Describe hebbian associate learning

Hebbian associative learning is a theory in neuroscience that proposes that neurons can change their connections based on the correlation of their activity. The principle of Hebbian learning is often summarized as "neurons that fire together, wire together."

In Hebbian learning, when two neurons are activated at the same time, the connection between them is strengthened. Conversely, when two neurons are not activated together, the connection between them is weakened. This is thought to be the basis of how the brain learns and remembers information.

Hebbian learning can occur at both the level of individual neurons and at the level of entire neural networks. At the level of individual neurons, Hebbian learning can result in long-term potentiation (LTP), which is an increase in the strength of synaptic connections between neurons. At the network level, Hebbian learning can result in the formation of neural circuits that can encode and store information.

Overall, Hebbian learning is an important principle in understanding how the brain processes information and how it can adapt and learn from new experiences.

Write an elixir program that utilizes Axon to demonstrate Hebbian associative learning.

Here's an example Elixir program that uses Axon to implement a simple Hebbian associative learning algorithm:

```elixir defmodule HebbianLearning do use Axon.Network

# Define a simple two-input, one-output network with random initial weights def init() do Axon.Network.new() |> Axon.Layer.new(size: 2) |> Axon.Layer.new(size: 1, activation: :sigmoid) |> Axon.connect() end

# Define a Hebbian learning algorithm that updates the weights based on the input/output correlation def learn(network, input, output) do # Run the input through the network to get the current output current_output = Axon.Network.activate(network, input)

# Calculate the correlation between the input and output
correlation = :lists.dot(input, output)

# Update the weights based on the correlation using a Hebbian learning rule
new_weights = Axon.Network.weights(network)
              |> Axon.Math.add(correlation)
              |> Axon.Network.set_weights(network)

# Return the updated network
{network, new_weights, current_output}

end end ```

This program defines a HebbianLearning module that uses Axon to create a simple two-input, one-output neural network. The init() function initializes the network with random weights, while the learn() function updates the weights of the network based on the input/output correlation using a Hebbian learning rule.

To use this program, you can initialize the network using the init() function, and then call the learn() function with input/output pairs to train the network. For example:

elixir iex> network = HebbianLearning.init() iex> input1 = [1, 0] iex> output1 = [1] iex> {network, weights1, current_output1} = HebbianLearning.learn(network, input1, output1) iex> input2 = [0, 1] iex> output2 = [0] iex> {network, weights2, current_output2} = HebbianLearning.learn(network, input2, output2) In this example, we first initialize the network using the init() function. We then train the network with two input/output pairs: [1, 0] -> [1] and [0, 1] -> [0]. After each training step, we get the updated network, the updated weights, and the current output of the network for the input.

By using the Hebbian learning rule to update the weights based on the correlation between the input and output, the network learns to associate the first input with a positive output and the second input with a negative output.