Wednesday 20 July 2011

SCHEMENAUER AND THE XOR GATE

SCHEMENAUER AND THE XOR GATE

IMPLEMENTING ANN IN PYTHON

I was searching for Artificial Neural Networks (ANN) implementation in Python. I came across the following;
  1. FANN - C library with python bindings
  2. PyBrain
  3. NeuroLab
  4. PyNN 
  5. BPNN - Not a library, solitary script by Neil Schemenauer
THE XOR PROBLEM

The XOR problem has some history in the evolution of ANN methods. The XOR function is not linearly separable and cannot be realised using only one layer of ANN.

TINKERING WITH SCHEMENAUER'S CODE

Schemenauer's code has default training values for a 2 input XOR gate.


Schemenauer recommends using of a (2,2,1) network (viz. a network with two input, two hidden, and one output nodes) and the output is very much as desired, in the limits of errors of the ANN.  

XOR Output for a (2,2,1) Back Propogation Neural Network;
([0, 0], '==', [0.025608579041218795])
([0, 1], '==', [0.98184578447794768])
([1, 0], '==', [0.98170742564066216])
([1, 1], '==', [-0.021030064439813451])
However, playing around with the number of hidden layers has interesting results,

XOR Output for a (2,1,1) Back Propagation Neural Network; 
([0, 0], '==', [0.0020536886211772179])
([0, 1], '==', [0.68437587415369783])
([1, 0], '==', [0.68413753288547252])
([1, 1], '==', [0.6856616998850974])
The output of (2,1,1) clearly confirms the XOR problem !

Increasing the number of hidden layers indiscriminately, leads to anomalous output.

As an example, XOR Output for a (2,25,1) Back Propagation Neural Network;
([0, 0], '==', [0.99999643777993841])
([0, 1], '==', [0.99999911082329096])
([1, 0], '==', [0.99999280130316026])
([1, 1], '==', [0.99999824824488848])

Anomalous behaviour comes into play from about 12 hidden nodes.


REFERENCES
(1) An introduction to neural networks

Wednesday 28 July 2010

FIREFOX EASTER EGGS

FIREFOX EASTER EGGS

In mozilla firefox type in about:robots and then see the magic unfurl !


ABRACADABRA ! .......


..... if you can handle surprises then try about:mozilla



Sunday 20 June 2010

MPLAYER !

I will keep it short and simple ! I had never come across a movie player which is controlled - NOT by a GUI, but command line in the terminal window ! ..... and then I came across MPLAYER .

I guess using Unix/Ubuntu is a 'learning' experience !