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John von Neumann made so many fundamental contributions that Paul Halmos remarked that it was almost like von Neumann maintained a list of various subjects that he wanted to touch and develop and he systematically kept ticking items off. This sounds to be remarkably true if one just has a glance at the dizzyingly long “known for” column below his photograph on his wikipedia entry.

John von Neumann with one of his computers.

John von Neumann with one of his computers.

Since Neumann died (young) in 1957, rather unfortunately, there aren’t very many audio/video recordings of his (if I am correct just one 2 minute video recording exists in the public domain so far).

I recently came across a fantastic film on him that I would very highly recommend. Although it is old and the audio quality is not the best, it is certainly worth spending an hour on. The fact that this film features Eugene Wigner, Stanislaw UlamOskar Morgenstern, Paul Halmos (whose little presentation I really enjoyed), Herman Goldstein, Hans Bethe and Edward Teller (who I heard for the first time, spoke quite interestingly) alone makes it worthwhile.

Update: The following youtube links have been removed for breach of copyright. The producer of the film David Hoffman, tells us that the movie should be available as a DVD for purchase soon. Please check the comments to this post for more information.

Part 1

Find Part 2 here.

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The first part is just to motivate this upcoming Stanford video series.

Deep Learning? Supervised Learning is the process where an entity has to “teach” or “supervise” the learning. The learning algorithm (such as a neural network) is shown some features (which are carefully extracted) and then it is told the correct answer (training). Over time it learns a function that maps features to labels. It thus  focuses on finding what would be the class label given a set of features i.e. P(Y|X) where Y is the class and X the features. For example in face recognition, after we have extracted features using a technique such as PCA or ICA, the task is to use these features and label information (person name or ID etc) to learn a function that can make predictions. But we see in everyday life that label information is not as important in learning. Humans do some kind of “clustering” and generative modeling of whatever they see all the time. Given a set of objects we tend to form a generative model of those objects, and then assign labels, labels thus give very little information in actual learning. Another interesting question is how features are learnt in the first place? Is it an unsupervised task? How can a computer learn features in an unsupervised manner?

Unsupervised Feature Learning? Now consider a task where you have to improve accuracy on classifying an image as that of an elephant or a Rhino. But the catch is that you are not given any labeled examples of elephants or Rhinos, not even that, suppose you are not even given unlabeled examples of them. But you are given random images of rivers and mountains and you have to learn a feature representation from these that can help you in your task. This can be done by sparse coding as shown by Raina et al.

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Lectures: Recently I came across a series of lectures (which are a work in progress) by Professor Andrew Y. Ng on Unsupervised Feature Learning and Deep Learning. This course will help present some issues such as the above to a wider audience. Though still not yet uploaded, I am really excited about these as I had really enjoyed his CS 229 lectures a long time ago. This course needs some basic knowledge of Machine Learning, but does brush up some basics.

I have been working on Meta-Learning for a while, but have been getting more interested in Deep Learning Methods recently and hence am looking forward for these lectures to come online.

I wrote to Professor Ng about them and in his opinion it would take a few months before they can be put up. I think that works fine as I plan to work on Deep Learning in the summers and that these would really help. Even now expertise in Deep Learning Methods is restricted to only a few places and thus such lectures would be a great advantage.

Here is a description to the Unsupervised Feature Learning and Deep Learning course:

Machine learning has seen numerous successes, but applying learning algorithms today often means spending a long time hand-engineering the input feature representation. This is true for many problems in vision, audio, NLP, robotics, and other areas. In this course, you’ll learn about methods for unsupervised feature learning and deep learning, which automatically learn a good representation of the input from unlabeled data. You’ll also pick up the “hands-on,” practical skills and tricks-of-the-trade needed to get these algorithms to work well.

Basic knowledge of machine learning (supervised learning) is assumed, though we’ll quickly review logistic regression and gradient descent.

I hope this would be as widely viewed as the CS 229 lectures. I say that as I know these would be fantastic.

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N is a Number : A Portrait of Paul Erdős is one of the most delightful, endearing and probably one of the best documentaries I have seen on an individual. I have always regarded Paul  Erdős as one of my personal heroes and hence It seems weird that I had not seen this rather old documentary earlier. Especially given it’s extremely high quality, appeal and not to mention the character it is based on.  However, it is never late to discover something so good.

There is an extremely good wikipedia entry on Paul Erdős. However I would still write a few words on him before linking to the videos.

A Mathematician is a machine for turning coffee into theorems.

— An extremely famous quote attributed to Alfréd Rényi. It was originally intended for Hungarian mathematicians and the mathematical-circles culture that flourished there giving the world so many mathematical giants.

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Erdős was an extremely prolific and famously eccentric mathematician, producing more papers and collaborating with more people than anybody in history. His eccentricity made him an extremely lovable character, and he made a fair share in contributing to human comedy.

He had no home and no full time job, he traveled around the world for half a century. Surviving on living with collaborators, fees from lectures and other appearances. His dis-interest in anything carnal or materialistic was almost Zen like I would dare say. Just having two pairs of half empty suitcases as his only belongings as he moved along from one location onto another.

It is often said (and quite correctly) that if you finish all bees in the world, the world would not survive for long. We could use that as an allegory for the sciences /mathematics as well. Erdős was essentially a bee. Brilliant in many areas of mathematics, he traveled from place to place using one idea from one area into another, cross-pollinating them, generating interest with his lovable anecdotes and enriching Mathematics as a consequence. A welcome departure from the so called purists.

His mathematical output was so prolific that a tribute is the famous Erdős number that gives the collaborative distance of a mathematician with him. The reason for such astounding output was not just his love for only mathematics but a brilliant memory. Colleagues have remarked that he could remember problems discussed years ago and exactly what the details that were talked about. If a mathematical problem was left half way, he could still remember where was the point they stopped, even if revisited after years. Not just that, he had this knack of knowing the mind of other mathematicians in where their interests lay. So he knew who would like to work on what kind of problems.

Though Mathematics was his only love, his knowledge was extremely wide and he could talk with most people about most things they might be interested in. Almost educated in the classical European style, with interests spreading across other basic sciences, politics, history. literature etc.

His work was not rich just in quantity. He displayed an extremely good taste in choosing and posing problems. The solutions to some of which have resulted in entirely new areas of Mathematics. Paul Erdős had been a towering figure even while he was alive, but as more time passes by, he only grows taller.

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N is a Number : A Portrait of Paul Erdős – Videos

Total Runtime : 57 Minutes

[View Here]

– Based on the book “The man who only loves numbers” by Paul Hoffman.

– Made by George Paul Csicsery 1993

– Narrated by James Locker

– Music by Mark Adler (I have to mention the music as I thought it was pretty beautiful, especially towards the end)

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Hat Tip : To Dr Vitorino Ramos’ ever thoughtful blog

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