## Archive for the ‘source code’ Category

## Backpropagation Networks

Forward Feed Back Propagation networks (aka Three Layer Forward Feed Networks) have been very successful. Some uses include teaching neural networks to play games, speak and recognize things. If a non-linear activation function is used (usually the sigmoid function) then one hidden layer is sufficient to solve almost any equation with reasonable accuracy.

Back-propagation supervised training for Forward-Feed neural nets uses pairs of input and output patterns.

The weights on all the vectors are set to random values.

Then input is fed to the net and propagates to the output layer

hidden layer = sigmoid( sum ( inputs * weights + bias ) )

output layer = sigmoid( sum ( hidden * weights + bias ) )

The errors are calculated.

Error = Output * ( 1 – Output ) * ( expected value – Output )

Then the error correction is propagated back through the hidden layer

adjust output weights

Wnew = Wold + ( Error * Output ) * learningRate

then to the input layer in the network.

Error = Hidden * ( 1 – Hidden ) * ( OutputError * Weight + OutputError * Weight….. )

Wnew = Wold + ( Error * Output ) * learningRate

There is one input neurode for each number (dimension) in the input vector, there is one output neurode for each dimension in the output vector. So the network maps in-dimensional space to out-dimension space.

The weight adjustment is gradient descent. You are calculating the derivative and finding the quickest route to zero error.

The learningRate is a small number ~0.1 to keep the network from blowing up or over shooting a minimum. If the rate is too small the network will be slow to learn.

There is no set rule for determining the number of hidden layers or the number of neurodes in the hidden layer. However, if too few hidden neurodes are chosen then the network can not learn. If too many are chosen, then the network memorizes the patterns rather than learning to extract relevant information. A rule of thumb for choosing the number of hidden neurodes is to choose log ( 2)X where X is the number of patterns. So if you have 8 distinct patterns to be learned, then log ( 2)8 = 3 and 3 hidden neurodes are probably needed. This is just a rule of thumb, experiment to see what works best for your situation.

The error vector is aimed at zero during training.

Error = ( 1/2 * (sum (desired-actual)^2))

To get the error close to zero, with in a tolerance, we use iteration. Each iteration we move a step downward. We take the gradient, the derivative of a vector, and use the steepest descent to minimize the error. So thenewweight = oldW eight + stepsize (-gradientW (e(W )).

The error may be backpropagated after each training example, or more commonly after a batch of examples.

Other resources:

GitHub source code for a backpropagtion network in Swift using the Accelerate Library

Backpropagation Tutorial

An Introduction to Neural Networks, textbook by Krose and van der Smagt

## Perceptron

Perceptrons separate data linearly, if the data is linearly separable.

y = mx + b

m => the weights which give the slope of the line

b => the bias, the place where the line crosses the y axis

x => input data

y => output

Rosenblatt added the learning law to the McCulloch-Pitts neurode to make it Perception, which is the first of the neural net learning models. The perception has one layer of inputs and one layer of outputs, and one group of weights. If data points on a plot are linearly separable (we can draw a straight line separating points that belong in different categories), then we can use this learning method to teach the neural net to properly separate the data points.

The McCulloch-Pitts neurode fires a +1 if the neurode’s total input the sum of each input * its weight is greater than the set threshold. If it is less than the set threshold, or if there is any inhibitory input a 0 is fired. Any logical function can be created using only AND, OR and NOT gates so a neural net can be created with McCulloch-Pitts neurodes to solve any logical function.

We start with a weight vector that is set to zeros or random numbers. During training weights are increased or decreased by adding or subtracting the input to the weights. This is done until all data points are input and the neurode gives the correct output for each point.

The perception fell out of favor since it can only handle linearly separable functions which means simple functions like XOR, or parity can not be computed by them. Minsky and Papert published a book ‘Perceptions’, in the 1980’s, that proved that one and two layer neural nets could not handle many real world problems and research fell off for about twenty years in neural nets.

An additional layer and set of weights can enable the Perception to handle functions that are not linear. A separate layer is needed for each vertex needed to separate the function. A 1950’s paper by A.N. Kilmogorov published a proof that a three layer neural network could perform any mapping exactly between any two sets of numbers.

Multi layered perceptrons were developed than can handle XOR functions. Hidden layers are added and they are trained using backpropagation or a similar training algorithm. Using one layer linearly separable problems can be solved. Using two layers regions can be sorted and with three layers enclosed regions can be sorted.

More information:

GitHub source code for a Swift Perceptron network

An Introduction to Neural Networks, textbook by Krose and van der Smagt

## Braitenberg Vehicles

Synthetic psychology is a field where biological behavior is synthesized rather than analyzed. The father of such behavior Valentino Braitenberg ( home page ) did some interesting work with toy vehicles in the 1986 book “Vehicles: Experiments in Synthetic Psychology“.

