Must Know Tips for Deep Learning Neural Networks

By Xiu-Shen Wei, Nanjing University.

Deep Neural Networks, especially Convolutional Neural Networks (CNN), allows computational models that are composed of multiple processing layers to learn representations of data with multiple levels of abstraction. These methods have dramatically improved the state-of-the-arts in visual object recognition, object detection, text recognition and many other domains such as drug discovery and genomics.

In addition, many solid papers have been published in this topic, and some high quality open source CNN software packages have been made available. There are also well-written CNN tutorials or CNN software manuals. However, it might lack a recent and comprehensive summary about the details of how to implement an excellent deep convolutional neural networks from scratch. Thus, we collected and concluded many implementation details for DCNNs. Here we will introduce these extensive implementation details, i.e., tricks or tips, for building and training your own deep networks.

We assume you already know the basic knowledge of deep learning, and here we will present the implementation details (tricks or tips) in Deep Neural Networks, especially CNN for image-related tasks, mainly in eight aspects:

1. data augmentation
2. pre-processing on images
3. initializations of Networks
4. some tips during training
5. selections of activation functions
6. diverse regularizations
7. some insights found from figures
8. methods of ensemble multiple deep networks

Additionally, the corresponding slides are available at [slide]. If there are any problems/mistakes in these materials and slides, or there are something important/interesting you consider that should be added, just feel free to contact me.

Since deep networks need to be trained on a huge number of training images to achieve satisfactory performance, if the original image data set contains limited training images, it is better to do data augmentation to boost the performance. Also, data augmentation becomes the thing must to do when training a deep network.

There are many ways to do data augmentation, such as the popular horizontally flipping, random crops and color jittering. Moreover, you could try combinations of multiple different processing, e.g., doing the rotation and random scaling at the same time. In addition, you can try to raise saturation and value (S and V components of the HSV color space) of all pixels to a power between 0.25 and 4 (same for all pixels within a patch), multiply these values by a factor between 0.7 and 1.4, and add to them a value between -0.1 and 0.1. Also, you could add a value between [-0.1, 0.1] to the hue (H component of HSV) of all pixels in the image/patch.

Krizhevsky et al. [1] proposed fancy PCA when training the famous Alex-Net in 2012. Fancy PCA alters the intensities of the RGB channels in training images. In practice, you can firstly perform PCA on the set of RGB pixel values throughout your training images. And then, for each training image, just add the following quantity to each RGB image pixel (i.e., I_xy=[I_xy^R,I_xy^G,I_xy^B]^T): p₁,p₂,p₃][α₁ λ₁,α₂λ₂,α₃λ₃]^T where, p_i and λ_i are the i-th eigenvector and eigenvalue of the 3 × 3 covariance matrix of RGB pixel values, respectively, and α_i is a random variable drawn from a Gaussian with mean zero and standard deviation 0.1. Please note that, each α_i is drawn only once for all the pixels of a particular training image until that image is used for training again. That is to say, when the model meets the same training image again, it will randomly produce another α_i for data augmentation. In [1], they claimed that “fancy PCA could approximately capture an important property of natural images, namely, that object identity is invariant to changes in the intensity and color of the illumination”. To the classification performance, this scheme reduced the top-1 error rate by over 1% in the competition of ImageNet 2012.

Now we have obtained a large number of training samples (images/crops), but please do not hurry! Actually, it is necessary to do pre-processing on these images/crops. In this section, we will introduce several approaches for pre-processing.

The first and simple pre-processing approach is zero-center the data, and then normalize them, which is presented as two lines Python codes as follows:

>>> X -= np.mean(X, axis = 0) # zero-center
>>> X /= np.std(X, axis = 0) # normalize

where, X is the input data (NumIns×NumDim). Another form of this pre-processing normalizes each dimension so that the min and max along the dimension is -1 and 1 respectively. It only makes sense to apply this pre-processing if you have a reason to believe that different input features have different scales (or units), but they should be of approximately equal importance to the learning algorithm. In case of images, the relative scales of pixels are already approximately equal (and in range from 0 to 255), so it is not strictly necessary to perform this additional pre-processing step.

Another pre-processing approach similar to the first one is PCA Whitening. In this process, the data is first centered as described above. Then, you can compute the covariance matrix that tells us about the correlation structure in the data:

>>> X -= np.mean(X, axis = 0) # zero-center
>>> cov = np.dot(X.T, X) / X.shape[0] # compute the covariance matrix

After that, you decorrelate the data by projecting the original (but zero-centered) data into the eigenbasis:

>>> U,S,V = np.linalg.svd(cov) # compute the SVD factorization of the data covariance matrix
>>> Xrot = np.dot(X, U) # decorrelate the data

The last transformation is whitening, which takes the data in the eigenbasis and divides every dimension by the eigenvalue to normalize the scale:

>>> Xwhite = Xrot / np.sqrt(S + 1e-5) # divide by the eigenvalues (which are square roots of the singular values)

Note that here it adds 1e-5 (or a small constant) to prevent division by zero. One weakness of this transformation is that it can greatly exaggerate the noise in the data, since it stretches all dimensions (including the irrelevant dimensions of tiny variance that are mostly noise) to be of equal size in the input. This can in practice be mitigated by stronger smoothing (i.e., increasing 1e-5 to be a larger number).

Please note that, we describe these pre-processing here just for completeness. In practice, these transformations are not used with Convolutional Neural Networks. However, it is also very important to zero-center the data, and it is common to see normalization of every pixel as well.