40

Algorithms for Binary Neural Networks

Feature Maps

Reconstructed

Filters

Feature Maps

Center Loss

Unbinarized

Filters

Average

Feature Maps

MCConv

Binarized

Filters

Binarize

Filter Loss

Loss Function

Softmax Loss

M-Filters

Modulation Module

(MCconv layer)

Loss layer





forward propagation

backward propagation

MCconv

MCconv

Feature

Maps

Average

Feature

Maps

Output

Fully Connected

Layers

Convolution

Layers

Input

Cat

FIGURE 3.1

The overall frameworks of Modulated Convolutional Networks (MCNs).

3.4

MCN: Modulated Convolutional Network

In [199], XNOR-Network is presented where both the weights and inputs attached to the

convolution are approximated with binary values, which allow an efficient implementation

of convolutional operations, i.e., particularly by reconstructing unbinarized filters with a

single scaling factor and a binary filter. It has been theoretically and quantitatively demon-

strated that simplifying the convolution procedure via binarized filters and approximating

the original unbinarized filters is a very promising solution for CNNs compression.

However, the performance of binarized models generally drops significantly compared

with using the original filters. It is mainly due to the following reasons: 1) The binarization

of CNNs could be solved based on discrete optimization, which has long been neglected in

previous works. 2) Existing methods do not consider quantization loss, filter loss, and intr-

aclass compactness in the same backpropagation pipeline. 3) Rather than a single binarized

filter, a set of binarized filters can better approximate the full-precision convolution.

As a promising solution, Modulated Convolutional Network (MCN) [236] is proposed as

a novel binarization architecture to tackle these challenges toward highly accurate yet robust

compression of CNNs. Unlike existing work that uses a single scaling factor in compression

[199, 159], we introduce modulation filters (M-Filters) into CNNs to better approximate

convolutional filters. The proposed M-Filters can help the network fuse the feature in a

unified framework, significantly improving the network performance. To this end, a simple

and specific modulation process is designed that is replicable at each layer and can be easily

implemented. A complex modulation is also bounded as in [283]. In addition, we further

consider the intraclass compactness in the loss function and obtain modulated convolutional

networks (MCNs) ¹. Figure 3.1 shows the architecture of MCN. MCNs are designed based

on binarized convolutional and modulation filters (M-Filters). M-Filters are mainly de-

signed to approximate unbinarized convolutional filters in the end-to-end framework. Since

an M-Filter (matrix) can be shared at each layer, the model size of MCNs is marginally in-

1The work has been commercialized.