stat441w18/Convolutional Neural Networks for Sentence Classification

Presented by

1. Ben Schwarz

2. Cameron Miller

3. Hamza Mirza

4. Pavle Mihajlovic

5. Terry Shi

6. Yitian Wu

7. Zekai Shao

Model

Theory of Convolutional Neural Networks

Let [math]\displaystyle{ \boldsymbol{x}_{i:i+j} }[/math] be the concatenation of words [math]\displaystyle{ \boldsymbol{x}_i, \boldsymbol{x}_{i+1}, \dots, \boldsymbol{x}_{i+j} }[/math] with the concatenation operation [math]\displaystyle{ \oplus }[/math]. Then, [math]\displaystyle{ \boldsymbol{x}_{i:i+j} = \boldsymbol{x}_i \oplus \boldsymbol{x}_{i+1} \oplus \dots \oplus \boldsymbol{x}_{i+j} }[/math]. Thus, a sentence of length [math]\displaystyle{ n }[/math] is the concatenation of [math]\displaystyle{ n }[/math] words, denoted as [math]\displaystyle{ \boldsymbol{x}_{1:n} }[/math], [math]\displaystyle{ \boldsymbol{x}_{1:n} = \boldsymbol{x}_1 \oplus \boldsymbol{x}_2 \oplus \dots \oplus \boldsymbol{x}_n }[/math]. Let [math]\displaystyle{ \boldsymbol{x}_i \in \mathbb{R}^k }[/math] denote the [math]\displaystyle{ i }[/math]-th word in the sentence, [math]\displaystyle{ i \in \{ 1, \dots, n \} }[/math].

A Convolutional Neural Network (CNN) is a nonlinear function [math]\displaystyle{ f: \mathbb{R}^{hk} \to \mathbb{R} }[/math] that computes a series of outputs [math]\displaystyle{ c_i = f \left( \boldsymbol{w} \cdot \boldsymbol{x}_{i:i+h-1} + b \right) }[/math] from windows of [math]\displaystyle{ h }[/math] words [math]\displaystyle{ \boldsymbol{x}_{i:i+h-1} }[/math] in the sentence, where [math]\displaystyle{ \boldsymbol{w} \in \mathbb{R}^{hk} }[/math] is call a filter and [math]\displaystyle{ i \in \{ 1, \dots, n-h+1 \} }[/math]. The outputs form a [math]\displaystyle{ (n-h+1) }[/math]-dimensional vector [math]\displaystyle{ \boldsymbol{c} = \left[ c_1, c_2, \dots, c_{n-h+1} \right] }[/math] called a feature map.

To capture the most important feature from a feature map, we take the maximum value [math]\displaystyle{ \hat{c} = max \{ \boldsymbol{c} \} }[/math].

Datasets and Experimental Setup

Hyperparameters and Training

MR:

SST-1:

SST-2:

Subj:

TREC:

CR:

MPQA:

Model Variations

CNN-rand:

CNN-static:

CNN-static:

CNN-non-static:

CNN-multichannel: