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(CVPR 2017) Aggregated residual transformations for deep neural networks

Keyword [ResNeXt]

Xie S, Girshick R, Dollár P, et al. Aggregated residual transformations for deep neural networks[C]//Computer Vision and Pattern Recognition (CVPR), 2017 IEEE Conference on. IEEE, 2017: 5987-5995.



1. Overview


1.1. Motivation

  • transition from feature engineering to network engineering
  • human effort has been shifted to designing better network architecture for learning representation
  • important strategy of Inception model is split-transform-merge

In this paper, it proposed ResNeXt Network

  • aggregate a set of transformations with the same topology
  • homogeneous multi-branch architecture
  • increase cardinality (the size of the set of transformation) is more effective than going deeper or wider


1.2.1. Multi-branch Convolutional Network

  • Inception. multi-branch
  • ResNet. two-branch

1.2.2. Group Convolution

  • channel-wise convolution

1.2.3. Compressing Convolutional Network

  • decomposition. at spatial or channel

1.2.4. Ensembling



2. Method


2.1. Simple Neurons




Inner Product. can be recast as a combination of splitting, transforming and aggregating.

  • D. the number of channel
  • x=[x_1, x_2, …, x_D]

2.2. Aggregated Transformations

  • Network-in-Neuron. replace the elementary transformation (wx) with a more generic function


    All T_i have the same topology.
  • T. arbitrary function; projects x into low-dimension embedding and then transforms it
  • C. the size of the set of transformations

2.3. Relation to Grouped Convolutions



2.4. Depth ≥ 3

  • The block depth must ≥ 3.


2.5. Capacity



  • Left. 25664 + 336464 + 64*256 ≈ 70k parameters and proportional FLOPs
  • Right. C(256d + 33dd + d256) ≈ 70k, when C=32, d=4



3. Experiments


3.1. Cardinality vs Width




  • with complexity preserved, increasing cardinality at the price of reducing width starts to show saturating accuracy


  • more training data will enlarge the gap of validation error, shown in ImageNet-5K set
  • the saturation is caused by the complexity of dataset, not the capacity of models

3.2. Cardinality vs Deeper/Wider




  • incrase cardinality better

3.3. w/o Residual



3.4. Comparison



3.5. Detection