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 a 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]. Since each filter corresponds to one feature, we obtain several features from multiple filters the model uses which form a penultimate layer. The penultimate layer then gets passed into a fully connected softmax layer which produces the probability distribution over labels.

Below is a slight variant of CNN with two "channels" of word vectors: static vectors and fine-tuned vectors via backpropagaton. We calculate [math]\displaystyle{ c_i }[/math] by applying each filter to both channels and then adding them together. The rest of the model is equivalent to a single channel CNN architecture.

Datasets and Experimental Setup

Hyperparameters and Training

There are various benchmark for classification, for example:

MR: Movie reviews with one sentence per review, Class: positive/negative (Pang and Lee, 2005).

SST-1: Standford Sentiment Treebank (An extension of MR) with train/dev/test splits.

      Class: very positive, positive, neutral, negative, very negative. 
      *dev set: The set used for selecting the best performing model.
      (re-labeled by Socher er al. 2013)

SST-2: Same as SST-1 but with neutral reviews removed and binary labels.

      Class: positive/negative

Subj: To classify a sentence as subjective or objective.

     Class: subjective/objective (Pang and Lee, 2004)

TREC:

CR:

MPQA:

Model Variations

CNN-rand:

CNN-static:

CNN-static:

CNN-non-static:

CNN-multichannel: