I searched for the reason a lot but I didn't get it clear, May someone explain it in some more detail please?
In theory you do not have to attach a fully connected layer, you could have a full stack of convolutions till the very end, as long as (due to custom sizes/paddings) you end up with the correct number of output neurons (usually number of classes).
So why people usually do not do that? If one goes through the math, it will become visible that each output neuron (thus - prediction wrt. to some class) depends only on the subset of the input dimensions (pixels). This would be something among the lines of a model, which only decides whether an image is an element of class 1 depending on first few "columns" (or, depending on the architecture, rows, or some patch of the image), then whether this is class 2 on a few next columns (maybe overlapping), ..., and finally some class K depending on a few last columns. Usually data does not have this characteristic, you cannot classify image of the cat based on a few first columns and ignoring the rest.
However, if you introduce fully connected layer, you provide your model with ability to mix signals, since every single neuron has a connection to every single one in the next layer, now there is a flow of information between each input dimension (pixel location) and each output class, thus the decision is based truly on the whole image.
So intuitively you can think about these operations in terms of information flow. Convolutions are local operations, pooling are local operations. Fully connected layers are global (they can introduce any kind of dependence). This is also why convolutions work so well in domains like image analysis - due to their local nature they are much easier to train, even though mathematically they are just a subset of what fully connected layers can represent.
note
I am considering here typical use of CNNs, where kernels are small. In general one can even think of MLP as a CNN, where the kernel is of the size of the whole input with specific spacing/padding. However these are just corner cases, which are not really encountered in practise, and not really affecting the reasoning, since then they end up being MLPs. The whole point here is simple - to introduce global relations, if one can do it by using CNNs in a specific manner - then MLPs are not needed. MLPs are just one way of introducing this dependence.
Every fully connected (FC) layer has an equivalent convolutional layer (but not vice versa). Hence it is not necessary to add FC layers. They can always be replaced by convolutional layers (+ reshaping). See details.
Why do we use FC layers then?
Because (1) we are used to it (2) it is simpler. (1) is probably the reason for (2). For example, you would need to adjust the loss fuctions / the shape of the labels / add a reshape add the end if you used a convolutional layer instead of a FC layer.
I found this answer by Anil-Sharma on Quora helpful.
We can divide the whole network (for classification) into two parts:
Feature extraction:
In the conventional classification algorithms, like SVMs, we used to extract features from the data to make the classification work. The convolutional layers are serving the same purpose of feature extraction. CNNs capture better representation of data and hence we don’t need to do feature engineering.
Classification:
After feature extraction we need to classify the data into various classes, this can be done using a fully connected (FC) neural network. In place of fully connected layers, we can also use a conventional classifier like SVM. But we generally end up adding FC layers to make the model end-to-end trainable.
The CNN gives you a representation of the input image. To learn the sample classes, you should use a classifier (such as logistic regression, SVM, etc.) that learns the relationship between the learned features and the sample classes. Fully-connected layer is also a linear classifier such as logistic regression which is used for this reason.
Convolution and pooling layers extract features from image. So this layer doing some "preprocessing" of data. Fully connected layrs perform classification based on this extracted features.
Related
I understand that Batch Normalisation helps in faster training by turning the activation towards unit Gaussian distribution and thus tackling vanishing gradients problem. Batch norm acts is applied differently at training(use mean/var from each batch) and test time (use finalized running mean/var from training phase).
Instance normalisation, on the other hand, acts as contrast normalisation as mentioned in this paper https://arxiv.org/abs/1607.08022 . The authors mention that the output stylised images should be not depend on the contrast of the input content image and hence Instance normalisation helps.
But then should we not also use instance normalisation for image classification where class label should not depend on the contrast of input image. I have not seen any paper using instance normalisation in-place of batch normalisation for classification. What is the reason for that? Also, can and should batch and instance normalisation be used together. I am eager to get an intuitive as well as theoretical understanding of when to use which normalisation.
Definition
Let's begin with the strict definition of both:
Batch normalization
Instance normalization
As you can notice, they are doing the same thing, except for the number of input tensors that are normalized jointly. Batch version normalizes all images across the batch and spatial locations (in the CNN case, in the ordinary case it's different); instance version normalizes each element of the batch independently, i.e., across spatial locations only.
In other words, where batch norm computes one mean and std dev (thus making the distribution of the whole layer Gaussian), instance norm computes T of them, making each individual image distribution look Gaussian, but not jointly.
A simple analogy: during data pre-processing step, it's possible to normalize the data on per-image basis or normalize the whole data set.
Credit: the formulas are from here.
Which normalization is better?
The answer depends on the network architecture, in particular on what is done after the normalization layer. Image classification networks usually stack the feature maps together and wire them to the FC layer, which share weights across the batch (the modern way is to use the CONV layer instead of FC, but the argument still applies).
This is where the distribution nuances start to matter: the same neuron is going to receive the input from all images. If the variance across the batch is high, the gradient from the small activations will be completely suppressed by the high activations, which is exactly the problem that batch norm tries to solve. That's why it's fairly possible that per-instance normalization won't improve network convergence at all.
On the other hand, batch normalization adds extra noise to the training, because the result for a particular instance depends on the neighbor instances. As it turns out, this kind of noise may be either good and bad for the network. This is well explained in the "Weight Normalization" paper by Tim Salimans at al, which name recurrent neural networks and reinforcement learning DQNs as noise-sensitive applications. I'm not entirely sure, but I think that the same noise-sensitivity was the main issue in stylization task, which instance norm tried to fight. It would be interesting to check if weight norm performs better for this particular task.
Can you combine batch and instance normalization?
Though it makes a valid neural network, there's no practical use for it. Batch normalization noise is either helping the learning process (in this case it's preferable) or hurting it (in this case it's better to omit it). In both cases, leaving the network with one type of normalization is likely to improve the performance.
Great question and already answered nicely. Just to add: I found this visualisation From Kaiming He's Group Norm paper helpful.
Source: link to article on Medium contrasting the Norms
I wanted to add more information to this question since there are some more recent works in this area. Your intuition
use instance normalisation for image classification where class label
should not depend on the contrast of input image
is partly correct. I would say that a pig in broad daylight is still a pig when the image is taken at night or at dawn. However, this does not mean using instance normalization across the network will give you better result. Here are some reasons:
Color distribution still play a role. It is more likely to be a apple than an orange if it has a lot of red.
At later layers, you can no longer imagine instance normalization acts as contrast normalization. Class specific details will emerge in deeper layers and normalizing them by instance will hurt the model's performance greatly.
IBN-Net uses both batch normalization and instance normalization in their model. They only put instance normalization in early layers and have achieved improvement in both accuracy and ability to generalize. They have open sourced code here.
IN provide visual and appearance in-variance and BN accelerate training and preserve discriminative feature.
IN is preferred in Shallow layer(starting layer of CNN) so remove appearance variation and BN is preferred in deep layers(last CNN layer) should be reduce in order to maintain discrimination.
I just started to learn about neural networks and so far my knowledge of machine learning is simply linear and logistic regression. from my understanding of the latter algorithms, is that given multiples of inputs the job of the learning algorithm is to come up with appropriate weights for each input so that eventually I have a polynomial that either describes the data which is the case of linear regression or separates it as in the case of logistic regression.
if I was to represent the same mechanism in neural network, according to my understanding, it would look something like this,
multiple nodes at the input layer and a single node in the output layer. where I can back propagate the error proportionally to each input. so that also eventually I arrive to a polynomial X1W1 + X2W2+....XnWn that describes the data. to me having multiple nodes per layer, aside from the input layer, seems to make the learning process parallel, so that I can arrive to the result faster. it's almost like running multiple learning algorithms each with different starting points to see which one converges faster. and as for the multiple layers I'm at a lose of what mechanism and advantage does it have on the learning outcome.
why do we have multiple layers and multiple nodes per layer in a neural network?
We need at least one hidden layer with a non-linear activation to be able to learn non-linear functions. Usually, one thinks of each layer as an abstraction level. For computer vision, the input layer contains the image and the output layer contains one node for each class. The first hidden layer detects edges, the second hidden layer might detect circles / rectangles, then there come more complex patterns.
There is a theoretical result which says that an MLP with only one hidden layer can fit every function of interest up to an arbitrary low error margin if this hidden layer has enough neurons. However, the number of parameters might be MUCH larger than if you add more layers.
Basically, by adding more hidden layers / more neurons per layer you add more parameters to the model. Hence you allow the model to fit more complex functions. However, up to my knowledge there is no quantitative understanding what adding a single further layer / node exactly makes.
It seems to me that you might want a general introduction into neural networks. I recommend chapter 4.3 and 4.4 of [Tho14a] (my bachelors thesis) as well as [LBH15].
