md`## How do the tadpoles "think"? Each tadpole organism is controlled by a simple, fully connected neural network implemented using the [Tensorflow](https://www.tensorflow.org/) library. The input for the neural network of each tadpole consists of the spacial information its nearest particle: - how far on the x axis (horizontal) is the food particle (dx) - how far on the y axis (vertical) is the food particle (dy) This information is processed by a hidden layer consiting of 10 neurons, and the neural network then outputs two values scaled in the interval [-1, +1] that will dictate a change in velocity (acceleration/deceleration) in the x and y axis. Below is the diagram of the neural network that each tadpole is equipped with:
## Optimization of the neural network The "learning" process of a tadpole is based on the optimization of the weights of each of its neurons. Here, this optimization is not performed by backpropagation but using a genetic algoritmm approach instead. Genetic algorithms fall under the larger umbrella of evolutionaty algorithms and are designed to imitate the natural biological process of evolution: starting off with an initial population, and through selection, crossover, and mutations over many generations, an optimal solution emerges. Note that this approach does not guaranty to find the global minimum of our optimization problem, but given proper initial conditions they are in fact quite good at searching through the problem space and finding near optimal solutions. #### Selection The simplest form of selection is called elitism, and consits at carrying over to the next generation only the top n% performing individuals. #### Breeding/Crossover Using this pool of top individuals, new offsprings will be generated by randomly pairing two individuals. Several strategies are implemented here to create the new weights for the neurons of the offspring: - Weighted contribution: The neurons's weights of the offsprings are the result of a weighted contribution of the corresponding neuron of each parent. The weighted contribution of the parents is randomly picked for each layer. - Swapping neurons: Each neuron in a layer is a random pick of the corresponding neuron of either parents. - Neural layer crossover: Each layer of neurons of the offspring is the concatenation of the n first neurons of one parent and (layer length - n) last neurons of the other parent. The crossover point is randomly drawn for each layer of neurons. - Neuron's weights crossover: Each neuron in a layer is generated by crossover of the weights the corresponding neurons of both of its parents. The crossover point is randomly drawn for each neuron. #### Mutations After a new neural network is created for an offspring, random mutation of some of the weights are applied. This is vital as it allows to traverse the search space of the problem we are trying to optimize. The mutated values are randomly picked from a uniform distribution so that they'll still be within +/- 10% of the original value. This will create just a slight variation within the organism that could potentially lead to a fitter organism (or to a less fit organism ... but the variation is limited to +/- 10% to avoid catastrophic changes in the network that could be deletarious for our tadpole). `