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Title: Rethinking the Smaller-Norm-Less-Informative Assumption in Channel Pruning of Convolution Layers

Paper content:
Model pruning has become a useful technique that improves the computational efficiency of deep learning, making it possible to deploy solutions in resource-limited scenarios.
A widely-used practice in relevant work assumes that a smaller-norm parameter or feature plays a less informative role at the inference time.
In this paper, we propose a channel pruning technique for accelerating the computations of deep convolutional neural networks (CNNs) that does not critically rely on this assumption.
Instead, it focuses on direct simplification of the channel-to-channel computation graph of a CNN without the need of performing a computationally difficult and not-always-useful task of making high-dimensional tensors of CNN structured sparse.
Our approach takes two stages: first to adopt an end-to-end stochastic training method that eventually forces the outputs of some channels to be constant, and then to prune those constant channels from the original neural network by adjusting the biases of their impacting layers such that the resulting compact model can be quickly fine-tuned.
Our approach is mathematically appealing from an optimization perspective and easy to reproduce.
We experimented our approach through several image learning benchmarks and demonstrate its interest- ing aspects and competitive performance.
Not all computations in a deep neural network are of equal importance.
In a typical deep learning pipeline, an expert crafts a neural architecture, which is trained using a prepared dataset.
The success of training a deep model often requires trial and error, and such loop usually has little control on prioritizing the computations happening in the neural network.
Recently researchers started to develop model-simplification methods for convolutional neural networks (CNNs), bearing in mind that some computations are indeed non-critical or redundant and hence can be safely removed from a trained model without substantially degrading the model's performance.
Such methods not only accelerate computational efficiency but also possibly alleviate the model's overfitting effects.Discovering which subsets of the computations of a trained CNN are more reasonable to prune, however, is nontrivial.
Existing methods can be categorized from either the learning perspective or from the computational perspective.
From the learning perspective, some methods use a dataindependent approach where the training data does not assist in determining which part of a trained CNN should be pruned, e.g. BID7 and , while others use a datadependent approach through typically a joint optimization in generating pruning decisions, e.g., BID4 and BID1 .
From the computational perspective, while most approaches focus on setting the dense weights of convolutions or linear maps to be structured sparse, we propose here a method adopting a new conception to achieve in effect the same goal.Instead of regarding the computations of a CNN as a collection of separate computations sitting at different layers, we view it as a network flow that delivers information from the input to the output through different channels across different layers.
We believe saving computations of a CNN is not only about reducing what are calculated in an individual layer, but perhaps more importantly also about understanding how each channel is contributing to the entire information flow in the underlying passing graph as well as removing channels that are less responsible to such process.
Inspired by this new conception, we propose to design a "gate" at each channel of a CNN, controlling whether its received information is actually sent out to other channels after processing.
If a channel "gate" closes, its output will always be a constant.
In fact, each designed "gate" will have a prior intention to close, unless it has a "strong" duty in sending some of its received information from the input to subsequent layers.
We find that implementing this idea in pruning CNNs is unsophisticated, as will be detailed in Sec 4.Our method neither introduces any extra parameters to the existing CNN, nor changes its computation graph.
In fact, it only introduces marginal overheads to existing gradient training of CNNs.
It also possess an attractive feature that one can successively build multiple compact models with different inference performances in a single round of resource-intensive training (as in our experiments).
This eases the process to choose a balanced model to deploy in production.
Probably, the only applicability constraint of our method is that all convolutional layers and fully-connected layer (except the last layer) in the CNN should be batch normalized BID9 .
Given batch normalization has becomes a widely adopted ingredient in designing state-of-the-art deep learning models, and many successful CNN models are using it, we believe our approach has a wide scope of potential impacts.
We proposed a model pruning technique that focuses on simplifying the computation graph of a deep convolutional neural network.
Our approach adopts ISTA to update the γ parameter in batch normalization operator embedded in each convolution.
To accelerate the progress of model pruning, we use a γ-W rescaling trick before and after stochastic training.
Our method cleverly avoids some possible numerical difficulties such as mentioned in other regularization-based related work, hence is easier to apply for practitioners.
We empirically validated our method through several benchmarks and showed its usefulness and competitiveness in building compact CNN models.
Figure 1 : Visualization of the number of pruned channels at each convolution in the inception branch.
Colored regions represents the number of channels kept.
The height of each bar represents the size of feature map, and the width of each bar represents the size of channels.
It is observed that most of channels in the bottom layers are kept while most of channels in the top layers are pruned.

assistant: text: A CNN model pruning method using ISTA and rescaling trick to enforce sparsity of scaling parameters in batch normalization.