stat441w18/Convolutional Neural Networks for Sentence Classification: Difference between revisions

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=== Theory of Convolutional Neural Networks ===
=== Theory of Convolutional Neural Networks ===


Let <math> \boldsymbol{x}_i \in \mathbb{R}^k </math> be the <math> i </math>-th word in <math> \boldsymbol{x}_{1:n} </math>, a sentence of length <math> n </math>, <math> \boldsymbol{x}_{1:n} = \boldsymbol{x}_1 \oplus \boldsymbol{x}_2 \oplus \dots \oplus \boldsymbol{x}_{n} </math>, where <math> \oplus </math> is the concatenation operator.
Let <math> \boldsymbol{x}_{i:i+j} </math> be the concatenation of k-dimensional words <math> \boldsymbol{x}_i, \boldsymbol{x}_{i+1}, \dots, \boldsymbol{x}_{i+j} </math>. Then, a sentence of length <math> n </math> is the concatenation of k-dimensional words <math> \boldsymbol{x}_1, \boldsymbol{x}_2, \dots, \boldsymbol{x}_n </math>, represented as <math> \boldsymbol{x}_{1:n} </math>, <math> \boldsymbol{x}_{1:n} = \boldsymbol{x}_1 \oplus \boldsymbol{x}_2 \oplus \dots \oplus \boldsymbol{x}_n </math>, where <math> \oplus </math> is the concatenation operation.


A Convolutional Neural Network (CNN) is a nonlinear function <math> \boldsymbol{f}: \mathbb{R}^{hk} \to \mathbb{R} </math> that computes a series of outputs <math> c_i </math> from a concatenation of words <math> \boldsymbol{x}_i, \boldsymbol{x}_{i+1}, \dots, \boldsymbol{x}_{i+h-1} </math>, represented by <math> \boldsymbols{x}_{i:i+h-1} </math>
A Convolutional Neural Network (CNN) is a nonlinear function <math> \boldsymbol{f}: \mathbb{R}^{hk} \to \mathbb{R} </math> that computes a series of outputs <math> c_i </math> from a concatenation of words <math> \boldsymbol{x}_i, \boldsymbol{x}_{i+1}, \dots, \boldsymbol{x}_{i+h-1} </math>, represented by <math> \boldsymbol{x}_{i:i+h-1} </math>


=== Model Regularization ===
=== Model Regularization ===

Revision as of 17:57, 4 March 2018

Presented by

1. Ben Schwarz

2. Cameron Miller

3. Hamza Mirza

4. Pavle Mihajlovic

5. Terry Shi

6. Yitian Wu

7. Zekai Shao

Introduction

Model

Theory of Convolutional Neural Networks

Let [math]\displaystyle{ \boldsymbol{x}_{i:i+j} }[/math] be the concatenation of k-dimensional words [math]\displaystyle{ \boldsymbol{x}_i, \boldsymbol{x}_{i+1}, \dots, \boldsymbol{x}_{i+j} }[/math]. Then, a sentence of length [math]\displaystyle{ n }[/math] is the concatenation of k-dimensional words [math]\displaystyle{ \boldsymbol{x}_1, \boldsymbol{x}_2, \dots, \boldsymbol{x}_n }[/math], represented 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], where [math]\displaystyle{ \oplus }[/math] is the concatenation operation.

A Convolutional Neural Network (CNN) is a nonlinear function [math]\displaystyle{ \boldsymbol{f}: \mathbb{R}^{hk} \to \mathbb{R} }[/math] that computes a series of outputs [math]\displaystyle{ c_i }[/math] from a concatenation of words [math]\displaystyle{ \boldsymbol{x}_i, \boldsymbol{x}_{i+1}, \dots, \boldsymbol{x}_{i+h-1} }[/math], represented by [math]\displaystyle{ \boldsymbol{x}_{i:i+h-1} }[/math]

Model Regularization

Datasets and Experimental Setup

Hyperparameters and Training

MR:

SST-1:

SST-2:

Subj:

TREC:

CR:

MPQA:

Pre-trained Word Vectors
Model Variations

CNN-rand:

CNN-static:

CNN-static:

CNN-non-static:

CNN-multichannel:

Training and Results

Criticisms

More Formulations/New Concepts

Conclusion

Source