The Braitenberg vehicles were simple toy cars with light sensors as headlights. In some cars the wire for each headlight went to the real wheel directly behind it, in some the wires went to the opposite back wheel. The headlight receptors were aimed slightly off to the outside. The more light received by a receptor the faster the wheel wired to that receptor would turn.

Each vehicle exhibited realistic behavior when placed in a plane with several randomly placed light sources. A vehicle wired straight back when placed near a light source will then rush towards the light veering off as it gets closer to the light. As it gets more distant from the light sources the vehicle slows down. The reason is the wheel receiving the most light spins fastest turning the car away from the light source.

The vehicle with the crossed wires will turn and drive towards the brightest light in its field of view. The closer it gets, the faster it goes eventually running into the light.

Pretty interesting behavior from a very simple machine. But what if we add in a neurode to each wire and instead of a plain wire we use a wire that inhibits signals? Neurodes are set to only fire if they receive signals over a certain threshold. In this case zero is to be our threshold. So now our cars send signals to the wheels if there is no light, and do not send a signal if there is a light. Now the vehicle with the wires straight back moves toward a light and slows as it approaches, facing the light. The second vehicle now avoids light sources, speeding off to the darkest corner it can find.

Using thresholds ( see logic version ) you begin to see group behavior, one set of vehicles herds and traps another set.

So what has this all to do with current artificial intelligence? Some of our best stuff right now came from earlier work that was done and stopped. Some of our best mathematical algorithms come from extremely early math. And to remind you ( and me ) that simple rules can create very complex behavior in game characters and artificial life forms.

Four neurode versions of these vehicles have been built and they will exhibit more complex, non-linear behavior. “The question of whether a computer can think is no more interesting than the question of whether a submarine can swim.” (Edsger Dijkstra) At what point does the behavior become realist enough to be considered a life form?

Source Code:

ObjC simulation of Braitenberg Vehicles( #2 fear and aggression )

ObjC simulation of Braitenberg Vehicles( #3 love, explore and complex )

ObjC simulation of Braitenberg Vehicles( #4 values and tastes )

ObjC simulation of Braitenberg Vehicles( #5 Logic )

More information:

Braitenberg Vehicles ( Java and Lisp simulators here )

Papers:

Swarm modelling. The use of Swarm Intelligence to generate architectural form. ( pdf)

## Java Neural Network Framework Neuroph

Neuroph is lightweight Java neural network framework to develop common neural network architectures. It contains well designed, open source Java library with small number of basic classes which correspond to basic NN concepts. Also has nice GUI neural network editor to quickly create Java neural network components. It has been released as open source under the Apache 2.0 license, and it’s FREE for you to use it.

Neuroph simplifies the development of neural networks by providing Java neural network library and GUI tool that supports creating, training and saving neural networks.

If you are beginner with neural networks, and you just want to try how they work without going into complicated theory and implementation, or you need them quickly for your research project the Neuroph is good choice for you. It is small, well documented, easy to use, and very flexible neural network framework.

## Polyworld open source artificial life software

Polyworld is an evolutionary environment with simulated physics that allows you create creatures that will evolve. The creatures are free form neural networks. It was created by Larry Yaeger. They will learn to find food, become or hunt prey and mate and have children. It is open source, code is available at Source Forge ( link below ) and it does have versions for Windows, Linux and OSX.

Although we have had great success solving toy problems in artificial environments evolved creatures in virtual environments haven’t found great success in solving real world problems yet.

PolyWorld is a computational ecology that I developed to explore issues in Artificial Life. Simulated organisms reproduce sexually, fight and kill and eat each other, eat the food that grows throughout the world, and either develop successful strategies for survival or die. An organism’s entire behavioral suite (move, turn, attack, eat, mate, light) is controlled by its neural network “brain”. Each brain’s architecture–it’s neural wiring diagram–is determined from its genetic code, in terms of number, size, and composition of neural clusters (excitatory and inhibitory neurons) and the types of connections between those clusters (connection density and topological mapping). Synaptic efficacy is modulated via Hebbian learning, so, in principle, the organisms have the ability to learn during the course of their lifetimes. The organisms perceive their world through a sense of vision, provided by a computer graphic rendering of the world from each organism’s point of view. The organisms’ physiologies are also encoded genetically, so both brain and body, and thus all components of behavior, evolve over multiple generations. A variety of “species”, with varying individual and group survival strategies have emerged in various simulations, displaying such complex ethological behaviors as swarming/flocking, foraging, and attack avoidance.” ( introduction to PolyWorld: Life in a new context ( link below ))

More information:

Poly’s world

Download source code for PolyWorld

Papers:

Polyworld, Yaeger ( pdf)

Computational Genetics, Physiology, Metabolism, Neural Systems, Vision and Behavior or PolyWorld: Life in a new context ( pdf)

You Tube:

PolyWorld: Google Tech Talks