. Experiments in two tasks reveal the phenomenon that distilling knowledge from cumbersome embeddings is better than directly training neural networks with small embeddings.Comment: Accepted by CIKM-16 as a short paper, and by the Representation Learning for Natural Language Processing (RL4NLP) Workshop @ACL-16 for presentatio