[Tho14a]
M. Thoma, “On-line recognition of handwritten mathematical symbols,”
Karlsruhe, Germany, Nov. 2014. [Online]. Available: https://arxiv.org/abs/1511.09030
[LBH15]
Y. LeCun,
vol. 521,
Y. Bengio,
no. 7553,
and G. Hinton,
pp. 436–444,
“Deep learning,”
Nature,
May 2015. [Online]. Available:
http://www.nature.com/nature/journal/v521/n7553/abs/nature14539.html
Are there known methods of continuous training and graceful degradation of a neural net while it shrinks or grows in size (by number of nodes, connections, whatever)?
To the best of my memory, everything I've read about neural networks is from a static perspective. You define the net and then train it.
If there is some neural network X with N nodes (neurons, whatever), is it possible to train the network (X) so that while N increases or decreases, the network is still useful and capable of performing?
In general, changing network architecture (adding new layers, adding more neurons into existing layers) once the network was already trained makes sense and a rather common operation in Deep Learning domain. One example is the dropout - during training half of the neurons randomly get switched off completely and only remaining half participates in training during specific iteration (each iteration or 'epoch' as it often is named has different random list of switched off neurons). Another example is transfer learning - where you learn network on one set of input data, cut off part of the outcoming layers, replace them with new layers and re-learn the model on another dataset.
To better explain why it makes sense lets step back for a moment. In deep networks, where you have lots of hidden layers each layer learns some abstraction from the incoming data. Each additional layer uses abstract representations learned by previous layer and builds upon them, combining such abstraction to form a higher level of the data representation. For instance, you could be trying to classify the images with DNN. First layer will learn rather simple concepts from images - like edges or points in data. Next layer could combine this simple concepts to learn primitives - like triangles or circles of squares. Next layer could drive it further and combine this primitives to represent some objects which you could find in images, like 'a car' or 'a house'and using softmax it calculates the probabilities of the answer you are looking for (what to actually output). I need to mention that these facts and learned representations could be actually checked. You could visualize the activation of your hidden layer and see what it learned. For example this was done with google's project 'inceptionism'. With that in mind let's get back to what I mentioned earlier.
Dropout is used to improve generalization of the network. It forces each neuron to 'not be so sure' that some pieces of the information from the previous layer will be available and makes it to try to learn the representations relying on less favorable and informative pieces of abstractions from previous layer. It forces it to consider all of the representations from previous layer to make decisions instead of putting all of its weight into couple of neurons it 'likes most of all'. By doing this the network is usually better prepared to new data where the input will be different from the training set.
Q: "As far as you're aware is the quality of the stored knowledge (whatever training has done to the net) still usable following the dropout? Maybe random halves could be substituted by random 10ths with a single 10th dropping, that might result in less knowledge loss during the transition period."
A: Unfortunately I can't properly answer why precisely half of the neurons is switched off and not 10% (or any other number). Maybe there is an explanation but I haven't seen it. In general it just works and that's it.
Also I need to mention that the task of dropout is to ensure that each neuron doesn't consider just several of the neurons from previous layer and is ready to make some decision even if neurons which usually helped it to make correct decision are not available. This is used for generalization only and helps the network to better cope with the data it haven't seen previously, nothing else is achieved with a dropout.
Now let's consider Transfer Learning again. Consider that you have a network with 4 layers. You train it to recognize specific objects in pictures (cat, dog, table, car etc). Than you cut off last layer, replace it with three additional layers and now you train the resulting 6-layered network on a dataset which, for instance, wrights short sentences about what is shown on this image ('a cat is on the car', 'house with windows and tree nearby' etc). What we did with such operation? Our original 4-layer network was capable to understand if some specific object is in the image we feed it with. Its first 3 layers learned good representations of the images - first layer learned about possible edges or points or some extremely primitive geometric shapes in images. Second layer learned some more elaborate geometric figures like 'circle' or 'square'. Last layer knows how to combine them to form some higher level objects - 'car', 'cat', 'house'. Now, we could just re-use this good representation which we learned in different domain and just add several more layers. Each of them will use abstractions from last (3rd) layer of original network and learn how combine them to create meaningful descriptions of images. While you will perform learning on new dataset with images as input and sentences as output it will adjust first 3 layers which we got from original network but these adjustments will be mostly minor, while 3 new layers will be adjusted by learning significantly. What we achieve with transfer learning is:
1) We can learn a much better data representations. We could create a network which is very good at specific task and than build upon that network to perform something different.
2) We can save training time - first layers of network will already be trained well enough so that your layers which are closer to output already get a rather good data representations. So the training should finish much faster using pre-trained first layers.
So the bottom line is that pre-training some network and than re-using part or whole network in another network makes perfect sense and is not something uncommon.
