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Structured Receptive Fields in CNNs

Structured receptive field networks (RFNNs) are CNNs whose filters are learned from a low-order symmetric basis, rather than from mere pixel values as done in vanilla CNNs. RFNNs can operate on restricted, low-order feature spaces that allow them to outperform classical CNNs by large margins when data is scarce.

Reference: J.-H. Jacobsen, J.v. Gemert, Z. Lou, A.W.M. Smeulders; Structured Receptive Fields in CNNs. Proceedings of the Conference of Vision and Pattern Recognition (CVPR), 2016


Some first layer filters as trained on ILSVRC2012 and the basis they are learned from. The filters are mainly rotated versions of the basis itself that learned to recombine input channels. Note that all filters in all layers of an RFNN are learned from such a Gaussian derivative basis.


We focus on the following experimental questions

  • Are low-order Gaussian derivatives a sufficient basis for challenging tasks like Imagenet
  • How does an RFNN compare to CNNs when training data are limited
  • How does an RFNN compare on a task where Scattering Networks excel

Accuracy ILSVRC-2012 Subsets

We evaluate our RFNN on multiple subsets of Imagenet.

  • ILSVRC 2012 1000 class standard
  • ILSVRC 2012 100 biggest classes
  • ILSVRC 2012 10 biggest classes

We show an RFNN outperforms plain CNNs when data and presented visual variety are limited.

Model ILSVRC2012val-10 ILSVRC2012val-100 ILSVRC2012val-full
Network in Network [6] 76.97 67.30 56.78
RFNiN 83.36 70.78 54.04
RFNiN BN 84.77 72.30 55.92

Top-1 accuracy is reported, default Caffe pre-processing and no data augmentation was used. The Network in Network was used as provided in the Caffe model zoo.


We evaluate our RFNN on multiple subsets of MNIST as done in [2].

We show an RFNN can be as stable as Scattering when the number of training samples is limited while it outperforms plain CNNs by large margins.


Note that CNN-B and RFNN share the same architecture, the only difference is our RF approach on the individual filters. Hyperparameter settings to reproduce the results can be found here.


Tested with: cudnn v3; cuda 7.0; + standard caffe requirements

cd /path/to/RFNN/caffe_rfnn

set Makefile.config paths

make all
make runtest
make test

Train an RFNN on 10 biggest classes of ILSVRC2012

Download data

cd /path/to/RFNN/data/ILSVRC2012/10class/
follow instructions in .txt file

Train model (before execution change "/path/to/" everywhere)

$ /path/to/RFNN/caffe-rfnn/build/tools/caffe train -solver=solver_RFNN_Small_ILSVRC2012_train_val_10class.prototxt

Full Imagenet pre-trained RFNN that achieves 55.92% top-1 accuracy corresponding to "RFNN_BN_ILSVRC2012_train_val.prototxt" model definition and "solver_RFNN_BN_ILSVRC2012_train_val.prototxt" solver file can be downloaded here:

$ cd /path/to/RFNN_beta/caffe-rfnn/models/rfnn
$ bash

Our added module: Basis Convolution Layer

Options implemented for Gaussian derivative basis: gaussian_basis_1st_order; gaussian_basis_2nd_order; gaussian_basis_3rd_order; gaussian_basis_4th_order

layer {
  bottom: "data"
  top: "basisconv"
  name: "basisconv"
  type: "BasisConvolution"
  param {
    lr_mult: 0
    decay_mult: 0
  param {
    lr_mult: 0
    decay_mult: 0
  basis_convolution_param {
    num_basis: [number of basis filters, is eg 37 for 4-scale basis of order 3]
    kernel_size: [2 times largest sigma is sensible, can be chosen lower if computation time is an issue]
    stride: [subsampling]
    group: [number of input channels, so basis convolves over all input channels without sum]
    weight_filler {
      type: "gaussian_basis_3rd_order" [Initializes Gaussian derivative basis of 3rd order]
      num_basis: [number of basis filters, is eg 37 for 4-scale basis of order 3, allows to truncate basis]
      sigma: [Lowest scale in basis. Denotes standard deviation of smallest Gaussian kernel in basis, is sampled with 2^scale from there. For 37 basis filters and "gaussian_basis_3rd_order", we get 10 filters with sigma=1, 9 filters with sigma=2, 9 filters with sigma=4, 9 filters with sigma=8]
    bias_filler {
      type: "constant"
      value: 0

Requirements: Python, Theano, Lasagne, Pylearn2, Numpy, Pylab, Scipy, cudnn v5

Download MNIST data

$ cd /path/to/RFNN/data/
$ bash

Train an RFNN on MNIST in Theano

$ python /path/to/RFNN/theano-rfnn/ --epochs 100 --ntrain 60000

ntrain determines the number of randomly chosen samples from MNIST, to reproduce figure 5 from paper.


If you use our code or ideas from our method, please be so kind to cite:

author = {Jacobsen, Jorn-Henrik and van Gemert, Jan and Lou, Zhongyu and Smeulders, Arnold W. M.},
title = {Structured Receptive Fields in CNNs},
booktitle = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2016}

Related Work

  1. Scale and the differential structure of images, Florack et al., 1992
  2. Invariant Scattering Convolutional Networks, Bruna and Mallat, 2012
  3. Deep Roto-Translation Scattering for Object Classification, Oyallon and Mallat, 2014
  4. A Mathematical Motivation for Complex-Valued Convolutional Networks, Tygert et al., 2016
  5. Group Equivariant Convolutional Networks, Cohen and Welling, 2016
  6. Network in Network, Lin et al., 2014


Structured Receptive Fields in Convolutional Neural Networks







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