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Learning Efficient Convolutional Networks through Network Slimming

2022.10.25

I actually tried this out, and got similar results!
Keywords: #Pruning #Quantization #Batch Normalization

0. Abstract

  • Goal

    1. Reduce the model size
    2. Decrease the run-time memory footprint
    3. Lower the number of computing operation without compromising accuracy

  • Distinction

    • Directly applies to modern CNN architectures
    • Minimum overhead to the training process
    • Requires no special software/hardware accelerators for the resulting models

1.Introduction

  • CNN constraints

    1. Model size: trainable parameters, along with network structure information need to be stored on disk and loaded into memory during inference time (ex) typical CNN trained on ImageNet ⇒ 300MB

    2. Run-time memory: During inference time, the intermediate activations/responses of CNNs could even take more memory space than storing the model parameters, even with batch size 1.

    → 가중치를 저장하는 것보다 forward pass에서 하나의 데이터를 연산하는 과정에서 발생하는 ‘중간값’ 자체의 용량이 더 클 수 있다.

    1. Number of computing operations: Convolution operations are computationally intensive → 컨볼루션 연산 자체가 빡세다

  • Main approach

    • Imposes L1 regularization on the scaling factors in BN layers → Push the values of BN scaling factor towards zero → enables us to identify insignificant channels
    • each scaling factor corresponds to a specific convolutional channel

3. Network Slimming

Advantages of Channnel-level Sparsity

  • Sparsity - can be realized at different levels (ex) weight level, kernel level, channel level, layer level
  • Weight-level (fine-grained level): highest flexibility and generality, higher compression rate → but requires special software/hardware accelerators to do fast inference
  • Layer-level (coarsest level): does not require special packages to harvest the inference speedup → but less flexible, only effective in depth is sufficiently large (>50 layers)
  • Channel-level: nice tradeoff between flexibility and ease of implementation → for FC, treat each neuron as a channel

    Challenges for channel-level sparsity

  • channel-level sparsity requires pruning all the incoming and outgoing connections associated with a channel → the method of directly pruning weights on a pre-trained model is ineffective → because it is unlikely that all the weights at the input/output end of a channel happen to have near zero values
  • Channel-level sparsity: 채널과 연결되어 있는 모든 연결들을 pruning 해야 한다. → 따라서, pre-trained model에서 pruning 시도하는 것은 의미가 없다. → channel input (이전 kernel weights), output (다음 kernel weights)이 전부 다 ‘unimportant’(near zero values) 할 리가 없기 때문이다.

Solution for challenge: Scaling Factors and Sparsity-induced Penalty

  • Introduce a scaling factor $\gamma$ for each channel, which is multiplied to the output of that channel

[ L = \Sigma_{(x,y)} l(f(x, W), y) +\lambda \Sigma _{\gamma \in \Gamma} g(\gamma) ]

  • Then, jointly train the network weights and these scaling factors, with sparsity regularization imposed on the latter

  • $g()$ is a sparsity induced penalty on the scaling factors; we choose L1-norm $g(s) = |s|$, to achieve sparsity

  • The scaling factors act as the agents for channel selection.

    Leveraging the Scaling Factors in BN Layers

  • BN layer normalizes the internal activaions using mini-batch statistics
  • γ and β are trainable affine transformation parameters (scale and shift)
  • It is common practice to insert a BN layer after a convolutional layer, with channel-wise scaling/shifting parameters. Therefore, we can directly leverage the γ parameters in BN layers as the scaling factors we need for network slimming. ⇒ It has the great advantage of introducing no overhead to the network

  • 위는 일반적인 BN 식이다. 즉, 새로운 scaling factor $\gamma$ 를 소개할 필요 없이, BN에 사용되는 scaling factor을 그대로 사용하면 된다. → 추가적인 overhead가 발생하지 않는다.

  • 정당성

    1. BN 없이 scaling factor $\gamma$만 사용할 경우: the value of the scaling factors are not meaningful for evaluating the importance of a channel, because both convolution layers and scaling layers are linear transformations. → weights 값 키우고, scaling factor 줄이면, weights 값 줄이고, scaling factor 키우는 거랑 같은 효과를 낼 수 있음. 중요성의 정도 파악 안 됨.

    2. scaling layer before BN: BN의 normalization 과정으로 인해 scaling 효과 무의미해짐

    3. scaling layer after BN: scaling 두 번 되는 꼴, BN 내에서 scaling, scaling factor 두 번 → redundancy ⇒ scaling factor로 BN의 scaling을 활용하겠다!

Channel Pruning and Fine-tuning

  • After training under channel-level sparsity-induced regularization, we obtain a model in which many scaling factors are near zero
  • Then, we prune channels with near-zero scaling factors → (ex) prune 70% channels with lower scaling factors by choosing the percentile threshold as 70%

5. Analysis

  • Two crucial hyper-parameters in network slimming
    1. pruned percentage $\text{t}$
    2. regularization term $\lambda$

Effect of Pruned Percentage

  • Too high? → may not be able to recover the accuracy by fine-tuning
  • Too low? → resource saving can be very limited

Channel Sparsity Regularization

  • Purpose of the L1 sparsity term ⇒ to force many of the scaling factors to be near zero
  • High? the scaling factors are more and more concentrated near zero
  • Low? No sparsity regularization, the distribution is relatively flat
  • This process can be seen as a feature selection happening in intermediate layers of deep networks, where only channels with non-negligible scaling factors are chosen.