This is something I have seen in the likes of this video...
https://youtu.be/qv6UVOQ0F44
There are links to further resources in the video description.
And is based on a process called NEAT. Neuro Evolution of Augmenting Topologies.
It uses a genetic algorithm and evolutionary process to design and evolve a neural net from scratch with no prior assumptions of structure or complexity of the neural net.
I believe this is what you are looking for.
I've been doing a lot of reading on Conv Nets and even some playing using Julia's Mocha.jl package (which looks a lot like Caffe, but you can play with it in the Julia REPL).
In a Conv net, Convolution layers are followed by "feature map" layers. What I'm wondering is how does one determine how many feature maps a network needs to have to solve some particular problem? Is there any science to this or is it more art? I can see that if you're trying to make a classification at least that last layer should have number of feature maps == number of classes (unless you've got a fully connected MLP at the top of the network, I suppose).
In my case, I 'm not doing a classification so much as trying to come up with a value for every pixel in an image (I suppose this could be seen as a classification where the classes are from 0 to 255).
Edit: as pointed out in the comments, I'm trying to solve a regression problem where the outputs are in a range from 0 to 255 (grayscale in this case). Still, the question remains: How does one determine how many feature maps to use at any given convolution layer? Does this differ for a regression problem vs. a classification problem?
Basically, like any other hyperparameter - by evaluting results on separate development set and finding what number works best. It also worth checking publications that deal with similar problem and finding what number of feature maps they were using.
More art. The only difference between imagenet winners that use conv-nets has been changing the structure of layers and maybe some novel ways of training.
VGG is a neat example. Begins with filter sizes beginning with 2^7, then 2^8, then 2^9 followed by fully connected layers, then an output layer which will give you your classes. Your maps and layer depths can be completely unrelated to the number of output classes.
You would not want a fully connected layer at the top. That kind of defeats the purpose that convolutional nets were designed to solve (overfitting and optimizing hundreds of thousands of weights per neuron)
Training on big sets will require some heavy computational resources. If you're working with imagenet - there's a set of pre-trained models with caffe that you could build on top of http://caffe.berkeleyvision.org/model_zoo.html
I'm not sure if you can port these to mocha. There's a port to tensor flow though if you're interested in that https://github.com/ethereon/caffe-tensorflow
I need help in figuring out a suitable activation function. Im training my neural network to detect a piano note. So in this case I can have only one output. Either the note is there (1) or the note is not present (0).
Say I introduce a threshold value of 0.5 and say that if the output is greater than 0.5 the desired note is present and if its less than 0.5 the note isn't present, what type of activation function can I use. I assume it should be hard limit, but I'm wondering if sigmoid can also be used.
To exploit their full power, neural networks require continuous, differentable activation functions. Thresholding is not a good choice for multilayer neural networks. Sigmoid is quite generic function, which can be applied in most of the cases. When you are doing a binary classification (0/1 values), the most common approach is to define one output neuron, and simply choose a class 1 iff its output is bigger than a threshold (typically 0.5).
EDIT
As you are working with quite simple data (two input dimensions and two output classes) it seems a best option to actually abandon neural networks and start with data visualization. 2d data can be simply plotted on the plane (with different colors for different classes). Once you do it, you can investigate how hard is it to separate one class from another. If data is located in the way, that you can simply put a line separating them - linear support vector machine would be much better choice (as it will guarantee one global optimum). If data seems really complex, and the decision boundary has to be some curve (or even set of curves) I would suggest going for RBF SVM, or at least regularized form of neural network (so its training is at least quite repeatable). If you decide on neural network - situation is quite similar - if data is simply to separate on the plane - you can use simple (linear/threshold) activation functions. If it is not linearly separable - use sigmoid or hyperbolic tangent which will ensure non linearity in the decision boundary.
UPDATE
Many things changed through last two years. In particular (as suggested in the comment, #Ulysee) there is a growing interest in functions differentable "almost everywhere" such as ReLU. These functions have valid derivative in most of its domain, so the probability that we will ever need to derivate in these point is zero. Consequently, we can still use classical methods and for sake of completness put a zero derivative if we need to compute ReLU'(0). There are also fully differentiable approximations of ReLU, such as softplus function
The wikipedia article has some useful "soft" continuous threshold functions - see Figure Gjl-t(x).svg.
en.wikipedia.org/wiki/Sigmoid_function.
Following Occam's Razor, the simpler model using one output node is a good starting point for binary classification, where one class label is mapped to the output node when activated, and the other class label for when the output node is not activated.