In my last blog post I talked about trying out my code for training neural nets on a simple one-layer network which consists of a single weight layer and a softmax output. In this post I share results for training a fully connected two-layer network.
In this network, the input goes from 28×28 image pixels down to 50 hidden units. Then there is a rectified linear activation function. The second layer goes from the 50 hidden units down to 10 units, and finally there is the softmax output stage for classification.
When I train this network on the MNIST handwriting dataset I get a test error rate of 2.89% which is pretty good and actually lower than other results quoted on the MNIST web site. It is interesting to inspect the patterns of the weights for the first layer below (here I organized the weights for the 50 hidden units as a 10×5 matrix):
Recently I have been experimenting with a C++ deep learning library that I have written by testing it out on the MNIST handwritten digits data set. In this dataset there are 60,000 training images and 10,000 test images which are of size 28×28 pixels. I have been trying to reproduce some of the error rates that Yann LeCun reports on the MNIST site. The digits written in many different styles and some of them are quite hard to classify, and so it makes a good test for neural net learning.
I am passionate about machine learning, intelligence, and robotics. I have a number of robot projects on the go. I wanted to build a platform that would allow me to do a lot of complex experiments on sensor fusion and creating intelligent emergent behaviors. I needed to make a robot that has quite a number of sensor inputs, but not so many that it would overload the processing capability to do anything useful. I decided to make a simple two-wheeled robotic platform that has a lot of flexibility and load it up with appropriate sensors.
One of the aspects of my robotics philosophy is that information from simple sensors can be highly informative and that current robot designs jump too quickly to complex high bandwidth data sources and they then do a marginal job of interpreting the information from those sources in software. I am inspired by insects and other small creatures that seem to have small numbers of sensors, for example eyes with only a few photoreceptors, but still have very complex adaptive behaviors which are often leagues beyond what we can do with today’s machines. Part of this is due to the efficiency with which they extract every little bit of useful information out of the sensory data, including correlations we would never think of. I am interested in applying experience gained from machine learning in order to extract from sensors information that could not easily be determined by using hand coded algorithms.
My rolling robot has two wheels and these have wheel encoders to give a feedback of position or wheel rotation speed. It also has an infra red range finder that can indicate the Continue reading
I’m struggling with a health issue at the moment so I’m doing some some small projects to stay sane…
I’ve been helping a friend fix old pinball games which typically make use of 8-bit micros like the 6800 or 6502. Often we want to know what’s on these old ROM chips that even some modern device readers can’t easily scan. I built a shield for Arduino that can read them by listing the file over the serial link. The only components other than the Arduino Uno and a prototyping shield were a couple of 74HCT573s and a 24-pin socket.
Recent strides in artificial intelligence from big name players such as Google, Facebook, and Baidu, as well as increasingly successful heterogenous systems like IBM’s Watson have provoked fear and excitement amongst the intelligentsia in equal measures. Public figures, such as Steven Hawking, are concerned, and not surprisingly the popular press are excited to cover it. Recently, Elon Musk has become worried that AI might eventually spell doom for the human race. He donated $10 million to fund the Future of Life organization whose stated goal is to ensure AI remains beneficial and does not threaten our wellbeing. An open letter by this organization, titled “Research Priorities for Robust and Beneficial Artificial Intelligence,” was signed by hundreds of research leaders. Influential futurist, Ray Kurzweil, has popularized the idea of the technological singularity where intelligent systems surpass human capabilities and leave us marginalized at best.
I read with interest the recent paper out of Baidu about scaling up image recognition. In it they talk about creating a supercomputer to carry out the learning phase of training a deep convolutional network. Training such things is terribly slow, with their typical example taking 212 hours on a single GPU machine because of the enormous number of weight computations that need to be evaluated and the slow stochastic gradient process over large training sets.
Baidu has built a dedicated machine with 36 servers connected by an InfiniBand switch, each server with four GPUs. In the paper they describe different ways of partitioning the problem to run on this machine. They end up being able to train the model using 32 GPUs in 8.6 hours.
In recent years the concept of deep learning has been gaining widespread attention. The media frequently reports on talent acquisitions in this field, such as those by Google and Facebook, and startups which claim to employ deep learning are met with enthusiasm. Gratuitous comparisons with the human brain are frequent. But is this just a trendy buzz word? What exactly is deep learning and how is it relevant to developments in machine intelligence?
For many researchers, deep learning is simply a continuation of the multi-decade advancement in our ability to make use of large scale neural networks. Let’s first take a quick tour of the problems that neural networks and related technologies are trying to solve, and later we will examine the deep learning architectures in greater detail.
Machine learning generally breaks down into two application areas which are closely related: classification and regression. Continue reading
Recently NASA has been in the news with the successful launch and recovery of the Orion space craft. This was a four hour two orbit test of the new capsule that is intended to support future manned missions beyond the Earth. In addition, there has been a huge growth of the space industry in the last decade including commercial ventures such as Space X and Blue Origin, as well as proposals to mine the asteroids. There is always a tremendous interest in sending people to space, and in fact it seems to be an imperative for the human race to escape potential future disaster scenarios on the Earth by seeking solace among the stars.
I am currently working on improving this blog and putting more projects and documentation on here that might be useful or interesting for people to see. I’ve spent a long time looking for a slightly better theme, but every time I find something I like, it ends up being the case that it won’t install properly or else it has issues on mobile, etc. Most frustrating. I’m trying to make the blog a bit easier to use from mobile devices.
I’m doing some simple exploration of image statistics on a large database of natural images. The first thing that I tried was computing the histogram of neighboring image pixel intensity differences. Here is the graph for that using a log y axis, for a few pixel separations.
It is clear that large differences occur much more rarely and that the most probable pixel to pixel spatial change in intensity is zero. However the tails are heavy, so it is nothing like a Gaussian distribution. The adjacent pixel intensity difference log probabilities were fairly well fitted by a function that goes like , and the pixels further apart require a smaller exponent.