View source for deep Convolutional Neural Networks For LVCSR

= Introduction =
Deep Neural Networks (DNNs) have been explored in the area of speech recognition. They outperformed the-state-of-the-art Gaussian Mixture Models-Hidden Markov Model (GMM-HMM) systems in both small and large speech recognition tasks
<ref name=firstDBN>
A. Mohamed, G. Dahl, and G. Hinton, “Deep belief networks for phone recognition,” in Proc. NIPS Workshop Deep Learning for Speech Recognition and Related Applications, 2009.
</ref>
<ref name=tuning_fb_DBN>A. Mohamed, G. Dahl, and G. Hinton, “Acoustic modeling using deep belief
networks,” IEEE Trans. Audio Speech Lang. Processing, vol. 20, no. 1, pp. 14–22,
Jan. 2012.</ref>
<ref name=finetuningDNN>
A. Mohamed, D. Yu, and L. Deng, “Investigation of full-sequence training
of deep belief networks for speech recognition,” in Proc. Interspeech, 2010, pp.
2846–2849.
</ref>
<ref name=bing>
G. Dahl, D. Yu, L. Deng, and A. Acero, “Context-dependent pretrained deep
neural networks for large-vocabulary speech recognition,” IEEE Trans. Audio
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<ref name=scrf>
N. Jaitly, P. Nguyen, A. Senior, and V. Vanhoucke, “An application of pretrained
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Convolutional Neural Networks (CNNs) can model temporal/spacial variations while reduce translation variances. CNNs are attractive in the area of speech recognition for two reasons: first, they are translation invariant which makes them an alternative to various speaker adaptation techniques. Second, spectral representation of the speech has strong local correlations, CNN can naturally capture these type of correlations.

CNNs have been explored in speech recognition <ref name=convDNN>
O. Abdel-Hamid, A. Mohamed, H. Jiang, and G. Penn, “Applying convolutional
neural networks concepts to hybrid NN-HMM model for speech recognition,”
in Proc. ICASSP, 2012, pp. 4277–4280.
</ref>, but only one convolutional layer was used. This paper explores using multiple convolutional layers, and the system is tested on one small dataset and two large datasets. The results show that CNNs outperform DNNs in all of these tasks.

= CNN Architecture =

A typical CNN, as shown in Fig 1, consists of a convolutional layer for which the weights are shared across the input space, and a max-poolig layer.

<center>
[[File:Convnets.png |300px | thumb | center |Fig 1. A typical convolutional neural network. ]]
</center>

== Experimental Setup ==
A small 40-hour dataset is used to learn the behaviour of CNNs for speech tasks. The results are reported on EARS dev04f dataset. Features of 40-dimentional log mel-filter bank coeffs are used. The size of the hidden fully connected layer is 1024, and the softmax layer size is 512. For fine-tuning, the learning rate is halved after each iteration for which the objective function doesn't improve sufficiently on a held-out validation set. After 5 times of halving the learning rate, the training stops. 

== Number of Convolutional vs. Fully Connected Layers ==
In image recognition tasks, a few convolutional layers are used before fully connected layers. These convolutional layers tend to reduce spectral varitaion, while fully connected layers use the local information learned by the the convolutional layers to do classification. In this work and unlike what have been explored before for speech recognition tasks <ref name=convDNN></ref>, multiple convolutional layers are used followed by fully connected layers similar to image recognition framework. The following table shows the word error rate (WER) for different number of convolutional and fully connected layers.

{| class="wikitable"
|+ Word error rate as a function of the number of convolutional and fully-connected layers.
! Number of convolutional and fully-connected layers
! WER
|-
| No conv, 6 full
| 24.8
|-
| 1 conv, 5 full
| 23.5
|-
| 2 conv, 4 full
| 22.1
|-
| 3 conv, 3 full
| 22.4
|-
|}

== Number of Hidden Units ==
Speech is different than images in the sense that different frequencies have different features, hence Osama et. al. <ref name=convDNN></ref> proposed to have weight sharing across nearby frequencies only. Although this solves the problem, it limits adding multiple convolutional layers. In this work, weights sharing is done across the entire feature space while using more filters - compared to vision - to capture the differences in the low and high frequencies.
The following table shows the WER for different number of hidden units for convolutional layers for 2 convolutional and 4 fully-connected configuration. The parameters of the network is kept constant for fair comparisons.
{| class="wikitable"
|+ Word error rate as a function of the number of hidden units.
! Number of hidden units
! WER
|-
| 64
| 24.1
|-
| 128
| 23.0
|-
| 220
| 22.1
|-
| 128/256
| 21.9
|-
|}

== Optimal Feature Set ==
The following features are used to build the table below, WER is used to decide the best set of features to be used.
# Vocal Tract Length Normalization (VTLN)-warping to help map features into a canonical space.
# feature space Maximum Likelihood Linear Regression (fMLLR).
# Delte (d) which is the difference between features in consecutive frames and double delta (dd).
# Energy feature.

{| class="wikitable"
|+ Word error rate as a function of input features.
! Feature
! WER
|-
| Mel FB
| 21.9
|-
| VTLN-warped mel FB
| 21.3
|-
| VTLN-warped mel FB + fMLLR
| 21.2
|-
| VTLN-warped mel FB + d + dd
| 20.7
|-
| VTLN-warped mel FB + d + dd + energy
| 21.0
|-
|}

== Pooling Experiments ==
Pooling helps with reducing spectral variance in the input features. The pooling is done only on the frequency domain which was shown to be working better for speech <ref name=convDNN></ref>.  The word error rate is tested on two different dataset with two different sampling rates (8khz switchboard telephone conversations SWB and 16khz English Broadcast news BN), and the pooling size of 3 is found to be the optimal size.
{| class="wikitable"
|+ Word error rate as a function of the pooling size.
! Pooling size
! WER-SWB
! WER-BN
|-
| No pooling
| 23.7
| '-'
|-
| pool=2
| 23.4
| 20.7
|-
| pool=3
| 22.9
| 20.7
|-
| pool=4
| 22.9
| 21.4
|-
|}
= Results =

= Conclusions and Discussions =

= References =

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