Homomorphism vs Homeomorphism


1 mainDid you get the joke in the picture to the left? If not, you will do so in a few minutes. I was recently reading an article and I came across the terms mentioned in the title. From the looks of it, they are very close to each other, right? In many fields within mathematics, we talk about objects and the maps between them. Now you may ask why we would want to do that? Well, transformation is one of the most fundamental things in any field. For example, how do we transform a line into a circle, or fuel into mechanical energy, or words into numbers? There are infinitely many types of transformations that can exist. Obviously, we cannot account for every single type of transformation that can possibly exist. So we limit ourselves to only the interesting ones. So what exactly is it all about? How does it even relate to the title of…

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Tensor Methods in Machine Learning

From http://www.offconvex.org/2015/12/17/tensor-decompositions/


Tensors are high dimensional generalizations of matrices. In recent years tensor decompositions were used to design learning algorithms for estimating parameters of latent variable models like Hidden Markov Model, Mixture of Gaussians and Latent Dirichlet Allocation (many of these works were considered as examples of “spectral learning”, read on to find out why). In this post I will briefly describe why tensors are useful in these settings. Continue reading

Understanding Convolutional Neural Networks for NLP

From http://www.wildml.com/2015/11/understanding-convolutional-neural-networks-for-nlp/

When we hear about Convolutional Neural Network (CNNs), we typically think of Computer Vision. CNNs were responsible for major breakthroughs in Image Classification and are the core of most Computer Vision systems today, from Facebook’s automated photo tagging to self-driving cars.

More recently we’ve also started to apply CNNs to problems in Natural Language Processing and gotten some interesting results. In this post I’ll try to summarize what CNNs are, and how they’re used in NLP. The intuitions behind CNNs are somewhat easier to understand for the Computer Vision use case, so I’ll start there, and then slowly move towards NLP.
Continue reading

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