Deep Learning and an Information Theory of Aging. In this case, we are overcompressing to the point that the representation is now too simple to capture the label information. Hot In that sense, Deep Learning is a method for solving the Information Bottleneck problem for large-scale supervised learning problems.The theory provides a new computational understating of the benefit of the hidden layers and gives concrete predictions for the structure of the layers of Deep Neural Networks and their design principles. But now we start doing random walks in the remaining millions of irrelevant dimensions and their total averaged effect increases the entropy in the irrelevant dimensions of the problem. Using this we get the probabilityand we also have the same property for the conditionals:Since all the patterns are equally likely, as the size of X grows large, we have approximately This now means that for each bit of compression of the layers, we need to double the number of examples. How can we quantify the difference between two sentences? Below is an image of the snapshots of the information plane for three different stages during the SGD optimization process. In mathematical terms, the coordinates can be seen as As we move forward through the hidden layers, we slowly reach the optimal line with the finite sample after possibly pruning irrelevant information from X and thus compressing the representation but increasing the distortion in the process. this gives us a better bound than before as now, to compress the information by k bits, we need to increase the size of our sample by Revisiting the information plane graph, we see that we need to minimize two kinds of losses as given in the graph (the compression loss and the finite sample loss).In order for us to understand the dynamics of the drift and the diffusion phase, Tishby talks about the role of noise induced by the mini-batches in the SGD process. Tishby says that this is what we desire (thing getting concentrated in large limits) and it happens when we have The image above shows the trajectory that the hidden layers follow (the different random initializations are averaged to get the trajectory of each hidden layer). Information theory. In the case with a large number of samples, on the other hand, the label information is clearly increasing during the compression phase. a starting point, rather than caring about the knowledge, we may build The colors signify the different hidden layers (orange one being the farthest from the input layer) and the points correspond to 50 different random initializations. maximizing the log-likelihood function.Verify that the card examples from the first section indeed have the distributions.Cross Entropy can be viewed as an objective function of multi-class learning and information theory. classification. Stack Exchange Network Stack Exchange network consists of 177 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. off the idea that information represents the degree of surprise or the Hence, the network learns to consider the high-level feature Thanks to the effort by Tishby and colleagues, we now have with the IB theory one promising candidate for a more rigorous study of deep learning at our disposal. both Indeed, this is a valid definition for the mutual information. interesting signals from data and make critical predictions. elements which have probability zero.The information we gain by observing two random variables is no more So, we can say that exp 1 is inherently more uncertain/unpredictable than exp 2. Information Theory: Coding Theorems for Discrete Memoryless Systems Akademiai Kiado: 2nd edition, 1997.


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