Machine Learns

Paper: https://arxiv.org/pdf/1611.03530v1.pdf

This paper states the following phrase. Traditional machine learning frameworks (VC dimensions, Rademacher complexity etc.) trying to explain how learning occurs are not very explanatory for the success of deep learning models and we need more understanding looking from different perspectives.

They rely on following empirical observations;

• Deep networks are able to learn any kind of train data even with white noise instances with random labels. It entails that neural networks have very good brute-force memorization capacity.
• Explicit regularization techniques - dropout, weight decay, batch norm - improves model generalization but it does not mean that same network give poor generalization performance without any of these. For instance, an inception network trained without ant explicit technique has 80.38% top-5 rate where as the same network achieved 83.6% on ImageNet challange with explicit techniques.
• A 2 layers network with 2n+d parameters can learn the function f with n samples in d dimensions. They provide a proof of this statement on appendix section. From the empirical stand-view, they show the network performances on MNIST and CIFAR-10 datasets with 2 layers Multi Layer Perceptron.

Above observations entails following questions and conflicts;

• Traditional notion of learning suggests stronger regularization as we use more powerful models. However, large enough network model is able to memorize any kind of data even if this data is just a random noise. Also, without any further explicit regularization techniques these models are able to generalize well in natural datasets.  It shows us that, conflicting to general belief, brute-force memorization is still a good learning method yielding reasonable generalization performance in test time.
• Classical approaches are poorly suited to explain the success of neural networks and more investigation is imperative in order to understand what is really going on from theoretical view.
• Generalization power of the networks are not really defined by the explicit techniques, instead implicit factors like learning method or the model architecture seems more effective.
• Explanation of generalization is need to be redefined in order to solve the conflicts depicted above.

My take :  These large models are able to learn any function (and large does not mean deep anymore) and if there is any kind of information match between the training data and the test data, they are able to generalize well as well. Maybe it might be an explanation to think this models as an ensemble of many millions of smaller models on which is controlled by the zeroing effect of activation functions.  Thus, it is able to memorize any function due to its size and implicated capacity but it still generalize well due-to this ensembling effect.

paper: http://arxiv.org/pdf/1511.07543v3.pdf
code : https://github.com/yixuanli/convergent_learning

This paper is an interesting work which tries to explain similarities and differences between representation learned by different networks in the same architecture.

To the extend of their experiments, they train 4 different AlexNet and compare the units of these networks by correlation and mutual information analysis.

They asks following question;

• Can we find one to one matching of units between network , showing that these units are sensitive to similar or the same commonalities on the image?
• Is the one to one matching stays the same by different similarity measures? They first use correlation then mutual information to confirm the findings.
• Is a representation learned by a network is a rotated version of the other, to the extend that one to one matching is not possible  between networks?
• Is clustering plausible for grouping units in different networks?

Answers to these questions are as follows;

• It is possible to find good matching units with really high correlation values but there are some units learning unique representation that are not replicated by the others. The degree of representational divergence between networks goes higher with the number of layers. Hence, we see large correlations by conv1 layers and it the value decreases toward conv5 and it is minimum by conv4 layer.
• They first analyze layers by the correlation values among units. Then they measure the overlap with the mutual information and the results are confirming each other..
• To see the differences between learned representation, they use a very smart trick. They approximate representations  learned by a layer of a network by the another network using the same layer.  A sparse approximation is performed using LASSO. The result indicating that some units are approximated well with 1 or 2 units of the other network but remaining set of units require almost 4 counterpart units for good approximation. It shows that some units having good one to one matching has local codes learned and other units have slight distributed codes approximated by multiple counterpart units.
• They also run a hierarchical clustering in order to group similar units successfully.

For details please refer to the paper.

My discussion: We see that different networks learn similar representations with some level of accompanying uniqueness. It is intriguing  to see that, after this paper, these  are the unique representations causing performance differences between networks and whether the effect is improving or worsening. Additionally, maybe we might combine these differences at the end to improve network performances by some set of smart tricks.

One deficit of the paper is that they do not experiment deep networks which are the real deal of the time. As we see from the results, as the layers go deeper,  different abstractions exhumed by different networks. I believe this is more harsh by deeper architectures such as Inception or VGG kind.

One another curious thing is to study Residual netwrosk. The intuition of Residual networks to pass the already learned representation to upper layers and adding more to residual channel if something useful learned by the next layer. That idea shows some promise that two residual networks might be more similar compared to two Inception networks. Moreover, we can compare different layers inside a single Residual Network to see at what level the representation stays the same.