# [Paper] MorphNet: Fast & Simple Resource-Constrained Structure Learning of Deep Networks (Image Classification)

## Shrink & Expand to Improve the Networks: Inception-v2, ResNet & MobileNetV1

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In this story, **MorphNet: Fast & Simple Resource-Constrained Structure Learning of Deep Networks (MorphNet)**, by Google AI, Google Brain, Energy-efficient multimedia systems group, MIT, and, Georgia Institute of Technology, is briefly presented. In this paper:

**A simple and general technique for a resource-constrained optimization of DNN architectures**which is adaptable to specific resource constraints (e.g. FLOPs), and capable of increasing the network’s performance.- First,
**shrink**an existing model such as ResNet using sparsifying regularizer. Then,**expand**all layers uniformly with width multiplier. - With the above shrink & expand process performed iteratively, the network is shrunken with improved performance.

This is a paper in **2018 CVPR **with over **100 citations**. (Sik-Ho Tsang @ Medium)

# Outline

**Naive Solution: Simply Using Width Multiplier****MorphNet: Shrink & Expand****Experimental Results**

**1. Naive Solution: Simply Using Width Multiplier**

- Assume we already got a network where
*O*1:*M*are the output widths of all layers, and we want to have a constraint on the network, e.g.: fewer FLOPs, or smaller model size. - According to the constraint, we would like to shrink the network to fit the constraint while having the smallest loss by the network:

- where the constraint is denoted by
monotonically increasing in each dimension,*F*(*O*1:*M*) ≤*ζ*for*F*is either the number of*F***FLOPs**per inference**or**the**model size**(i.e., number of parameters). **One naive solution is to find the largest**when we want to shrink the network. (If it is larger than one, the network is expanded.)*w*such that F(*w*· O1:M) ≤*ζ*, where*w*is the width multiplier which can be smaller than one- (This approach is used in many papers to increase the size of network to a similar network size of other SOTA models, for fair comparison.)
- In most cases the network, i.e. the form of
*F*, allows for easily finding the optimal*w*. **Despite its simplicity, this approach suffers, however, with decreased quality of the initial network design.**

# 2. **MorphNet: Shrink & Expand**

## 2.1. Shrink (Steps 1 & 2)

- In the shrinking phase,
**MorphNet identifies inefficient neurons and prunes them from the network by applying a sparsifying regularizer**such that the total loss function of the network includes a cost for each neuron.*G*(*θ*) - Suppose a layer has 6 weights from
*a*to*f*.

**Left**: If*c*and*f*are set as zero, the network cannot be shrunk.**Middle**: But if*e*and*f*are set as zero, the network can be shrunk to as the**Right**one. In this paper, this is done by Group Lasso regularizer.- Unlike the width multiplier approach, this approach is able to change the relative sizes of layers.

For example, when targeting FLOPs, higher-resolution neurons in the lower layers of the DNN tend to be sacrificed more than lower-resolution neurons in the upper layers of the DNN.

The situation is the exact opposite when the targeted resource is model size rather than FLOPs.

## 2.2. Expand (Step 3)

- During expansion, a simple method is used only, namely
**uniformly expanding all layer sizes via a width multiplier**as much as the constrained resource allows.

## 2.3. Iteration of Step 1–3 (Step 4)

- Thus, the above completed one cycle of improving the network architecture.
- We can
**continue this process iteratively until the performance is satisfactory**, or until the DNN architecture has converged (i.e., further iterations lead to a near-identical DNN structure). - Yet, it is found a single iteration of Steps 1–3 to be enough to yield a noticeable improvement over the naive solution of just using a uniform width multiplier, while subsequent iterations can bring additional benefits in.

## 2.4. **ResNet**** & ****Inception-v2**** As **Examples

- When a layer has 0 neurons, this effectively changes the topology of the network by cutting the affected branch from the network.
**Left**: For ResNet, MorphNet might keep the skip-connection but remove the residual block as shown below (left).**Right**: For Inception-v2, MorphNet might remove entire parallel towers as shown on the right.- To do this,
**Group Lasso**is used as the regularizer. (CondenseNet has also used Group Lasso to “condense” the network.)

**The FLOP regularizer primarily prunes the early, compute-heavy layers.**It notably learns to remove whole layers to further reduce computational burden.- By contrast,
**the model size regularizer focuses on removal of 3×3 convolutions at the top layers**as those are the most parameter-heavy. - (There are more detailed explanation/equations for the regularizer in the paper. If interested, please feel free to read the paper.)

**3. Experimental Results**

## 3.1. Study on MorphNet

- Using MorphNet approach (Blue) has better performance than just using naive width multiplier (Red).
- Pentagon: Re-expanding one of the networks induced by the FLOP regularizer.
- Star point: Performing the sparsifying and expanding process a second time.

- With more iterations, the accuracy is improved.
- (Dropout rate was increased to mitigate overfit caused by the increased model capacity.)

## 3.2. Study on Different Models on Different Datasets

**MorphNet can be applied to a variety of datasets and model architectures while maintaining FLOP cost.**- The 1% improvement on MobileNet is especially impressive because MobileNet was specifically hand-designed to optimize accuracy under a FLOPs-constraint.

- It is clear that the structures induced when targeting FLOPs form a better FLOPs/performance tradeoff curve, but poor model size/performance tradeoff curves, and vice versa when targeting model size.

**References**

[2018 CVPR] [MorphNet]

MorphNet: Fast & Simple Resource-Constrained Structure Learning of Deep Networks

[Google AI Blog about MorphNet]

https://ai.googleblog.com/2019/04/morphnet-towards-faster-and-smaller.html

## Image Classification

[LeNet] [AlexNet] [Maxout] [NIN] [ZFNet] [VGGNet] [Highway] [SPPNet] [PReLU-Net] [STN] [DeepImage] [SqueezeNet] [GoogLeNet / Inception-v1] [BN-Inception / Inception-v2] [Inception-v3] [Inception-v4] [Xception] [MobileNetV1] [ResNet] [Pre-Activation ResNet] [RiR] [RoR] [Stochastic Depth] [WRN] [ResNet-38] [Shake-Shake] [Cutout] [FractalNet] [Trimps-Soushen] [PolyNet] [ResNeXt] [DenseNet] [PyramidNet] [DRN] [DPN] [Residual Attention Network] [DMRNet / DFN-MR] [IGCNet / IGCV1] [Deep Roots] [MSDNet] [ShuffleNet V1] [SENet] [NASNet] [MobileNetV2] [CondenseNet] [IGCV2] [IGCV3] [FishNet] [SqueezeNext] [ENAS] [PNASNet] [ShuffleNet V2] [BAM] [CBAM] [MorphNet] [AmoebaNet] [ESPNetv2] [MnasNet]